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Kinetic spectroscopic studies of alkyl, alkylperoxy and acetyl radicals Adachi, Hiroyuki 1978

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KINETIC SPECTROSCOPIC STUDIES OF ALKYL, ALKYLPEROXY AND ACETYL RADICALS by HIROYUKI ADACHI B.Eng., OSAKA INSTITUE OF TECHNOLOGY, 1972 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF GRADUATE STUDIES in the Department of Chemistry We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1978 © Hiroyuki Adachi, I978 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I further agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thes is fo r f inanc ia l gain sha l l not be allowed without my written permission. Department of Chemistry The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date 3 Oct 1978 i i ABSTRACT The main objectives of this investigation are (i) the characterization of the absorption spectra of four radicals: the ethyl, methylperoxy, ethylperoxy and acetyl radicals, and ( i i ) the measurement of the rate constants of some of their characteristic rapid reactions. The spectral and kinetic measuements reported in this dissertation were made possible by an advance in experimental technique that increased the sensitivity of measurement of absorbance by an order of magnitude. This increase was achieved by a combination of (i) an increase in the intensity of the analytical light source by the application of a square wave voltage pulse, and ( i i ) the use of a dual beam optical system with balanced photomultipliers. The parameters that characterize the absorption spectra of the four principal radicals ( and related species ) are l i s t e d in Table-1. The rate constants measured for reactions of the four principal radicals ( and related species ) are liste d in Table -2. i i i Table-1 Characteristics of absorption spectra Radical (nm) ^max ( 1 mole - 1 cm - 1) h a l f width (nm) o s c i l l a t o r strength CH^ CH<2 247 4.8 x 1 0 2 25 9 . 1 x 1 0 " 3 240 1 .55 x 1 0 3 55 6 . 3 x 1 0 " 2 CH 3CH 2 00' 235 1 .02 x 1 0 3 50 3.4 x 1 0 " 2 CH-jCO- 215 ( 1 . 0 i 0 . 1 ) x 1 0 4 15 ~ 17-5 ( 2 . 3 ± 0 . 3 ) x 1 0 " 1 CD^CO- 2 0 7 . 5 ( 1 . 0 1 0 . 0 5 ) x 10** 15 ( 2 . 5 t 0 . 3 ) x 1 0 " 1 CHj 216.4 ( 9 . 5 + 0.4 ) x 1 0 3 0.8 1 . 0 7 x 10~ 2 CDj 214 .5 1 .71 x 10** 0.4 1.14 x 1 0 " 2 Table-2 Rate constants of radical reactions Reaction k ( 1 mole - 1 s e c - 1 ) Reaction k ( 1 mole - 1 sec" 1 ) 2 CHjCHj ( 1.41 1 0.26 ) x 1 0 1 0 2 CH-jOO' - ( 3 - 5 + 0 . 4 ) x 1 0 8 2 CH 3CH 2 00' • ( 6 . 0 • 0 . 4 ) x 1 0 7 2 CH-jCO- ( 4 . 5 4 t 0 . 2 0 ) x 1 0 1 0 CH-jCO' + CHj -'( 7 . 5 2 • 0 . 2 5 ) x 1 0 1 0 2 CHj — : — - ( 3 . 2 • 0 . 5 ) x 1 0 1 0 iv TABLE OF CONTENTS PAGE Tit l e Page i Abstract • • • • i i Table of Contents i v List of Figures xv List of Tables x x i i Acknowledgemets • xxxli CHAPTER 1. INTRODUCTION 1 A. The nature of research 1 B. Environmental aspects 4 C. Mechanistic studies 6 (1) The oxidation of alkanes and alkyl radicals • • 6 (2) The formation of photochemical smog 9 (a) The contributing reactions 9 (b) Kinetic problems of relevance to the present investigation 13 (3) Characteristic reactions of free radicals at high concentrations 14 (a) The special conditions of flash photolysis 14 (b) Mutual interaction of free radicals 17 (c) Cross interactions of free radicals 18 D. Advances in experimental technique 21 V CHAPTER 2. EXPERIMENTAL METHODS 23 A. Introduction 23 (1) Plash photolysis and kinetic spectroscopy 23 (2) A comparison of the photographic and photoelectric methods 24 B. A general description of the apparatus with with photoelectric detection 27 C. A detailed description of the apparatus 33 (1) The monitoring light source • 33 (2) The xenon lamp housing and collimator housing 3^ (3) The adjustment unit of the xenon lamp 3^ (4) The delay control unit 37 (5) The beam spl i t t e r 40 (6) The photoflash lamp 42 (7) The reaction vessels 43 (8) The focussing lens housing and gas f i l t e r holder 44 (9) The optical f i l t e r s 44 (10) The xenon lamp power supply 49 (11) The xenon pulse power supply and pulsed xenon lamp system control unit 50 (12) The photomultipliers and power supply ....... 51 (13) The oscilloscope 56 (14) The camera and film 59 (15) The optical shutter 60 v i (16) The spectrometer 60 (17) Wavelength calibration 6 l (18) The photographic detection system 63 (19) Materials and purification 67 CHAPTER 3 . MUTUAL COMBINATION OP METHYL RADICALS ... 73 A. Introduction 73 (1) Absorption spectrum of the methyl radical 73 (2) The measurement of the rate constant for mutual combination 75 (a) An assessment of published work 75 (b) The previous work in this laboratory ... 78 B. Experimental 79 (1) Apparatus 79 (2) Method 80 (a) General principles 80 (b) The measurement of k/eKA) 80 (c) The measurement of extinction coefficient, £ 82 C. Results and Discussion 87 (1) The values of k/£(X) and of £(A) measured at 216.4 nm 87 (2) The absorption spectrum of the methyl radical in the range from 215 "to 217 nm .... 90 D. Appendix: The validi t y of the Beer-Lambert Law for methyl radical absorption 95 v i i (1) Introduction 95 (2) The variable band pass method 96 (a) Experimental procedure and results 96 (b) Discussion 97 (3) The variable path length method 105 (a) Experimental procedure 105 (b) Theory 106 (c) Results • I l l (d) Discussion I l l (4) Conclusion •••• • 116 CHAPTER 4. MUTUAL INTERACTION OF ETHYL RADICALS .... 117 A. Introduction 117 (1) Absorption spectrum of the ethyl radical 117 (2) The rate constant for mutual interaction of ethyl radicals 122 (a) Absolute measurements 122 (b) Methods involving the thermochemistry of the ethyl radical 128 (3) The combination and disproportionation of ethyl radical 135 (a) General principles 135 (b) Energies of activation 135 B. Experimental method 139 (1) General principles 139 (2) Kinetic measurements 140 v i i i (3) The measurement of absolute values of £(*) and k 141 C. Results (1) Values of E(A)/k 144 (2) The disproportionation: combination ratio 148 (3) The rate constant for mutual combination, k 2 ... 150 (4) The absorption spectrum of the ethyl radical 150 D. Discussion 156 CHAPTER 5. THE MUTUAL INTERACTION OP METHYLPEROXY RADICALS 159 A. Introduction 159 (1) The absorption spectrum of the methylperoxy radical • 159 (2) The mechanism of photooxidation of azomethane 162 (3) Values of rate constants used in the computer programmes 163 (a) Assessment of existing data I 6 3 (b) Mutual interactions 163 (c) Generation of the CH-^ 00* radical 168 (d) Generation of the H00* radical 170 (e) Cross interactions of the CH^ OO* radical 170 i x (f) Cross interactions of the CH30* radical 173 (g) A comparison with the values selected by Parkes in 1977 174 (h) Excluded reactions 175 (4) Method 178 (a) Generation of the methylperoxy radicals • 178 (b) A computer study of the generation 179 B. Experimental 187 (1) Apparatus 187 (2) Method 187 (a) Choice of reaction conditions 187 (b) The measurement of k^'/SCA) 189 (c) The measurement of S(A) 190 (d) The measurement of k^ 1 9 1 C. Results 205 (1) The value of k^'/StA) 205 (2) The values of E(A) 209 (3) The value of 212 (4) The absorption spectrum of methylperoxy radical • 216 (a) The absorption spectrum of CH^ OO* by photographic detection 216 (b) The absorption spectrum of CH-^ OO* by photoelectric detection 216 (5) The value of k^ 221 X (a) The output of the computer programme 221 (b) The evaluation of kj^ 230 D. Conclusions 233 CHAPTER 6. THE MUTUAL INTERACTION OP ETHYLPEROXY RADICALS 234 A. Introduction 234 (1) The absorption spectrum of the ethylperoxy radical 234 (2) The mechanism of the photooxidation of azoethane 236 (3) Values of rate constant used in the computer programme 236 (a) Assessment of existing data 236 (b) Mutual interaction 239 (c) Generation of the C 2H^00# radical 240 (d) Generation of the H00# radical 241 (e) Cross interactions of the C 2H^00' radical 242 (f) Cross interactions of the C2H^0* radical 244 (g) Excluded reactions • 245 (4) Method 24? (a) Generation of the ethylperoxy radicals 247 B. Experimental 253 ( 1 ) Apparatus 253 (2) Method 253 (a) Choice of reaction conditions 253 (b) The measurement of k^V^A) 253 (c) The measurement of £(A) 255 (d) The measurement of k^ 256 C. Results 265 ( 1 ) The value of k ^ / S C A ) 265 (2) The value of £(A) 267 (3) The value of k^» 270 (4) The absolute absorption spectrum of the ethylperoxy radical 270 (5) The value of k^ 274 D. Conclusions •••• 276 CHAPTER 7. THE SPECTRUM AND KINETIC BEHAVIOUR OP THE ACETYL RADICAL 277 A. Introduction 277 (1) The photochemistry of ketones 277 (2) The photodissociation of acetone 283 (a) Introduction 283 (b) Simultaneous and consecutive processes of dissociation 284 (c) Dissociation from the singlet and t r i p l e t states 290 (3) The absorbance spectra of the acetyl radical and of ketyl radical 295 x i i (4) The dissociation of the acetyl radical 296 (5) Patterns of cross combination of the acetyl radical and related radicals 302 (6) The mutual combination of acetyl radicals 307 B. Experimental method 309 (1) General principles 309 (a) Generation of the acetyl radical 309 (b) Mechanism for the photolysis of acetone 309 (2) The absorption spectrum of the acetyl radical 310 (a) The nature of the absorbance 310 (b) Methods of measurement 310 (c) The nature of the spectra 312 (d) The evaluation of A J U (216.4) and AcH 3C0( 2 1 6^) 314 (e) The evaluation of ^H 3CO< 2 l 6-*>^H 3CO< 2 1 5> 314 (f) The extrapolation to Ag§ ^ c o ( 2 1 5 ) and Ag§^(216.4) 314 (g) The evaluation of % E ^ Q Q i z l 5 ) 315 (h) The photosynthesis of the acetyl radical • 316 (3) The kinetic measurements 318 (a) The empirical second order equations 318 x i i i (b) The approximate rate equations 319 (c) The measurement of ^ [c^CO*] / [cH^])>.... 320 (d) The evaluation of k j and k^ 320 (e) The computer programme 322 (4) Apparatus and method 323 C. Results 330 (1) Absorption spectrum of the acetyl radical 330 (a) Acetone-h^ as the photolytic source .... 330 (b) Methyl ethyl ketone, MEK, as the photolytic source 335 (c) Biacetyl as the photolytic source 333 (d) Acetone-d^ as the photolytic source .... 3^3 (e) The extinction coefficient 3^3 (f) The oscillator strength 3^8 (g) The characterization of the absorption spectrum 3^3 (h) The photosynthesis of the acetyl radical 3^9 (2) Fast reactions of the acetyl radical 355 (a) The product ratio: C0/C2H6 355 (b) Displacement reactions 356 (c) Disproportionation reactions 359 (3) The evaluation of k^ and k^ 360 (a) The second order kinetic analysis 360 (b) The iterative method 366 D. Conclusions 370 x i v APPENDIX. S.C.P. M.O. CALCULATIONS FOR THE CH-^ CO* AND CH3CO* RADICALS 371 A. Molecular orbital methods 371 B. The CNDO/2 method 373 C. The INDO method 375 (1) General principles 375 (2) The geometry of the CH^CO' radical 377 (3) The geometry of the CH^ QO* radical 377 D. Conclusions 335 BIBLIOGRAPHY 386 X V LIST OF FIGURES FIGURE PAGE CHAPTER 2. EXPERIMENTAL METHODS 2.1 The f l a s h p h o t o l y s i s apparatus w i t h p h o t o e l e c t r i c d e t e c t i o n 28 2.2 The xenon arc lamp assembly 35 2.3 Assembly f o r the f i n e adjustment of the p o s i t i o n of the xenon arc lamp 36 2.4 A schematic diagram of the delay u n i t complex 38 2 .5 The op e r a t i o n of the delay c o n t r o l u n i t 39 2.6 The beam s p l i t t e r assembly 41 2 .7 The housing of the r e a c t i o n v e s s e l s and the p h o t o f l a s h lamps 45 2.5 The f o c u s s i n g l e n s housing and gas f i l t e r holder 46 2 . 9 The a b s o r p t i o n spectrum of the gas f i l t e r 47 2.10 The t r a n s m i s s i o n curves f o r the g l a s s f i l t e r 48 2.11 The r e s i s t i v e voltage d i v i d e r f o r the p h o t o m u l t i p l i e r of EMI 9783 54 2.12 The r e s i s t i v e voltage d i v i d e r f o r the p h o t o m u l t i p l i e r of EMI 9783 55 2.13 The f l a s h p h o t o l y s i s apparatus w i t h photographic d e t e c t i o n 64 x v i 2.14 The a n a l y s i s of p u r i f i e d b i a c e t y l by gas chromatography 70 2.15 The i n f r a r e d spectrum of p u r i f i e d b i a c e t y l 71 2.16 The NMR spectrum of p u r i f i e d b i a c e t y l ....... 72 CHAPTER 3- MUTUAL COMBINATION OF METHYL RADICALS 3.1 Absorption spectrum of the methyl r a d i c a l according to H i c k e l , 1975 76 3.2 Values of the r a t e constant f o r the mutual combination of methyl r a d i c a l s 76 3 . 3 A diagram i l l u s t r a t i n g f o r the e x t r a p o l a t i o n of absorbance 85 3.4 Absorption spectrum of CH^ by p h o t o e l e c t r i c d e t e c t i o n 92 3 . 5 Absorption spectrum of CH^ by photographic d e t e c t i o n and the corre sponding microphotodensitometer trace 93 3.6 The r e l a t i o n s h i p between the value of the exponent n and the time delay between f i r i n g the p h o t o f l a s h and re c o r d i n g the absorbance 113 x v i i CHAPTER 4. MUTUAL INTERACTION OP ETHYL RADICALS 4.1 The r e l a t i v e and the normalized a b s o r p t i o n spectrum of C 2H^ 14? 4.2 The abso r p t i o n spectrum of the e t h y l r a d i c a l 152 CHAPTER 5. THE MUTUAL INTERACTION OF METHYLFEROXY RADICALS 5 . 1 .A The normalized concentrations of CH^ and CH^OO' i n the presence of a high oxygen c o n c e n t r a t i o n 183 5 . 1 . B The normalized concentrations of CH^ and CH^OO' i n the presence of a low oxygen c o n c e n t r a t i o n 184 5 . 2 . A The normalized concentrations of CH^OO*, CH^O* and H00* i n the presence of a high oxygen c o n c e n t r a t i o n 195 5 . 2 . B The normalized concentrations of CH^OO*, CH 3 0' and H00' i n the presence of a low oxygen c o n c e n t r a t i o n 196 5.3. A A simulated second order p l o t f o r the decay of the CH^OO' con c e n t r a t i o n : computed values of Co/C p l o t t e d against time f o r a system w i t h a high oxygen con c e n t r a t i o n 201 x v i i i 5-3«B A simulated second order p l o t f o r the decay of the CH^OO' con c e n t r a t i o n ! computed values of Co/C p l o t t e d a g a i n s t time f o r a system w i t h a low oxygen co n c e n t r a t i o n 202 5.4 Experimental values of 10" k^' w i t h mean, standard d e v i a t i o n and l i n e a r and quadratic r e g r e s s i o n l i n e s 214 5 . 5 Absorption spectrum of CH^OO' by photographic d e t e c t i o n and the corresponding microphotodensitometer t r a c e s 217 5.6 R e l a t i v e and normalized a b s o r p t i o n spectrum of CH^OO' by p h o t o e l e c t r i c d e t e c t i o n 219 5.7 The absolute a b s o r p t i o n spectrum of methylperoxy r a d i c a l 220 5.b" The e f f e c t upon the computed value of k^'/k^ of v a r y i n g s i n g l y the value of each of the r a t e constants k ^ , k^, kr,, k^, k 1 Q k-, -, , and k-, 9 used i n the programme 222 CHAPTER 6. THE MUTUAL INTERACTION OF ETHYLPEROXY RADICALS 6.1 The normalized concentrations of C^H^ and C 2Hj-00' i n the presence of a h i g h oxygen c o n c e n t r a t i o n 250 x i x 6.2 The normalized concentrations of C 2H^00*, C2H^0* and H00* i n the presence of a high oxygen c o n c e n t r a t i o n 260 6.3 A simulated second order p l o t f o r the decay of the C 2H^00* c o n c e n t r a t i o n : computed values of Co/C 3 (Y) p l o t t e d a gainst time f o r a system w i t h a h i g h oxygen co n c e n t r a t i o n *. 263 6 . 4 R e l a t i v e and normalized a b s o r p t i o n spectrum of ethylperoxy r a d i c a l 268 6 . 5 The absolute a b s o r p t i o n spectrum of the ethylperoxy r a d i c a l 273 CHAPTER 7- THE SPECTRUM AND KINETIC BEHAVIOUR OF THE ACETYL RADICAL 7.1 M o d i f i e d J a b l o n s k i diagram 279 7.2 E v a l u a t i o n of £ ( 2 1 5 ) f o r the a c e t y l r a d i c a l 313 7«3«M A simulated second order p l o t f o r the decay of the methyl r a d i c a l c o n c e n t r a t i o n 325 7 .4.A A simulated second order p l o t f o r the decay of the a c e t y l r a d i c a l c o n c e n t r a t i o n 327 7.5 Absorption spectrum of the a c e t y l r a d i c a l , formed by f l a s h p h o t o l y s i s of acetone at 50 t o r r 332 X X 7.6 Absorption spectrum of the a c e t y l r a d i c a l , formed by f l a s h p h o t o l y s i s of a mixture of 50 t o r r acetone and 580 t o r r argon 334 7-7 Absorption spectrum of the a c e t y l r a d i c a l , formed by f l a s h p h o t o l y s i s of methyl e t h y l ketone at 50 t o r r 337 7.8 Absorption spectrum of the a c e t y l r a d i c a l , formed by f l a s h p h o t o l y s i s of a mixture of 10 t o r r b i a c e t y l and 190 t o r r argon 340 7.9 Absorption due to se v e r a l t r a n s i e n t s p e c i e s , formed by f l a s h p h o t o l y s i s of a mixture of 10 t o r r b i a c e t y l and 190 t o r r argon 341 7-10 Absorption spectrum of the a c e t y l - d ^ r a d i c a l , formed by f l a s h p h o t o l y s i s of acetone-d^ a t 50 t o r r 345 7.11.A The normalized c o n c e n t r a t i o n of CH^ and CH^CO' i n the presence of the lower carbon monoxide co n c e n t r a t i o n .351 7.11.B The normalized c o n c e n t r a t i o n of CH^ and CH^GO' i n the presence of the higher carbon monoxide c o n c e n t r a t i o n 353 x x i 7.12 The r i s e and f a l l of the totalabsorbance at 216.4 nm, w i t h the c o n t r i b u t i o n s from the methyl and a c e t y l r a d i c a l s , as given i n Table - 7 . 1 3 362 7.13 Experimental second order p l o t f o r the de c l i n e of the absorbance of the methyl and a c e t y l r a d i c a l s 363 APPENDIX S.C.F. M.O. CALCULATIONS FOR THE CH^CO* AND CH-jOO* RADICALS 8.1 Values of E S C F f o r CH^CO* c a l c u l a t e d as a f u n c t i o n of the two geometric parameters. r(C-O) and LC-C-0 = 9 378 8.2 Values of E S C F f o r CH^OO' c a l c u l a t e d as a f u n c t i o n of the two geometric parameters: r(0-0) and Z.C-O-0 - 0 382 x x i i LIST OF TABLES TABLE PAGE CHAPTER 1. INTRODUCTION 1.1 C h a r a c t e r i s t i c r e a c t i o n s of f r e e r a d i c a l s i n t h i s i n v e s t i g a t i o n 16 CHAPTER 2. EXPERIMENTAL METHODS 2.1 E x i s s i o n l i n e s used f o r the c a l i b r a t i o n of the wavelength scale of the spectrometer 62 CHAPTER 3« MUTUAL COMBINATION OF METHYL RADICALS 3.1 Experimental values of the r a t e constant f o r the mutual combination of methyl r a d i c a l s 77 3 . 2 Values of k / E ( 2 l 6 . 4 ) and k measured f o r the mutual combination of methyl r a d i c a l s at 216.4 nm 88 3-3 Values of £(>J/k a t d i f f e r e n t wavelength .... 91 3 . 4 Values of k/£ f o r the mutual combination of methyl r a d i c a l s measured f o r two s l i t widths and two xenon arc energies at 216.4 nm 98 3.5 Values of £ f o r the methyl r a d i c a l at 216.4 nm, based upon experiments l i s t e d Table - 3 . 4 101 x x i i i 3.6 A summary of the r e s u l t s c a l c u l a t e d assuming that A = £ [cH^] 1 104 3.7 Summary of equation used to evaluate n f o r d i f f e r e n t masking patterns and the c o r r e c t i o n f o r asymmetry 109 3.8 The r e l a t i o n s h i p between the time of r e a c t i o n and n . 112 CHAPTER 4. MUTUAL INTERACTION OF ETHYL RADICALS 4.1 The c h a r a c t e r i z a t i o n of the abs o r p t i o n spectrum of the e t h y l r a d i c a l 121 4.2.A Values of the r a t e constant f o r the gas phase r e a c t i o n : 2 C 2H^ C^H 1 0, k 2 ( D i r e c t methods) 126 4.2.B Values of the r a t e constant f o r the gas phase r e a c t i o n : 2 C 2H^ • C^H 1 0, k 2 ( I n d i r e c t methods) 129 4.3 The vapour pressures of i n d i v i d u a l products at the r e l e v a n t temperatures 143 4.4 Values of the e x t i n c t i o n c o e f f i c i e n t and the r a t e constant f o r mutual i n t e r a c t i o n of e t h y l r a d i c a l s , measured near maximum abso r p t i o n 145 4.5 Values of £(A)/k f o r the mutual i n t e r a c t i o n of the e t h y l r a d i c a l s 146 x x i v 4 . 6 Values of the d i s p r o p o r t i o n a t i o n : combination r a t i o 149 4 . 7 The e x t i n c t i o n c o e f f i c i e n t of the e t h y l r a d i c a l at va r i o u s wavelengths 151 4 . 8 A comparison of values of the abso r p t i o n c o e f f i c i e n t of the e t h y l r a d i c a l as measured i n t h i s work and as reported by Parke s and Quinn 154 4 . 9 S p e c t r a l and k i n e t i c c h a r a c t e r i s t i c s of the e t h y l r a d i c a l 157 CHAPTER 5- THE MUTUAL INTERACTION OF METHYLPEROXY RADICALS 5.1 The mechanism of the photooxdation of azomethane 164 5.2 Recent values of k^ 2 ?or ^he mutual i n t e r a c t i o n of hydroperoxy r a d i c a l s 164 5.3 Recent values of k^ f o r the mutual i n t e r a c t i o n of methylperoxy r a d i c a l s 167 5.4 Recent values of k„„ and k 0. f o r the 7a 7b mutual i n t e r a c t i o n of methoxy r a d i c a l s 169 5.5 Recent values of k^ f o r the r e a c t i o n CH^O* + 0 2 CH 20 • H0 2 171 5 . 6 .A M a t e r i a l balance r a t i o s f o r the methyl r a d i c a l a t a h i g h oxygen c o n c e n t r a t i o n 185 5.6.B M a t e r i a l balance r a t i o s f o r the methyl r a d i c a l at a low oxygen c o n c e n t r a t i o n 186 XXV 5«7 T y p i c a l r e a c t i o n c o n d i t i o n s f o r the q u a n t i t a t i v e study of the methylperoxy r a d i c a l 188 5.8 Reactions used i n the computer s i m u l a t i o n of the decay of the methylperoxy r a d i c a l 192 5 . 9 .A Normalized concentrations and m a t e r i a l balance r a t i o s f o r : CH^OO'CP), CH^O*(A) and HOO'(Q) i n the presence of a high oxygen c o n c e n t r a t i o n 197 5 . 9 . B Normalized concentrations and m a t e r i a l balance r a t i o s f o r : CH^OO*(P), CH^O*(A) and HOO'(Q) i n the presence of a low oxygen co n c e n t r a t i o n I98 5.10. A F i t t i n g a second order r e g r e s s i o n l i n e to values of Co/C = (Y) computed f o r the decay of the CH^OO' con c e n t r a t i o n i n a system w i t h a high oxygen c o n c e n t r a t i o n 203 5.10.B F i t t i n g a second order r e g r e s s i o n l i n e to values of Co/C = (Y) computed f o r the decay of the CH^OO' co n c e n t r a t i o n i n a system w i t h a low oxygen co n c e n t r a t i o n 204 x x v i 5 . 1 1 .A Values of k^'/e(A) f o r the mutual i n t e r a c t i o n of methylperoxy r a d i c a l s at v a r i o u s wavelengths i n the presence of a high oxygen c o n c e n t r a t i o n 20? 5.11.B Values of k^'/£(A) f o r the mutual i n t e r a c t i o n of methylperoxy r a d i c a l s at 240 nm i n the presence of a low oxygen c o n c e n t r a t i o n 20b 5.12 Values of e x t i n c t i o n c o e f f i c i e n t of the methylperoxy r a d i c a l at v a r i o u s wavelengths 210 5.13 The maximum i n the abso r p t i o n spectrum of the methylperoxy r a d i c a l s 211 5.4 The apparent r a t e constant k^' f o r the mutual i n t e r a c t i o n of methylperoxy r a d i c a l s at v a r i o u s wavelengths 213 5.15 Values of £(A)A^' f o r the mutual i n t e r a c t i o n of the methylperoxy r a d i c a l s 21b 5.16 R e l a t i v e r a t e s of r e a c t i o n and patterns of consumption of r a d i c a l s at the h a l f l i f e of the r e a c t i n g system of Table - 5 . 9.A and F i g u r e - 5 . 2 . A Reactions and r a t e constants as l i s t e d i n Table - 5.b 225 xx v i i 5.17 Extent of r e a c t i o n f o r r e a c t i o n s 4 to 12 expressed as i n t e g r a l s : R n dt of the r a t e s R n 228 5.18 Values of k^', and r e l a t e d q u a n t i t i e s 232 CHAPTER 6 . THE MUTUAL INTERACTION OF ETHYLPEROXY RADICALS 6.1 The mechanism of the photooxidation of azoethane 237 6 . 2 M a t e r i a l balance r a t i o s f o r the e t h y l r a d i c a l a t a high oxygen co n c e n t r a t i o n 251 6 . 3 T y p i c a l r e a c t i o n c o n d i t i o n s f o r the q u a n t i t a t i v e study of the ethylperoxy r a d i c a l 254 6 . 4 Reactions used i n the computer s i m u l a t i o n of the decay of the ethylperoxy r a d i c a l 258 6 . 5 Normalized concentrations and m a t e r i a l balance r a t i o s f o r : C^^OO'(P), C 2H^0*(A) and HOO'(Q) i n the presence of a high oxygen c o n c e n t r a t i o n 261 6.6 F i t t i n g a r e g r e s s i o n l i n e to values of Co/C - (Y) computed f o r the decay of the C2H^00* c o n c e n t r a t i o n i n a system w i t h a high oxygen c o n c e n t r a t i o n 264 x x v i i i 6 . 7 Values of k^'/ECA) and o f the e x t i n c t i o n c o e f f i c i e n t £(A) of the ethylperoxy r a d i c a l at v a r i o u s wavelengths 266 6.fc> Values of £(A)/k^' f o r the ethylperoxy r a d i c a l at v a r i o u s wavelengths 269 6 . 9 Values of k^' at v a r i o u s wavelengths 271 CHAPTER 7. THE SPECTRUM AND KINETIC BEHAVIOUR OF THE ACETYL RADICAL 7.1.A The dependence of the primary quantum y i e l d <D = <t>^  + a>2, and of f r a c t i o n Q(a<t»1 / ( <t> 1 + <t>2 ), upon the temperature and the wavelength of the e x c i t i n g r a d i a t i o n i n the p h o t o l y s i s of acetone 286 7.1. B The dependence of 0(= • -j. / ( $ + <D2 )» . upon the wavelength of the e x c i t i n g r a d i a t i o n at 295 K 287 7.2. A L i m i t i n g high pressure values of the Arrhenius parameters, k*°(298) and t|(298) f o r the d i s s o c i a t i o n * CH^CO* CH^ + CO 303 x x i x 7.2.B Values of the r a t e constant at room temperature, f o r the d i s s o c i a t i o n of the a c e t y l r a d i c a l * CH^CO* CH^ + CO 303 7.3 M a t e r i a l balance r a t i o s f o r the methyl and a c e t y l r a d i c a l s 324 7«4 A f i t t i n g a second order r e g r e s s i o n l i n e s to values of Co/C = Y computed f o r the decay of the CH^ con c e n t r a t i o n 326 7.5 A f i t t i n g a second order r e g r e s s i o n l i n e s to values of Co/C = Y computed f o r the decay of the CH^CO* conc e n t r a t i o n 328 7.6 Absorbance of the a c e t y l r a d i c a l : measured 40 microsec a f t e r f i r i n g the p h o t o f l a s h on 50 t o r r of pure acetone vapour 331 7.7 Absorbance of the a c e t y l r a d i c a l : measured 40 microsec a f t e r f i r i n g the photofla s h on a mixture of acetone and argon 333 7.8 Absorbance of the a c e t y l r a d i c a l : measured 40 microsec a f t e r f i r i n g the photofla s h on a 50 t o r r of pure methyl e t h y l ketone vapour 336 X X X ? . 9 Absorbance of the a c e t y l r a d i c a l : measured 40 microsec a f t e r f i r i n g the pho t o f l a s h on a mixture of 10 t o r r b i a c e t y l and 190 t o r r argon 339 7.10 Absorbance of the a c e t y l - d ^ r a d i c a l : measured 40 microsec a f t e r f i r i n g the phot o f l a s h on 50 t o r r of pure acetone-d^ vapour 344 7.11 The h a l f l i v e s of t r a n s i e n t species formed by f l a s h p h o t o l y s i s from va r i o u s sources 346 7.12.A M a t e r i a l balance r a t i o s f o r the methyl r a d i c a l at the lower carbon monoxide con c e n t r a t i o n 351 7.12.B M a t e r i a l balance r a t i o s f o r the methyl r a d i c a l at the higher carbon monoxide con c e n t r a t i o n 353 7.13 Mean values from 16 experiments under i d e n t i c a l c o n d i t i o n of t r a n s i e n t absorbances measured at the st a t e d times a f t e r the f i r i n g of the p h o t o f a l s h on acetone i n a " Pyrex " v e s s e l 360 7.14 The separate e v a l u a t i o n of i c a / E C H QQ(215) from each of the 16 experiments that were evaluated c o l l e c t i v e l y i n Table - 7 . 1 3 36^ + x x x i 7.15 E v a l u a t i o n of and by an i t e r a t i v e method 367 APPENDIX S.C.F. M.O. CALCULATIONS FOR THE CH-^ CO* AND CH^OO* RADICALS 8.1 Values of Ean„ f o r CH oC0* c a l c u l a t e d as SCF 3 a f u n c t i o n of the two geometric parameters: r(C-O) and Z.C-C-0 - 9 376 8.2 The e q u i l i b r i u m geometry and e l e c t r o n i c p r o p e r t i e s of the ground s t a t e of CH^CO* 378 8.3 Values of E S C F f o r CH^OO' c a l c u l a t e d as a f u n c t i o n of the two geometric parameters: r ( 0 - 0 ) and ZLC-O-0 = e 380 8.4 The e q u i l i b r i u m geometry and e l e c t r o n i c p r o p e r t i e s of the ground sate of CH^OO* 3»2 x x x i i ACKNOWLEDGEMENTS I would l i k e to thank Dr. D.G.L. James and Dr. N. Basco f o r t h e i r continuous encouragement, guidance and generous support throughout the course of t h i s i n v e s t i g a t i o n . I should a l s o l i k e to thank Mr. E. F i s h e r f o r h i s i n v a l u a b l e a i d i n the c o n s t r u c t i o n of the e l e c t r o n i c apparatus and the members of the t e c h n i c a l s t a f f f o r t h e i r a s s i s t a n c e w i t h the c o n s t r u c t i o n and maintainance of the apparatus. F i n a l l y , I e s p e c i a l l y want to thank my w i f e , M i c h i e , f o r t y p i n g the manuscript and f o r her understanding encouragement over the past years. - 1 -CHAPTER 1 INTRODUCTION A, The nature of research. The physical influence of a single event of the simplest chemical reaction extends without limi t beyond the immediate time and place of that event. The philosophical significance of the method by which such an event is analysed is similarly far reaching. This method assumes that every detailed occurrence can be correlated with i t s antecedents in a perfectly definite manner which exemplifies general principles. Some of the implications of this method may be illustrated by the opinions of several well known scientists. Albert Einstein has said that almost every one of the profounder sort of scientific minds experiences a feeling of rapturous amazement at the harmony of the natural law, and that this feeling i s the guiding principle of the scientist's l i f e and work. Such a view could scarcely arise i f the ruling principle of the universe were believed to be either capricious or hostile. - 2 -Max Planck wrote that: Science Is a creative work of art, because when the pioneer sends forth the groping feelers of his thoughts he must have a vivid and intuitive imagination; for new ideas are not generated by deduction, but by an a r t i s t i c a l l y creative imagination ( 1 ). Jacob Bronowski shared this outlook when he said that the layman's key to science is its unity with the arts. There exists a wide misconception that science destroys culture. On the contrary the great ages of science have so often been the great ages of the arts. In ancient Greece Socrates taught in the heyday of the Greek drama. Leonardo da Vinci was a painter, a sculptor, a mathematician and an engineer; and the f i r s t table of logarithms was published within a few years of Shakespeare's First Folio. A scientific investigation is described as pure research i f i t s principal aim is a more complete understanding of the fundamental processes of nature. Much of the current research in chemical kinetics i s directed towards a more complete understanding of the changes that occur when two molecules approach, interact and separate, either with their original structures, or with the new structures of distinct product molecules. This i s the very essence of chemistry, and certainly a f i t subject for pure research. The present investigation contributes toward such an understanding. Many investigators consider that the ideal of pure research is admirable but insufficient. They wish their research to be applied to the improvement of the quality of human l i f e . This may consist of mitigating the adverse effects of affluence upon - 3 -the urban environment. In the following pages i t w i l l be argued that the present investigation is an example of beneficial applied research. - 4 -B. Environmental aspects. The present investigation encompasses the kinetic study of some of the fundamental rapid reactions of the low temperature oxidation of hydrocarbons which are also involved in the formation of photochemical smog in polluted urban atmospheres. Accordingly this study may be legitimately described both as fundamental research and as applied research. The latte r claim is clear from the report of the Committee on Medical and Biologic Effects of Environmental Pollutants: " Ozone and other photochemical oxidants issued by the National Acadency of Sciences in Washington in 1977 ( 2 ). Some of the conclusions of this report are given in the following paragraphs. Photochemical smog contains the toxic oxidants ozone, nitrogen dioxide and peroxyacetyl nitrate in significant concentrations. The acute lethal action of ozone due to i t s capacity to produce pulmonary edema. The latest data show a st a t i s t i c a l l y significant reduction of the pulmonary function in humans after an exposure of two hours to an ozone concentration above 0.37 ppm. The adverse effect on health of exposure to the oxidants is increased by exercise, and leads may people limit strenous exercise when oxidant pollution i s high. Oxidant injury to vegetation has been recognised since 19^4, and is mainly due to the action of ozone and peroxyacetyl nitrate. Visible injury may be acute or chronic. Acute injury breaks down the c e l l membrane and causes c e l l death, illustrated by the upper surface fleck on tobacco and the stipple of grape. Complete collapse of the leaf tissue can result. Chronic Injury is associated with the disruption of normal cellular activity, followed by chlorosis or other colour changes that may lead to c e l l death. The damage to materials in 1970 due to the action of ozone in the U.S.A. has been assessed as: elastomers $ 564 million, paint $ 5^0 million; textile fibres and dyes $ 84 million; giving a total of $ 1,22 b i l l i o n . Other adverse effects of the oxidants include eye i r r i t a t i o n due to peroxyacetyl nitrate, and the hazard of fogs due to the formation of aerosols accompanying the oxidation of sulphur dioxide. Remedial measures recommended by the Committee include the study of the mechanism of the formation of photochemical smog. Chemical modelling studies would constitute one aspect of this venture. A computer programme would be written to evaluate the concentration of each pollutant at regular intervals over the period of interest. Such a programme demands accurate values for the rate constants of the constituent reactions of the mechanism. In many important cases the experimental value i s either dubious or non-existent, and purely conjectural estimates must be used. This limitation severely restricts the value of chemical modelling studies. The present investigation i s largely concerned with the measurement of the rate constants of some of the more important reactions of the mechanism. Further details w i l l be given in Section C.2. - 6 -C* Mechanistlo studies. ( 1 ) The oxidation of alkanes and alkyl radicals. The oxidation of alkanes in the gas phase was reviewed by R.W.Walker in 1975 and 1977 ( 3 » 4 ) and the oxidation of the methyl radical at room temperature was discussed by Parkes in 1977 ( 5 )• Alkyl, alkylperoxy and acetyl radicals are Important chain carriers in those oxidations, and these radicals are the principal subjects of the present investigation. They also play an important role in the mechanism of photochemical smog formation, as the secondary pollutants include oxidants which are formed by the oxidation of hydrocarbons; this aspect w i l l be discussed in Section C . 2 . The ethyl, ethylperoxy and acetyl radicals w i l l be used to illu s t r a t e the relevance of the present investigation to the oxidation of ethane, selected as a representative alkane. Acetaldehyde i s an important product of this oxidation at room temperature and contributes to the process of i n i t i a t i o n . The ethyl radical i s the main chain carrier generated by the i n i t i a t i o n reactions: C H 3 C H 3 + 0 2 C H 3 C R 2 + HOC CH3CH3 + X* CH3CH2 + HX The radical X* may be one of the chain carriers of the mechanism, such as H00*, or may be generated by a sensitizer. The acetyl and methyl radicals w i l l be formed by the analogous ini t i a t i o n reactions with acetaldehyde: - 7 -CH3CHO + 0 2 • CH3CO' + HOO* * CH 3 + CO + HOO' CH3CHO + X' CH3CO* + HX • CH 3 + CO + HX Ethylperoxy radicals are formed almost exclusively from ethyl radicals and air at room temperature by the addition of oxygen: CH^CHJ + 0 2 + M CH 3CH 200' + M This i s a second order reaction at atmospheric pressure. The mutual interaction of ethylperoxy radicals forms peroxides and acetaldehyde in the terminating reactions: 2 CH 3CH 200* - CH 3CH 200CH 2CH 3 + 0 2 CH3CH2OH + CH3CHO + 0 2 Ethoxy radicals are formed in the non-terminating reaction: 2 CH 3CH 200 < 2 CH 3CH 20* + 0 2 and play an interesting role in the oxidation. Ethoxy radicals may be oxidized to acetaldehyde by oxygen, which is reduced to the hydroperoxy radical: CH 3CH 20* + 0 2 CH 3CH0 + H00* This reaction i s predominant i f the oxygen pressure is about one atmsphere. The hydroperoxy radical i s then the dominant D - 8 -secondary chain carrier after the ethylperoxy radical. The ethoxy radical can play a dominant role only i f the oxygen concentration i s relatively low and the radical concentrations are relatively high, and this situation may be conveniently studied by flash photolysis. Such a competition for predominance i s illustrated in Chapter 5 of the present investigation by the oxidation of the methyl radical, where the adjustment of the oxygen concentration is shown to determine whether the methoxy radical or the hydroperoxy radical i s predominant in the mechanism. The hydroperoxy radical usually plays a significant role in these oxidations. It i s a reducing agent in i t s disproportionation reactions: CH 3CH 200' + H00* CH^ CHgOOH + 0 2 CH3CH20* + HOC *- CH 3CH 20H + 0 2 2 H00* HOOH + 0 2 In contrast i t i s an important oxidizing agent in the formation of photochemical smog: H00* + CO T HO' + C 0 2 H00* + NO - HO* + N 0 2 H00* + S 0 2 HO* + S 0 3 Alkylperoxy radicals display an analogous set of reactions, and their significance w i l l be discussed In the next section. . 9 -(2) The formation of photochemical smog,  (a) The contributing reactions. The characteristics of photochemical smog include eye i r r i t a t i o n , aerosol formation and the degradation of rubber and paints, and a l l three are associated with oxidants. The commonest photochemical oxidants in polluted a i r are ozone, nitrogen dioxide and peroxyacetyl nitrate, P.A.N. These oxidants are secondary pollutants which are formed from the primary pollutants by photochemical reactions in the atmosphere. The primary pollutants include alkanes, alkenes, aldehydes, carbon monoxide, n i t r i c oxide and sulphur dioxide, and are formed mainly by the internal combustion engine. Alkyl radicals, alkylperoxy radicals and acetyl radicals are essential intermediates in the formation of ozone, nitrogen dioxide and P.A.N, from the primary pollutants, and thereby in the formation of photochemical smog. These radicals are very efficient intermediates, because they act as chain carriers in cyclic chain propagation sequences. Their action w i l l be bri e f l y described in the following paragraphs. Alkyl radicals are formed in polluted a i r either by the ozonolysis of alkenes or by metathesis between free radicals and alkanes. Sunlit polluted a i r contains several species of free radicals which are reactive enongh to generate alkyl radicals in significant concentrations from alkanes by the reaction: RH + X* R« + HX The nature and sources of the radicals X* w i l l be discussed at - 10 -the end of this section. Alkyl radicals combine rapidly with the oxygen in air to form alkylperoxy radicals: R. + o 2 *- R00* Alkylperoxy radicals rapidly oxidize n i t r i c oxide to nitrogen dioxide: R00* + NO RO* + N 0 2 and the resultant alkoxy radical reacts rapidly with atmospheric oxygen to form an aldehyde and the hydroperoxy radical: RO* + 0 2 -R'CHO + H00' The latter rapidly oxidizes n i t r i c oxide to nitrogen dioxide: H00 # + NO H0» + N 0 2 and is regenerated by the sequence: HO* + CO «-H* + C 0 2 H* + 0 2 + M H00* + M The participation of alkylperoxy radicals in the radical chain oxidation of n i t r i c oxide to nitrogen dioxide may be illustrated by the ethyl radical oxidation cycle: C H 3 C H 2 + 0 2 - C H 3 C H 2 0 0 ' C H 3 C H 2 0 0 * + NO • C H 3 C H 2 0 ' + N 0 2 C H 3 C H 2 0 * + 0 2 CH 3 CH0 + H00* H00* + NO -HO* + N 0 2 - 11 -HO* + CO H* + C 0 2 ' H* + O2 + Mi HOC + M HO* + CH3CH3 H 2 0 + CH3CH2 The intermediate hydroxy! radical and the product acetaldehyde play other important roles the formation of secondary pollutants. Nitrogen dioxide is the precursor of both ozone and peroxyacetyl nitrate and imparts the characteristic brown colour to photochemical smog. Ozone is formed by the photochemical cycle: N 0 2 + hi> • NO + 0 0 + 0 2 + H • O3 + M NO + H 0 0 * - N 0 2 + HO-which is efficient because the third reaction i s part of the alkyl radical oxidation cycle. Ozone reacts rapidly with alkenes, and the products of the ozonolysis include acyl, alkyl and alkylperoxy radicals, the Criegee blradicals R ] R 2 C 0 0 , and aldehydes and ketones, a l l of which play important role in smog formation. Ozonolysis initates the principal mechanism of the degradation of rubber and paints. Ozone is also poisonous to man, animals and plants. Peroxyacetyl nitrate is formed by the rapid interaction of acetyl radicals, atmospheric oxygent and nitrogen dioxide in the sequence: - 12 -CHoCO + 0 2 ^CHoC^ J c 1 \ 0 0 . CR\C\ + N 0 ? CH.C^ D ^ 0 0 * * ^ ^ 0 0 N 0 2 The acetyl radicals arise either from the ozonolysis of an alkene with the structure CH3CH = CR1R2 or from the ethyl radical oxidation cycle given above, Peroxyacetyl nitrate causes eye i r r i t a t i o n at a very low concentration and is poisonous to man, animals and plants. Aerosols arise from the homogeneous oxidation of sulphur dioxide in water droplets and from the heterogeneous oxidation of sulphur dioxide adsorbed on carbon particles. Ozone is not in i t s e l f a sufficiently reactive oxidizing agent, but oxidation by ozone is catalysed by alkenes in the sense that molozonides and Griegee biradicals are the effective oxidizing agents. Alkylperoxy and hydroperoxy radicals are also efficient oxidizing agents for sulphur dioxide: R00* + S 0 2 • RO* + SO3 H00* + S 0 2 - HO* + SO3 and these radicals are formed in the alkyl radical oxidation cycle given above. The sulphuric acid content of an aerosol fog causes damage to the human respiratory system, to plant l i f e , and to buildings and machinery. The generation of alkyl radicals in sunlit polluted air occurs principally by metathetical reactions of the type: - 13 -RH + X* R* + HX RCHO + X* RCO' + HX R' + CO + HX The radical X* may be H', HO*, RO* HOO* or ROO* generated in such reactions as: RCHO + hv RCO* + H R' + CO + H* H' + 0 2 + M • HOC + H R* + 0 2 + M -ROO' + M HOO* + CO HO' + C0 2 HOO* + NO HO' + N02 ROO* + NO •RO* + N0 2 (b) Kinetic problems of relevance to the present investigation . The chemistry of the formation of the oxidants in photochemical smog has been studied by the use of the smog chamber, A typical mixture of 2.09 ppm C3H6, 0.90 ppm NO and 0.09 ppm N02 in moist air with a relative humidity of 50 % at 31.5*C would be irradiated, and the concentrations of C 3 H 5 , N02, Qy CO, HCHO, CH3CHO and P.A.N, would be measured at 20 min intervals over 360 min ( 6 ). A computer programme would be written to simulate the progress of the reaction by the - 14 -Integration of an appropriate set of di f f e r e n t i a l rate; equations ( 7 ). The experimental and calculated values of the concentration of each constituent would be compared at corresponding times and the values of the rate constants adjusted to give the best f i t . These systems are very complex and d i f f i c u l t to treat quantitatively, since many of the reactions that appear to be important have not been studied in detail, and their rate constants must be assigned on a purely speculative basis. One of the most serious areas of uncertainty is due to the lack of direct determinations of almost a l l of the reactions of alkylperoxy radicals. With such a handicap the chemical modelling studies by the computer can achieve only s t r i c t l y limited success. The results obtained in the present investigation should promote these modelling studies, as rate constants have been estimated for typical fast reactions of methyl, ethyl, methylperoxy, ethylperoxy and acetyl radicals. (3) Characteristic reactions of free radicals at high concentrations. (a) The special conditions of flash photolysis. In the present investigation alkyl radicals were formed by the flash photolysis of a pure alkyl radical source such as an azoalkane. The corresponding alkylperoxy radicals were rapidly and -1 e f f i c i e n t l y formed i f — 0 . 0 2 mole 1 oxygen was also present in the reaction c e l l . This method generated i n i t i a l radical -6 -! concentrations of the order of 10 mole 1 . At such concentrations the only significant reactions of these radicals - 15 -are those with low energies of activation and high pre-exponential factors ( A ). Typical reactions of free radicals which were observed in this investigation are l i s t e d in Table 1.1. 1 Mutual and cross interactions of free radicals are favoured by the uniformly high values of the rate constants. Reactions with oxygen are favoured by the comparatively high oxygen concentration of 0.041 mole 1* corresponding to 1 atmosphere at 298 K, which offsets the relatively low values of the rate constants. Thus, in the oxidation of the methyl radical the reactions: CH^ + 0 2 CR^ OO* CH^ O* + 0 2 CH20 + H00* predominated over the reactions: 2 CH^ j • CH3CH3 2 CH30* • CH^ OOCH-j or CH3OH + CH20 -1 for an oxygen concentration of 0.023 mole 1 . Metathetical reactions of radicals with the alkyl radical source molecules are negligible because the rate constants are so low. For the reaction: CH3 + CH3-N=N-CH3 CB4 + CH3-N=N-CH2 k = 108'1 exp [- ( 7.6 ± 0.3 ) x 10 3 / HT] = 3.4 x 10 2 1 mole1 sec 1 at 298 K ( 8 ). For the reaction: Table-1.1 C h a r a c t e r i s t i c r e a c t i o n s of free r a d i c a l s i n t h i s i n v e s t i g a t i o n Class of reaction Example Rate constant at 298 K ( 1 mole - 1 s e c - 1 ) Mutual combination 2 CH^CH£ CH3CH2CH2CH3 1.24 x 1 0 1 0 Mutual disproportlonation 2 CH3CH2 CH-JCH-J + CH2=CH2 1 . 7 x 1 0 9 Cross combination CHjCH'2 «• CH^ CH^CHgCHg 4.2 x 1 0 1 0 Cross disproportlonation CH3CH2 + CH 3 CH2=CH2 + CH^ i .? x 1 0 9 Combination with oxgen CH3CH2 * 0 2 - CH 3CH 200" 1.4 x 1 0 8 Disproportlonation with oxygen CH 3CH 20" • 0 2 CH-jCHO + HOO* 1 x 1 0 6 Displacement CH3CH200' * CH3CH2O0' CH3CH20OCH2CH3 • 0 2 ^ 2.94 x 1 0 7 Displacement with scission CH3CH200' • CH3CH200" 2 CH-jCHgO' • 0 2 4 2.94 x 1 07 - 17 -CH^ + CH3COCH~3 CH^ + CH3COCH2 k = 1 0 8 , 6 exp [- ( 9.7 i 0.1 ) 1 10 3 / R T ] - 31 1 mole1 sec 1 at 298 K ( 9 )• (b) Mutual Interactions of free radicals (1) Mutual combination This class of reaction is s t r i c t l y termolecular: 2 H « + M R 2 + M» and the third body effect has been observed for the mutual combination of both methyl and ethyl radicals. However, a l l such interactions are effectively of the second order at the pressures used in the present investigation, ( i l ) Mutual disproportlonation The products of the reaction: CH3-CD2 + H-CH2-CD2 • CH^-CDg-H + CH2=CD2 demonstrate that the atom transferred was originally attached to the atom which was bound to the atom bearing the odd electron. Disproportlonation i s formally similar to metathesis, but there is an important kinetic distinction: a typical A-factor for disproportlonation i s characteristically at least two orders of magnitude greater than the A-factor for a corresponding metathesis. Indeed the A-factors for the mutual combination and disproportlonation of the same radical pair are often much more nearly commensurate, and i t has been suggested that the transition states for both processes must - 18 -be similar, i f not identical, ( i i i ) Displacement. The mutual disproportionation of ethyl radicals is formally also a displacement reactiont the displacement of the ethylene molecule from the second ethyl radical by the f i r s t ethyl radical. The mutual interaction of alkylperoxy radicals may occur at least in part by displacement: The carbon-carbon bond strength of the acetyl radical makes i t a most l i k e l y subject for a displacement reaction, and the participation of the displacement reaction: . CH3OOCH3 CI^OO' + C H 3 0 0 * 2 CH^ O* or CH3OH + CH 20 CHoCO* + CHo-CO* C H 3 C O - C H 3 + CO w i l l be proposed in Chapter 7 in relation to the C0/C 2H£ yield ratio in the photolysis of acetone. (c) Cross interactions of free radicals. The relationship of the rate constant for the cross combination: R j + R 2 Hi " R 2 k 1 2 to the rate constants for mutual combination: - 19 -2 R' R 2 - R 2 ; k 2 2 is expressed by the cross combination ratio: K 1 2 / k l l K 2 2 with a value of 4, i f the purely s t a t i s t i c a l value predicted by simple c o l l i s i o n theory is applicable. A value of 4 is found for pairs of radicals of very similar structure, such as CH3 and CD3 radicals. Values close to four have been found for the cross combination of many pairs of alkyl radicals in which polar interaction is negligible. Significant deviations from 4 are observed for pairs of radicals having substituents of dif f e r i n t electronegativities, as has been claimed for the pair ( 1 0 , 1 1 ) : CH3CO* + CH3 CH3COCH3 ; k 1 2 / k n k 2 2 = 1 This deviation may not be due simply to a polar effect; Gandinl and Hackett have suggested that the mutual combination of acetyl radicals may occur along a t r i p l e t potential surface ( 12 ). ( i i ) Cross disproportionation. This class of reaction i s especially important for alkoxy radicals in this investigation; thus, for the ethoxy radical: CH^C^OO* + C H 3 C H 2 0 * — — CH^ CHgOOH + CH3CHO 0 2 + C H 3 C H 2 0 # HOO' + CH3CHO The hydroperoxy radical displays two modes of cross disproportionation, involving the transfer of a hydrogen atom - 20 -and an oxygen atom respectively: CH3CH200* + HOO* - CH3CH 200H + 0 2 CO + HOC C 0 2 + HO' For the latter reaction: k * 1 x 1 0 8 exp [-1.0 x I O V R T ] = 5 1 mole1 sec 1 at 298 K ( 13 )• This reaction is far too slow to be significant in the present investigation, but i t appears to participate in the formation of photochemical smog, ( i i i ) Displacement. Probable examples include the reactions: CH^ O* + CH^ OO* CH3OCH3 + 0 2 CH*} + CH3C0' CH3CH3 + CO Evidence in support of the latter reaction w i l l be presented in Chapter 7. - 21 -D. Advances In experimental technique. This investigation has applied the techniques of flash photolysis and kinetic spectroscopy to the quantitative study of the fast reactions of methyl, ethyl, methylperoxy, ethylperoxy and acetyl radicals. At the outset, the absorption spectra of the last four radicals had not been characterized. The d i f f i c u l t i e s of characterization included a wide diversity in the maximum values of the corresponding extinction coefficients. These have now been estimated to be, in units of 1 moli 1 cm1: methyl 9.5 x 10 3, ethyl 4.8 x 10 2, methylperoxy 1.55 x 10 3, ethylperoxy 1.02 x 10^ and acetyl 1.0 x 10 • This diversity also determines the level of sensitivity required of the detecting system for the measurement of a characteristic rate constant for a particular radical. Thus a photographic detecting system was adequate for the study of the methyl radical with i t s high maximum extinction coefficient, but quite inadequate for the study of the ethyl radical. Much greater sensitivity was essentia! for a comprehensive study of the kind envisaged for this project. The desired increase in sensitivity was achieved by a change in the technique of measuring absorbance from a photographic method to an improved photoelectric method which incorporated an effective combination of two recent advances in technique. First, the intensity of the analytical l i g h t source was increased by two orders of magnitude for the period of measurement of absorbance by applying a square wave voltage pulse to the flash lamp for a period up to 5 millisec. Secondly, the accuracy of measurement of a small absorbance was increased - 22 -by using a dual beam o p t i c a l system w i t h balanced p h o t o m u l t l p l i e r s . In general, t h i s technique allowed the d i r e c t measurement of the absorbance of the d e s i r e d t r a n s i e n t species by the automatic s u b t r a c t i o n of the absorbance of a l l other species. The inf o r m a t i o n i s conveyed by an e l e c t r i c c u r r e n t which can be p r o j e c t e d on an o s c i l l o s c o p e screen and photographed. F u l l d e t a i l s w i l l be given i n Chapter 2. The dual beam technique has been used i n spectroscopy f o r a long time and i s w e l l known. A r e l a t e d technique was a p p l i e d to k i n e t i c spectroscopy by Paul and Dalby i n 1962 and B o x a l l and Simons i n 1972 ( I4a,b ). In that technique a s i n g l e beam was passed through the r e a c t i o n c e l l and was s p l i t subsequently to al l o w the i n t e n s i t i v e s of the two r e s u l t a n t beams to be measured at two d i f f e r e n t wavelengths. Such a technique i s l i m i t e d to r a d i c a l s possessing a narrow absorption spectrum. A dual beam system i n which both beams were monitored at the same wavelength was described by Kramer, Hanes and B a i r i n I 9 6 I (14c). In that system the p h o t o l y t i c f l a s h was followed by fo u r successive f l a s h e s from xenon spectroscopic lamp at minimum i n t e r v a l s of 200 microsec, and generates four s i g n a l s from each of the two p h o t o m u l t i p l i e r s . None of these systems provides the combination of s e n s i t i v i t y and time r e s o l u t i o n r e q u i r e d f o r the study of the r e a c t i o n s described i n t h i s d i s s e r t a t i o n . - 23 -CHAPTER 2 EXPERIMENTAL METHODS A, I n t r o d u c t i o n (1) Flash p h o t o l y s i s and k i n e t i c spectroscopy The technique of f l a s h p h o t o l y s i s and k i n e t i c spectroscopy was f i r s t described by R.G.W.Norrish and G.Porter (l4,15)in 19^9 and independently developed by G.Herzberg and D.A.Ramsay i n 1950-Since then many instrumental improvements have been made. This powerful and v e r s a t i l e experimental method has proved u s e f u l i n a number of f i e l d s such as gas phase and l i q u i d phase photochemistry, and var i o u s b i o p h y s i c a l systems. The main f e a t u r e s of the technique are e s s e n t i a l l y the same f o r most a p p l i c a t i o n s . E x c e l l e n t review a r t i c l e s on f l a s h p h o t o l y s i s and k i n e t i c spectroscopy have been published (16,17). The method of research that uses the techniques of f l a s h p h o t o l y s i s and k i n e t i c spectroscopy u s u a l l y proceeds i n s e v e r a l stages. The f i r s t stage i s a survey of the absorption spectra of the t r a n s i e n t species of i n t e r e s t . The absorption spectrum of each - Zk -t r a n s i e n t species i s examined over a s u f f i c i e n t l y wide range of wavelength and recorded on a photographic p l a t e ; t h i s process i s repeated f o r a s e r i e s of delay times a f t e r the i n i t i a t i o n of r e a c t i o n by the f i r i n g of the photof l a s h lamp. In t h i s way the growth and decay of .each t r a n s i e n t species may be observed, and a wavelength s e l e c t e d f o r q u a n t i t a t i v e measurements. The second stage i s the more pr e c i s e measurement of the v a r i a t i o n w i t h time of the absorbance of the t r a n s i e n t species at the s e l e c t e d wavelength by changing to a p h o t o e l e c t r i c d e t e c t i o n system which has p h o t o m u l t i p l i e r s and an o s c i l l o s c o p e as i t s e s s e n t i a l elements. The t h i r d i s the k i n e t i c a n a l y s i s of such measurement. T y p i c a l l y an order of r e a c t i o n and a r a t e constant i s deri v e d f o r each r e a c t i o n of each t r a n s i e n t species, and a r e a c t i o n mechanism proposed f o r the o v e r a l l system. Product a n a l y s i s i s o f t e n used to complete the k i n e t i c a n a l y s i s . Both the photographic technique and p h o t o e l e c t r i c technique were used i n t h i s i n v e s t i g a t i o n . ( 2 ) A comparison of the photographic and p h o t o e l e c t r i c methods For photographic d e t e c t i o n , the b a s i c form of the apparatus i s as shown i n F i g u r e - 2 . 1 3 i n Section C . 1 8 Absorption s p e c t r a of the rea c t a n t mixture were recorded at v a r i o u s s e l e c t e d delay times f o l l o w i n g the p h o t o l y t i c f l a s h . A. s e r i e s of such spectra was used to o b t a i n the time dependence of the absorbance of each observable species. A spectroscopic f l a s h lamp was used to produce monitoring l i g h t f o r the absorption spectra. This l i g h t was c o l l i m a t e d i n t o - 25 -the r e a c t i o n v e s s e l and focussed onto the s l i t of the spectrograph by a s p h e r i c a l quartz l e n s . The spectroscopic f l a s h lamp was u s u a l l y operated at the lower discharge energy. P h o t o l y t i c changes caused by the spectroscopic f l a s h were considered n e g l i g i b l e . For p h o t o e l e c t r i c d e t e c t i o n , the b a s i c form of the apparatus i s as shown i n F i g u r e - 2 . 1 . A beam s p l i t t e r of the m i r r o r type s p l i t the output of the monitoring l i g h t i n t o two beams of s i m i l a r i n t e n s i t y . These beams were passed through the r e a c t i o n v e s s e l and the reference v e s s e l r e s p e c t i v e l y , then through the spectrograph, and then onto the r e s p e c t i v e p h o t o m u l t i p l i e r s by two m i r r o r s , which were mounted at the e x i t s l i t of the spectrograph. The d i f f e r e n c e i n the i n t e n s i t y of the two beams caused by passage through the r e a c t i o n and reference v e s s e l s r e s p e c t i v e l y was monitored by these p h o t o m u l t i p l i e r tubes. I t can thus be seen that the p h o t o e l e c t r i c technique g i v e s a complete record of the time dependence of the i n t e n s i t y of the two beams i n one experiment at a s i n g l e wavelength. The experiment must be repeated f o r each d e s i r e d wavelength to b u i l d up a comprehensive record over the whole spectrum of absorbance. In c o n t r a s t , the photographic technique g i v e s , i n each experiment, an absorption spectrum across a wavelength range but only at a s i n g l e chosen time f o l l o w i n g the photoflash. Several experiments are r e q u i r e d to b u i l d up a time sequence. I t should be noted that p h o t o e l e c t r i c measurements are more accurate and a great deal more s e n s i t i v e than photographic measurements, and . only the p h o t o e l e c t r i c technique allows a r a p i d change i n the conc e n t r a t i o n of a t r a n s i e n t species to be followed c l o s e l y . - 26 -In a d d i t i o n the data of p h o t o e l e c t r i c experiments may be processed much f a s t e r than the data of photographic experiments. I t w i l l be c l e a r from these advantages th a t the development of a p h o t o e l e c t r i c apparatus was c r u c i a l to t h i s i n v e s t i g a t i o n . D e t a i l e d d e s c r i p t i o n s of i n d i v i d u a l components of the apparatus are given i n l a t e r s e c t i o n s of t h i s chapter. - 27 -B, A General D e s c r i p t i o n of the Apparatus w i t h P h o t o e l e c t r i c Detection. The present i n v e s t i g a t i o n has e x p l o i t e d the s p e c i a l advantages of the advanced design of our new double-beam f l a s h p h o t o l y s i s apparatus shown s c h e m a t i c a l l y i n Figure-2.1. The p r i n c i p a l components of t h i s apparatus are l i s t e d i n the order i n which they are placed along the o p t i c a l path. (1) The monitoring l i g h t source. This i s a 150 watt D.C. compact source xenon arc lamp. I t has two operating regimes; continuous emission at low power, and intense emission at approximately constant i n t e n s i t y f o r the p e r i o d of measurement of the absorbance of the r e a c t i n g system. This pulse of i n t e n s i t y i s provided by applying an approximately square wave pulse of high voltage to the arc while i t i s running at low power. (2) The c o l l i m a t i n g l e n s . A c o l l i m a t i n g l e n s converts the output of the pulsed xenon arc i n t o a p a r a l l e l beam. (3) The o p t i c a l s h u t t e r . The opening of t h i s s h u t t e r sends a s i g n a l f i r s t to the o s c i l l o s c o p e camera and l a t e r to the delay c o n t r o l u n i t . This u n i t generated successive pulses that t r i g g e r e d the operation of the o s c i l l o s c o p e , the p u l s i n g of the xenon a r c , and the f i r i n g of the photoflash tubes, as shown i n Figure-2.7 • This sequence Figure-2.1 The f l a s h p h o t o l y s i s apparatus with p h o t o e l e c t r i c d e t e c t i o n Continued .... - 29 -A. : Xenon Lamp Housing B : C o l l i m a t o r Lens C : O p t i c a l Shutter Switch D : Beam S p l i t t e r 2 : P h o t o f l a s h Lamp F : Reaction Vessel G : Hollow Cathode Lamp Device ( w i t h M i r r o r ) H : Focussing Lens I : C l 2 / B r 2 Gas F i l t e r Holder J : Monochromator K : Mi r r o r s L : Photomultipi1ers M : P h o t o m u l t i p l i e r Power Supply-N : Os c i l l o s c o p e 0 : Delay C o n t r o l Unit P : Capacitor Unit Q : Dual E l e c t r o n i c Switch ( Capacitor Coupler ) R : Phot o f l a s h High Voltage Power Supply S : I g n i t o r ( f o r Xenon Lamp ) T : Xenon Lamp P u l s e r U : Xenon Lamp Power Supply V : Sorensen D.C. Power Supply - 30 -ensured that a high energy pulse of l i g h t of approximately constant i n t e n s i t y over a r e l a t i v e l y long period was a v a i l a b l e to monitor the absorbance of r e a c t i n g system before and a f t e r the f i r i n g of the photoflash. (4) The beam s p l i t t e r . This u n i t s p l i t s the i n c i d e n t beam from the pulsed xenon arc i n t o two beams of approximately equal i n t e n s i t y , and d i r e c t s these beams along the axes of the r e a c t i o n and reference v e s s e l s r e s p e c t i v e l y . (5) The photof l a s h and v e s s e l assembly. (a) The r e a c t i o n v e s s e l contained the r e a c t i v e mixture of gases; i l l u m i n a t i o n generated the t r a n s i e n t species of i n t e r e s t . The gas mixture contained a lar g e excess of i n e r t "moderating" gas to increase the heat c a p a c i t y of system. Very pure samples of argon, n i t r o g e n , carbon monoxide or n-pentane were used as i n e r t gases. This measure l i m i t e d to a few degrees the r i s e i n temperature f o l l o w i n g the photoflash; the e f f e c t i v e temperature of a l l the r e a c t i n g systems was therefore close to room temperature. (b) The reference v e s s e l contained a reference mixture; t h i s d i f f e r e d from the r e a c t i v e mixture only i n the omission of the primary r a d i c a l source. (c) The two photof l a s h tubes: each tube emitted an intense f l a s h of a c t i n i c l i g h t when f i r e d ; the h a l f peak width of the f l a s h was of order of 10 jjsec. The f l a s h tubes and v e s s e l s were mounted i n the symmetrical c o n f i g u r a t i o n shown i n Figure-2.7 to - 31 -ensure that the i n t e n s i t y i n c i d e n t upon each tube was as intense and as uniform as p o s s i b l e . The twin beams from the pulsed xenon arc were passed along the axes of the r e a c t i o n v e s s e l and the reference v e s s e l ; the intense pulse began before the f i r i n g of the ph o t o f l a s h and was maintained over the whole period of observation. ( 6 ) The twin f o c u s s i n g lenses. These were used to focus the twin monitoring beams emerging from the r e a c t i o n and reference v e s s e l s onto the entrance s l i t of the spectrograph. (7) The o p t i c a l f i l t e r . The band pass was chosen to transmit only the r e g i o n of i n t e r e s t i n the absorbance measurements. The e l i m i n a t i o n of sc a t t e r e d and s t r a y l i g h t from the pho t o f l a s h i s e s s e n t i a l to the attainment of an adequate s i g n a l to noise r a t i o . A c h l o r i n e -bromine gas f i l t e r or a g l a s s f i l t e r was used f o r the observation of d i f f e r e n t species. (8) The spectrograph. The spectrograph was used as a monochromator w i t h a band pass of the order of O.lnm. I t re c e i v e d the twin monitoring beams from the r e a c t i o n and reference v e s s e l s , analyzed them, and t r a n s m i t t e d e s s e n t i a l l y monochromatic beams to the p h o t o m u l t i p l i e r s . (9) The twin p h o t o m u l t i p l i e r s . - 32 -These were c a r e f u l l y matched and balanced; they r e c e i v e d the twin monochromatic monitoring beams from monochromator and generated the corresponding output voltages. (10) The o s c i l l o s c o p e . This d i s p l a y e d the time r e s o l v e d outputs of the twin p h o t o m u l t i p l i e r s as two t r a c e s ; t y p i c a l l y , these represented the i n t e n s i t y of monochromatic l i g h t t r a n s m i t t e d by the reference v e s s e l and the d i f f e r e n c e of the i n t e n s i t i e s t r a n s m i t t e d by the reference v e s s e l and the r e a c t i o n v e s s e l r e s p e c t i v e l y . (11) The camera. The t r a c e s d i s p l a y e d on the screen of the o s c i l l o s c o p e were photographed by a " P o l a r o i d " camera. - 33 -C, A D e t a i l e d D e s c r i p t i o n of the Apparatus. (1) The monitoring l i g h t source. A Lyman tube has of t e n been used as a spectroscopic lamp i n f l a s h p h o t o l y s i s experiments which were designed f o r a photographic d e t e c t i o n system. However, our new apparatus has a p h o t o e l e c t r i c d e t e c t i o n system and employs a pulsed 150W D.C xenon arc as a monitoring l i g h t source. Power i s s u p p l i e d to the xenon arc from two u n i t s ; one s u p p l i e s power at a constant low l e v e l to maintain a continuous low emission of l i g h t , whereas the other s u p p l i e s a b r i e f intense pulse of power to provide a pulse of l i g h t at high i n t e n s i t y . These power supply u n i t s are discussed l a t e r i n t h i s chapter. Steady operation of the xenon lamp was maintained at 20 v o l t s and 7-5 amps. The xenon arc was pulsed by applying a constant h i g h voltage from an e x t e r n a l source f o r a short time to the c i r c u i t f o r steady operation. Under t y p i c a l p u l s i n g c o n d i t i o n s the lamp operated at 140 v o l t s . By t h i s method, the l i f e time of the monitoring l i g h t pulse from the xenon lamp can be e a s i l y adjusted w i t h i n a range from a few 100 Lisec to about 25 msec. The average l i f e of a xenon lamp was about one thousand to two thousand time pulses; of course t h i s a l s o depends on the pulsed voltages and the l i f e time of pulsed xenon l i g h t . The xenon lamps of Osram Inc ( XB0-150W/4 ) and I l l u m i n a t i o n I n d u s t r i e s Inc ( PEK 150W ) were used. The l a t t e r source was p r e f e r r e d because the l i g h t pulses were more s t a b l e ; longer l i f e , lower c o s t , and f a s t e r d e l i v e r y were added advantages. The design of xenon lamp i s shown i n Figure-2.2. . - 34 -(2) The xenon lamp housing and c o l l i m a t o r housing. A xenon lamp housing was designed to promote the d i s s i p a t i o n of heat and the removal of ozone, and to a f f o r d p r o t e c t i o n against the e x p l o s i o n of i t s lamp ( see Figure-2.2 ). The housing was made of brass, and was blackend using brass b l a c k i n g s o l u t i o n c o n t a i n i n g 30g of copper carbonate i n 357ml of concentrated ammonia s o l u t i o n . A l e n s was used to c o l l i m a t e the l i g h t from the xenon arc lamp before t r a n s m i s s i o n through the r e a c t i o n and reference v e s s e l s . The lens was mounted i n a housing i n a manner which allowed i t s p o s i t i o n to be v a r i e d i n order to c o l l i m a t e l i g h t of v a r i o u s wavelengths. The lens housing was attached d i r e c t l y to the lamp housing. Scattered l i g h t was reduced as much as p o s s i b l e by mounting a blackened brass p l a t e with a 17-5cm aperture on each side of the l e n s to act as a b a f f l e . A quartz p l a t e was mounted between the lens and the lamp to prote c t the lens from damage i f the lamp exploded. A f i n type of heat exchanger was b u i l t onto the lens housing u n i t to remove the heat conducted from the xenon lamp and prevent the d i s t o r t i o n of the lens by heat. The heat exchanger was made of s o l i d aluminium painted black. The temperature of the lamp t e r m i n a l was measured by a copper constantan thermocouple, and rose to about 443K when a 150W xenon lamp was used. (3) The adjustment u n i t of the xenon lamp. The alignment of the xenon lamp p o s i t i o n w i t h the o p t i c a l a x i s of the system i s very c r i t i c a l . An assembly was designed to o btain the continuous and smooth adjustment of the p o s i t i o n - 35 -Figure-2.2 . The xenon arc lamp assembly-Xenon Lamp F : C o l l i m a t o r Lens V e n t i l a t i o n Windows G : C o l l i m a t o r A d j u s t e r C 2 : Anode and Cathode H : F i n Type Heat Exchanger D 2 : Brass B a f f l e s I : L i g h t A x i s Quartz P l a t e - 3 6 -F i g u r e - 2 . 3 Assembly f o r the f i n e adjustment of the p o s i t i o n of the xenon arc lamp + r+V ro i ! r H i i . ! ! . 3 •B a s D A-p A 2 : Xenon Lamp Holder B : Asbestos Base C : Adjuster of H o r i z o n t a l D i r e c t i o n D : Adjuster of V e r t i c a l D i r e c t i o n - 37 -of the xenon lamp without using grease, which i s u n s u i t a b l e due to the high temperature of the housing ( see Figure-2.3 )• The adjustment u n i t provides independent v e r t i c a l and h o r i z o n t a l movement of the xenon lamp. Each piece of the adjustment u n i t was made of brass, except f o r the main plate which was made of 9ram t h i c k aluminium painted black. A 12mm t h i c k asbestos p l a t e was used f o r the base of the xenon lamp holder to reduce heat t r a n s f e r to the adjustment u n i t . (4) The delay c o n t r o l u n i t . The absorbance of the r e a c t i n g system was monitored f o r a period s t a r t i n g before the f i r i n g of the pho t o f l a s h and l a s t i n g f o r s e v e r a l h a l f l i v e s of the most l o n g - l i v e d observable t r a n s i e n t species. This r e q u i r e d that the pulsed xenon arc should emit a high energy pulse of l i g h t of approximately constant i n t e n s i t y over t h i s p e r i o d , which might be as long as 25 msec. I t a l s o r e q u i r e d the successive t r i g g e r i n g of the o s c i l l o s c o p e , of the p u l s i n g of the xenon a r c , and of the f i r i n g of the photoflash lamp. This sequence was c o n t r o l l e d by the delay u n i t marked 0 on Figure-2.1, and shown i n d e t a i l i n the complex diagram on Figure-2.4. An o p t i c a l s h u t t e r l i e s on the o p t i c a l a x i s between the housings of the monitoring lamp and the beam s p l i t t e r . The opening of t h i s shutter r e l a y e d on e l e c t r i c a l pulse f i r s t to the o s c i l l o s c o p e camera and then to Delay Unit No.5» and caused the generation of a succession of pulses as i l l u s t r a t e d i n Figure-2.5, which served to t r i g g e r the o s c i l l o s c o p e , to switch the xenon - 38 -Figure-2.4 A schematic diagram of the delay unit complex O p t i c a l S h u t t e r o r M a n u a l B u t t o m O s c i l l o s c o p e C a m e r a Open * D e l a y No .5 O s c i l l o s c o p e Triggered D e l a y No . 4 P h o t o f l a s h Lamp Firing Tine D e l a y N o . l Base Line D u r a t i o n P u l s e T r a n s f o r m e r T h y r i s t o r 1 X e n o n P u l s e S w i t c h ON D e l a y No . 2 X e n o n Lamp D u r a t i o n P u l s e T r a n s f o r m e r T h y r i s t o r 2 X e n o n P u l s e S w i t c h O F F D e l a y N o . 3 X e n o n Lamp D u r a t i o n P r e c a u t i o n S w i t c h O F F U n i t P u l T r a n s f T h y r i s se omer t o r 3 T r i g g e r 1 > C a p a c i t o r 1 P h o t o f l a s h 1 i — T r i g g S p a r k ; e r 2 g a p 2 > C a p a c i t o r 2 P h o t o f l a s h 2 - 3 9 -Figure-2.5 The operation of the delay c o n t r o l u n i t (a) A diagram of r e l a t i v e delay times and an i d e a l i z e d trace of the pulsed xenon l i g h t i n t e n s i t y . Oscilloscope Trigger 5> Ideal Xenon Pulse Output L D^/Photoflash Lump ON Shutter Open Xenon Pulse ON °2 D 3  Xenon Pulse OFF (D3 : Precaution Switch ) \ Shutter Dose (b) A photograph of a c t u a l t r a c e s - 40 -arc pulse ON and OFF, to switch the photof l a s h lamp ON. The f u n c t i o n of each delay u n i t i n the delay u n i t complex i s shown i n the schematic diagram. This complex was made i n the Departmental e l e c t r o n i c s shop by Mr.Eric F i s h e r . (5) The beam s p l i t t e r . The experimental method r e q u i r e s the measurement of the d i f f e r e n c e of the absorbances of the r e a c t i o n v e s s e l and the reference v e s s e l at a chosen wavelength f o r a s e r i e s of i n t e r v a l s a f t e r the f i r i n g of the photoflash. Two monitoring l i g h t beams are r e q u i r e d f o r t h i s purpose, and i d e a l l y these beams shoud d e l i v e r i d e n t i c a l i n c i d e n t i n t e n s i t i e s to the r e a c t i o n and reference v e s s e l s i n the wavelength s e l e c t e d f o r the measurement of absorbance. This c o n d i t i o n may be r e a l i z e d q u i t e c l o s e l y i f the two beams o r i g i n a t e from a s i n g l e l i g h t source; the output of t h i s source must f i r s t be c o l l i m a t e d and then s p l i t i n t o two beams by the p a r t i a l l y r e f l e c t i n g plane m i r r o r mounted i n the beam s p l i t t e r . The beam s p l i t t e r u n i t ( see Figure-2.6 ) contains one m i r r o r which r e f l e c t s ~ 4 0 % throughout the UV, and a second m i r r o r which r e f l e c t s 100 %. The f i r s t m i r r o r s p l i t s the beam, t r a n s m i t t i n g ~40$ along the a x i s of one of the v e s s e l s , and r e f l e c t i n g ~40% to the second m i r r o r which r e f l e c t s 100% along the a x i s of the other v e s s e l . These two m i r r o r s were v e r t i c a l l y mounted on the aluminium base and i n c l i n e d at 45° to the o p t i c a l a l i g n e d a x i s . Each m i r r o r was made by evaporating aluminium onto the clean surface of a 5«lcm x 5-lcm quartz p l a t e under high vacuum c o n d i t i o n s . The beam s p l i t t e r u n i t was mounted on the same base as the monitoring l i g h t housing - 41 -Figure-2.6 The beam s p l i t t e r assembly A : A l i g n e d L i g h t A x i s of Lower Beam 3 : A l i g n e d L i g h t A x i s of Upper Beam C : M i r r o r w i t h ~40# Transmission and ~40# R e f l e c t i o n D : M i r r o r w i t h 100% R e f l e c t i o n E : Aluminium Base of Beam S p l i t t e r F : O p t i c a l Shutter Holder ( Brass ) G : O p t i c a l Shutter ( I l l e x 3X ) - 42 -and the height and angles were adjusted using a set of four b o l t s and a s i n g l e centre b o l t r e s p e c t i v e l y . ( 6 ) The photofl a s h lamps. The photof l a s h lamps were 100cm long w i t h an i n s i d e diameter of 8mm and a w a l l t h i c k n e s s of 1 .5mm, and were made of " S u p r a s i l " quartz. The el e c t r o d e s were made of tungsten metal and were s i l v e r soldered i n t o s t a i n l e s s s t e e l B - 1 0 cones, which were cemented by bla'ck wax i n t o B - 1 0 sockets at the ends of the photoflash lamps. Many types of pho t o f l a s h lamp were designed i n an attempt to produce a s t a b l e , homogeneous f l a s h , and to minimize the l i f e time of the f l a s h and to reduce the v i b r a t i o n of the f l a s h tube. The f i n a l design of the el e c t r o d e s system that was used i n t h i s i n v e s t i g a t i o n i s shown i n F i g u r e - 2 . 7 -One t e r m i n a l of the photofl a s h lamp was connected to the high voltage lead of the c a p a c i t o r bank which c o n s i s t e d of 2.5uF and 5'OjjF c a p a c i t o r s , while another t e r m i n a l was connected to ground through the spark gap. The p h o t o f l a s h lamps were f i l l e d w ith argon gas to a pressure of about ? t o r r . A lar g e r e s i s t o r ( 2 0 0 k a ) connected the p o s i t i v e end of the c a p a c i t o r to the ground t e r m i n a l of the lamp and maintained both ends of the lamp and one end of the spark gap at high voltage u n t i l the spark gap was t r i g g e r e d , a l l o w i n g the c a p a c i t o r to discharge through the lamp and the spark gap to ground. The r i s e time of pho t o f l a s h was measured to be 4 jxsec and h a l f width was 6 jasec. The energy discharged through the pho t o f l a s h lamps can e a s i l y be changed by a d j u s t i n g the high - 43 -voltage and by using a d i f f e r e n t combination of c a p a c i t o r s . The output of r a d i a n t energy of the pho t o f l a s h was u s u a l l y c o n t r o l l e d i n t h i s way. The photof l a s h lamps and the v e s s e l s were mounted i n the symmetrical c o n f i g u r a t i o n shown i n F i g u r e -2.7, to promote the uniform i l l u m i n a t i o n of each v e s s e l . (7) The r e a c t i o n v e s s e l s . Each r e a c t i o n v e s s e l was 9 1 . 4 4 c m i n length w i t h an i n s i d e diameter of 20mm and a w a l l t h i c k n e s s of 1mm, and was made of " Pyrex ". Plane windows of " S u p r a s i l " quartz were cemented to both ends of the v e s s e l s by " A r a l d i t e " adhesive. One of the r e a c t i o n v e s s e l s was normally f i l l e d w i t h the r e a c t i v e gas mixture, whereas the other r e a c t i o n v e s s e l was f i l l e d w i t h the corresponding reference gas mixture. E i t h e r v e s s e l could be f i l l e d w ith the e i t h e r gas mixture, so that any e f f e c t of asymmetry was el i m i n a t e d . Quartz r e a c t i o n v e s s e l s could also be i n s t a l l e d when r e q u i r e d . The two r e a c t i o n v e s s e l s and the two photoflash-lamps were mounted symmetrically, w i t h a l l axes p a r a l l e l , w i t h i n a 'brass c y l i n d e r painted with White Reflectance Standard Paint f o r the 2 0 0 to 250nm wavelength r e g i o n , s u p p l i e d by the Eastman Kodak Co. The brass c y l i n d e r prevented the general escape of l i g h t from photo f l a s h lamps and prevented the s c a t t e r i n g of broken g l a s s chips from the e x p l o s i o n of the r e a c t i o n v e s s e l s and of the photoflash lamps. There was small clearance between the photoflash lamps and r e a c t i o n v e s s e l s to allow the i n s e r t i o n of s t r i p s of g l a s s to act as o p t i c a l f i l t e r s . A four-legged t r a p - <44 -was attached to the lower r e a c t i o n v e s s e l to a l l o w the condensation of v o l a t i l e components of the mixture. The housing of the r e a c t i o n v e s s e l s i s shown i n Figure-2.7. ( 8 ) The focussing lens housing and gas f i l t e r holder. The f o c u s s i n g lens system c o n s i s t e d of two le n s e s , one f o r the upper l i g h t beam and the other f o r the lower l i g h t beam, and was placed i n f r o n t of the entrance s l i t of the spectrograph. The focussing lens housing was made of s o l i d brass p l a t e , and the holder of the lens housing and the gas f i l t e r was made of a 2.5inch diameter brass c y l i n d e r ( see Figure-2.8 ). The p o s i t i o n of the lenses was e a s i l y adjusted to correspond to the d e s i r e d wavelength r e g i o n ; the two lenses were moved as a u n i t . A double gas f i l t e r and a g l a s s f i l t e r were u s u a l l y placed i n f r o n t of the s l i t of spectrograph to s e l e c t the range of wavelength t r a n s m i t t e d , and to remove s c a t t e r e d l i g h t and s t r a y l i g h t . A l t e r n a t i v e l y , these f i l t e r s can be placed i n f r o n t of the shutter which i s connected with the beam s p l i t t e r , but t h i s p o s i t i o n i s s u i t a b l e only when the removal of s t r a y and s c a t t e r e d l i g h t i s not very important. ( 9 ) The o p t i c a l f i l t e r s . (a) The gas f i l t e r . A fused quartz double gas f i l t e r was used. This f i l t e r was 5.1cm ( 2inches ) i n length w i t h 5'lcm ( 2inches ) outside diameter and c o n s i s t e d of two compartments separated by a window. In p r i n c i p l e a p a i r of s i n g l e gas f i l t e r s could be used, but the i n t e n s i t y of the monitoring l i g h t i s unfavourabley decreased Figure-2.7 The housing of the r e a c t i o n v e s s e l s and the photoflash lamps Perpendicular Cross Section Upper Reaction Vessel Lower Reaction Vessel Photoflash Lamps Brass Supports f o r Reaction Vessels Brass C y l i n d e r Painted with White Reflectance Standard P a i n t F : Quartz Windows G : Electrod e s of Photoflash Lamps P a r a l l e l Cross Section Figure-2.8 The focussing lens housing and gas f i l t e r holder Ai,A2 s Upper and Lower Beam Axes Bi,B2 • Focussing Lenses of the Upper and Lower Beams C : Rubber Supports f o r (the Lenses D : Lens Angle Adjuster E : Lens P o s i t i o n Adjuster F : Gas F i l t e r Holder - 47 -Figure-2.9 The absorption of the gas f i l t e r Absorbance of f i l t e r combination of 25mm ( O p t i c a l Path Length ) of C l 2 at 760 t o r r and 25mm of B r 2 at 250 t o r r . - 48 -( % ) UOJSSjUUSUDJJ_ - 49 -when the t o t a l number of windows i s increased i n t h i s way, and a high s i g n a l to noise r a t i o was e s p e c i a l l y important i n the u l t r a v i o l e t region. One compartment of the f i l t e r was f i l l e d w i t h 250torr of B r 2 gas i n the presence of 560torr of n i t r o g e n gas. Such a f i l t e r absorbs l i g h t e f f e c t i v e l y i n the range from 2b0 to 55°nm, whereas i t transmits l i g h t e f f e c t i v e l y i n the range from 190 to 270nm; see Figure-2.9. I t i s th e r e f o r e w e l l s u i t e d to prevent s c a t t e r e d l i g h t from the p h o t o f l a s h lamps from e n t e r i n g the spectrograph, and was placed between the r e a c t i o n v e s s e l assembly and the spectrograph f o r most of the experiments. (b) The g l a s s f i l t e r s . A number of g l a s s f i l t e r s such as Corning 7-51. 7-54, and 7-59 were used i n s t e a d of the C l 2 / B r 2 gas f i l t e r when the experiments were c a r r i e d out w i t h the monitoring wavelength i n the range from 270 to 400nm, as t h e i r t r a n s m i s s i o n regions l i e i n t h i s range. The t r a n s m i s s i o n curves of the f i l t e r s used are shown i n Figure-2.10. These f i l t e r s were al s o placed i n f r o n t of spectrograph on the o p t i c a l a x i s . (10) The xenon lamp power supply. An LPS-251 lamp power supply ( S c h o e f f e l Instrument Corp ) was used as a steady power supply of the xenon arc. This power supply was a c u r r e n t - r e g u l a t e d D.C. power source designed to operate xenon, mercury and xenon-mercury compact arc lamps i n the range from 75 watt to 250 watt. The operating ranges were 2 amp to 10 amp D.C. and 10V to 60V D.C. An input power voltage was allowed i n the range from 105V to 130V A.C, 50 to 60 c y c l e s . - 50 -We normally used a 150 watt xenon lamp. The operating c o n d i t i o n of this.lamp was around 7.5 amp D.C. and 20 v o l t D.G. These values were v a r i e d somewhat i n accordance w i t h the A.C. power vo l t a g e , and were e a s i l y adjusted to give the r e q u i r e d power of 150 watt c o r r e c t l y . The output of the i g n i t o r was about 20 k v o l t at r a d i o frequency during i g n i t i o n , and the output of the power supply was 10 amp D.C; therefore most of cables between power u n i t and xenon lamp housing were h i g h l y i n s u l a t e d . (11) The xenon pulse power supply and pused xenon lamp system c o n t r o l u n i t . I n k i n e t i c spectroscopy, the time v a r i a t i o n of the o p t i c a l t r a n s m i s s i o n of the sample under i n v e s t i g a t i o n i s observed by means of an a n a l y z i n g l i g h t source, a spectrograph and a photodetector. Very short time scales are o f t e n used, and the change i n t r a n s m i s s i o n may be as small as 1%, or even l e s s . In t h i s s i t u a t i o n the radiance of the a n a l y z i n g l i g h t source i s a c r i t i c a l f a c t o r i n determining the l i m i t of s e n s i t i v i t y . U s u a l l y f o r a given response time of the system the photodetector s i g n a l - t o - n o i s e r a t i o i n c r e a s e s as the square root of the l i g h t f l u x reaching i t and i n p r a c t i c e a very high f l u x i s o f t e n needed. High pressure xenon lamps are commonly used i n k i n e t i c photometry; i f a voltage pulse of large amplitude i s a p p l i e d to the lamp, a very l a r g e increase of l i g h t i n t e n s i t y i n the radiance of the arc can be produced temporarily. During such a pulse the voltage drop across the lamp te r m i n a l s does not change very much because of the very low incremental r e s i s t a n c e of the steady arc which i s already e s t a b l i s h e d , but the radiance i n c r e a s e s a great deal and - 51 -can be kept almost constant f o r s e v e r a l thousand microsecond's or more. Furthermore, as a s p e c i a l advantage, the increase i n radiance i s greater i n the u l t r a v i o l e t r e g i o n , where very l i t t l e l i g h t i s normally a v a i l a b l e , than i t i s i n v i s i b l e . A f t e r the pulse has passed the arc re t u r n s to i t s normal steady c o n d i t i o n and can be pulsed again. The pulsed arc discharge i n a xenon lamp occurs between two c l o s e l y spaced e l e c t r o d e s and most of the l i g h t comes from t h i s r e g i o n ; moreover the i n t e n s i t y of pulsed l i g h t i s g r e a t e s t over a small area near the cathode and f a l l s o f f a x i a l l y towards the anode and r a d i a l l y away from the a x i s of the el e c t r o d e s . The use of a l i g h t source of t h i s k i n d f o r k i n e t i c spectrophotometry was f i r s t described by H.C. Chris t e n s e n et a l i a ( 18 ). Our xenon p u l s i n g u n i t c o n s i s t e d of a Sorensen constant current D.C. Power Supply and a Xenon Pulse Unit which was made i n t h i s department. The Sorensen D.C. Power Supply DCR-300-1.25A was sup p l i e d by the Rayteon Company. The b a s i c c i r c u i t of the pulsed xenon lamp system c o n t r o l u n i t ( p u l s e r u n i t ) was designed by B.W. Hodgson and J.P. Keene ( 19 ). (12) The p h o t o m u l t i p l i e r s and power supply. EMI type 9783 ( EMI E l e c t r o n i c L t d ) photomultiers are nine dynodes tubes and were used f o r a l l measurements. They are 30nm ( 1 /8 ) side window tubes, and - 52 -t h e i r " S p e c t r o s i l " g l a s s windows have a s p e c t r a l range of trans m i s s i o n from 165 to 650nm. Their response maximum peak i s at about 300nm and i s very broad, but they r e t a i n q u i t e high quantum e f f i c i e n c i e s i n the range from 150 to 420nm. The response f a l l s o f f r a p i d l y outside t h i s r e g i o n . The maximum anode ( mean ) current was 0.5mA and the maximum voltage between anode and cathode was 1250V. Two of ABC1000M power supply u n i t s from the Kepco Inc were used as the power su p p l i e s of p h o t o m u l t i p l i e r tubes, and were very s t a b l e ; s t a b i l i t y i s e s s e n t i a l as the output s i g n a l of a p h o t o m u l t i p l i e r i s extremely s e n s i t i v e to v a r i a t i o n s i n the power supply volatage. The in t e r s t a g e voltage g r a d i e n t s f o r the p h o t o m u l t i p l i e r elements were provided by r e s i s t i v e voltage d i v i d e r placed across the high voltage source. Resistance values were chosen such that the current through the voltage d i v i d e r c h a in was about twenty times the maximum anode current used ( see Figure-2.11 ). As i t i s necessary to supply a maximum of 10 and p r e f e r a b l y 100 times the mean anode cu r r e n t , the value of the r e s i s t o r s used i s l i m i t e d at low values by heat d i s s i p a t i o n i n the d i v i d e r and by the current c a p a c i t y of the power supply, and at high values by i n t e r e l e c t r o d e leakage. For r o u t i n e a p p l i c a t i o n 10Oku per dynode i s a s u i t a b l e choice. An appropriate choice of values f o r the r e s i s t o r s and c a p a c i t o r s prevented the dynode voltages from v a r y i n g as the photocurrent passed through the p h o t o m u l t i p l i e r s . This e f f e c t i s e s p e c i a l l y important i n the l a s t two stages and can lead to a non - l i n e a r p h o t o m u l t i p l i e r response. Attempts to improve the o v e r a l l performance of the p h o t o m u l t i p l i e r s were made by s e t t i n g the f i r s t cathode to dynode - 5 3 -e l e c t r i c f i e l d at a high p o t e n t i a l . Therefore a 150kn. r e s i s t o r was connected across the R± stage and a second 150kn r e s i s t o r was connected across the Rg stage to improve performance. I t should a l s o be noted t h a t although a p h o t o m u l t i p l i e r a c t s e s s e n t i a l l y as a constant current device, the s i g n a l voltage developed across the load i s i n s e r i e s w i t h the l a s t dynode to anode voltage and consequently opposes i t . Non-linear o p e r a t i o n of the p h o t o m u l t i p l i e r may occur i f the load voltage becomes s i g n i f i c a n t compared to the l a s t dynode to anode voltage.'From these c o n s i d e r a t i o n s the l i n e a r i t y of the p h o t o m u l t i p l i e r s should be c a r e f u l l y confirmed f o r each set of operating c o n d i t i o n s . Good l i n e a r i t y was found f o r supply v o l t a g e s i n the range from 600 to 720 v o l t w i t h a lOkn load and a 75pF capacitance. Figure-2.12 shows the modified c i r c u t of voltage d i v i d e r f o r the p h o t o m u l t i p l i e r using the combination of r e s i s t o r s w i t h zener diodes. Most of the e l e c t r i c a l noise produced by the i n c i d e n t l i g h t a r i s e s i n the f i r s t dynode, and t h i s noise i s then i n c r e a s i n g l y a m p l i f i e d i n the succeeding stages of the p h o t o m u l t i p l i e r . Accordingly, the c i r c u i t was designed to maximize the s i g n a l - t o - n o i s e r a t i o by developing the maximum po s s i b l e g a i n i n the f i r s t stage. This was achieved by reducing the number of stages from nine to s i x without the penalty of undue l o s s of a m p l i f i c a t i o n . The p r i n c i p a l f u n c t i o n of two diodes i n the l a s t two stages was to maintain the l i n e a r i t y of the response of the p h o t o m u l t i p l i e r , and a large r e s i s t o r can perform t h i s f u n c t i o n e q u a l l y w e l l . Good l i n e a r i t y was obtained i n the response of the p h o t o m u l t i p l i e r w i t h t h i s c i r c u i t f o r supply voltages i n the Figure-2.11 The r e s i s t i v e voltage d i v i d e r f o r the p h o t o m u l t i p l i e r of EMI 9783 HV Cathode Anode f D! D 2 D 3 D A D 5 D 6 D 7 D 8 D 9 A/W—WV-LvV\—MrvLwV-^rVV—m—VA—M\—VWn R1 R 2 R3 R5 Re R7 RB R9 Rio H F— 1—I I— B c 6 °7 % c 9 °I0 4 i R A J Anode Load, 100 k a * 1 jnF C 1 0 1 20 |4F Rfi J 820 k n C 7 » 2 /4F R x and R^ : 150 k A C Q J k R 2 Rg and R 1 Q : 100 kA t 10 jiF Figure-2.12 The r e s i s t i v e voltage d i v i d e r f o r the p h o t o m u l t i p l i e r of EMI 9783 Cathode H D, D 2 D3 Cfc D 5 De Anode h Zl R1 R2 R3 < { > — W \ — w — W — W 1 Z2 D 7 C b D g Z3 q c 2 c 3 c< c 5 c 6 c 7 Z-j^  : Zener Diode, 100 V Z 2 : Zener Diode, 150 V Z^ : Zener Diode, 200 V R-L R^ and R^ 1 200 kn Rfi : b20 kn. C 1 1 0.1 JJF C 2 s 0.2 uF C 4 : 1.0 jiF : 2.0 jjF C 6 : 5-0 JiF ^ s 0.5 uF Crp » 10.0 jaF R. : 100 k n A - 5 6 -range 7 5 ° to 900 v o l t w i t h a lOkn load and a 75pF capacitance. Both the p h o t o m u l t i p l i e r s and t h e i r cables must be c a r e f u l l y s h i e l d e d to minimize e l e c t r o n i c and magnetic noise from r a d i a t i o n generated by the discharge of the photofl a s h lamps and from s t r a y l i g h t sources. A l l cables which lead to the p h o t o m u l t i p l i e r s were h i g h l y shielded using s h i e l d i n g wire ( braided tinned copper wire ) to prevent e l e c t r o n i c noise, and both p h o t o m u l t i p l i e r s were s h i e l d e d by s p e c i a l metal c y l i n d e r s which were designed f o r s h i e l d i n g electromagnetic noise. In a d d i t i o n the p h o t o m u l t i p l i e r housing was covered w i t h both copper p l a t e and i r o n p l a t e f o r a d d i t i o n a l s h i e l d i n g . (13) The o s c i l l o s c o p e . A Tektronix model 7704A o s c i l l o s c o p e system was used f o r most of the experiments. This o s c i l l o s c o p e system was f i t t e d w i t h four p l u g - i n u n i t s comprising: a d i f f e r e n t i a l comparator ( 7A13 ) which can read the voltage d i f f e r e n c e of two s i g n a l s , a dual trace a m p l i f i e r ( 7A12 ), a dual time base ( 7B53A ) which was used i n delayed sweep and i n mixed sweep operation, and ordi n a r y time base ( 7B50 ). In the present experiments, a l l u n i t s except the time base ( 7B50 ) were used. The s p e c i f i c a t i o n of each u n i t except time base ( 7B50 ) i s b r i e f l y described, (a) The 7704-A o s c i l l o s c o p e system. The system i s composed of two i n d i v i d u a l u n i t s , the A7?Ol4-a c q u i s i t i o n u n i t and the D7704 d i s p l a y u n i t . The A??04 a c q u i s i t i o n u n i t has four p l u g - i n u n i t s . The l e f t p a i r of p l u g - i n u n i t s i s connected to the v e r t i c a l system; the r i g h t p a i r i s connected the - 57 -h o r i z o n t a l system. E l e c t r o n i c s w i t c h i n g between the pl u g - i n s connected to each system allows a dual - t r a c e v e r t i c a l d i s p l a y and / or a dual-sweep h o r i z o n t a l d i s p l a y . The D7704 d i s p l a y u n i t f e a t u r e s a cathode ray tube with small spot s i z e and high w r i t i n g r a t e . The cathode ray tube s i z e i s 8 x 10cm. (b) The d i f f e r e n t i a l comparator 7A13-This d i f f e r e n t a l comparator i s a v e r t i c a l p l u g - i n u n i t . D i f f e r e n t i a l measurements were made by applying s i g n a l s to the +INPUT and -INPUT connectors. Then, both input mode switches were set to the same p o s i t i o n : A.C. or D.C, depending on the method of s i g n a l coupling d e s i r e d . When using t h i s u n i t f o r d i f f e r e n t i a l o p e ration, only the voltage d i f f e r e n c e between the two s i g n a l s i s a m p l i f i e d and displa y e d . The dynamic range allows common-mode s i g n a l s up to +10 or -10 v o l t to be a p p l i e d to the u n i t without a t t e n u a t i o n . A common-mode r e j e c t i o n r a t i o of at l e a s t 20,000 : 1 at D.C. to 100kHz permits measurements of d i f f e r e n t i a l s i g n a l s l e s s then lmv i n amplitude on 10 v o l t common-mode s i g n a l s . (c) The dual trace a m p l i f i e r 7A12. This a m p l i f i e r i s a v e r t i c a l p l u g - i n u n i t and i s a dual-channel,wide band a m p l i f i e r with 105MHz of upper frequency l i m i t . For s i n g l e trace o p eration, e i t h e r of the two i d e n t i c a l a m p l i f i e r channels can be used independently by s e t t i n g the d i s p l a y mode and t r i g g e r source switches to CH-1 or CH-2, and the i n t e r n a l g a i n and compensation c i r c u i t s are a u t o m a t i c a l l y switched to correspond to the s e t t i n g of the V0LT/DIV switch. A -UP/lNV switch f o r each channel allows e i t h e r channel to be inv e r t e d f o r d e f f e r e n t i a l measurements. - 58 -(d) The dual time base 7 B 5 3 A . This time base i s a h o r i z o n t a l p l u g - i n u n i t and provides main, i n t e n s i f i e d , delayed, and mixed sweep oper a t i o n f o r the 7704A o s c i l l o s c o p e system. C a l i b r a t e d sweep r a t e s from 5 S/DIV to 5ns/DIV ( 5 nanoseconds with xlO m a g n i f i c a t i o n )'and t r i g g e r i n g to 100MHz are provided. Other f e a t u r e s i n c l u d e 0 to 10 times continuous sweep delay, v a r i a b l e main and delayed sweep r a t e s , and v a r i a b l e main sweep hold o f f . Separate t r i g g e r i n g c o n t r o l s are provided f o r main and delayed sweep t r i g g e r i n g , and when operating i n the auto main t r i g g e r i n g mode, a b r i g h t l i n e i s dis p l a y e d i n the absence of t r i g g e r s i g n a l . This u n i t can a l s o be used as an a m p l i f i e r f o r X-Y operation. (e) Operation. A t r i g g e r i n g s i g n a l generated by the I l l e x mechanical s h u t t e r was f i r s t used to open the s h u t t e r of the o s c i l l o s c o p e camera, and was then passed to the delay time c o n t r o l u n i t , causing one of delayed t r i g g e r outputs from the D5 delay c i r c u i t to t r i g g e r the o s c i l l o s c o p e . The mixed sweep c i r c u i t used to s e l e c t s t a b l e pulsed l i g h t t r a c e s of the xenon a r c ; the d u r a t i o n time of the mixed sweep was u s u a l l y about 600JUS, where the s e l e c t i o n of d u r a t i o n time depends on the s t a b i l i t y of the xenon pulsed l i g h t t r a c e s and the l i f e time of the t r a n s i e n t . In the study of t r a n s i e n t species of widely d i f f e r e n t h a l f l i v e s i t was necessary to use a much wider v a r i a t i o n i n the c h a r a c t e r i s t i c time f o r the time base than f o r the time delay c o n t r o l u n i t . A l l cables which lead to the o s c i l l o s c o p e were completely s h i e l d e d using s h i e l d i n g wire to prevent e l e c t r o n i c noise from the r a d i a t i o n emitted by the discharge of the - 59 -photoflash lamps. As a very f a s t time response was r e q u i r e d i n our experiments, the length of the cable between the p h o t o m u l t i p l i e r and the o s c i l l o s c o p e was made as short as po s s i b l e to reduce the cable capacitance. I n a d d i t i o n the time constant of the CR c i r c u i t was al s o r e q u i r e d to be as small as p o s s i b l e . A CR c i r c u i t g i v e s a g r e a t l y improved s i g n a l to noise r a t i o ; t h e r e f o r e a c a p a c i t o r i s u s u a l l y placed i n p a r a l l e l w i t h the load r e s i s t o r . The time constant of t h i s arrangement i s T = CR The CR c i r c u i t u s u a l l y comprised 10leu of load r e s i s t o r and 75pF of c a p a c i t o r to give a time constant of 0.75 >*s« Much lar g e values (eq, 3000pF ) were used f o r R0'2 decay T ~ 3 0 ys. (14) The camera and f i l m . O s c i l l o s c o p e t r a c e s were photographed by a Model C-53 o s c i l l o s c o p e camera ( Model C-50/C-70 s e r i e s ), w i t h a maximum aperture of f / 1 . 9 and a m a g n i f i c a t i o n of 1 : 0 . 8 5 , which was supplied by Tektronix Inc. The o p t i c a l system of the camera permits d i s p l a y s to be simultaneously viewed and photographed. The camera was operated with a shutter speed of sec, an aperture of f / 5 - 6 , and a f i l m speed of ASA3200. This camera i s a v e r s a t i l e e l e c t r o n i c camera and was operated by a remote c o n t r o l system. I t can be adapted to experiments of var i o u s kinds by using combinations of the four d i f f e r e n t modes, such as the normal, bulb, time, and s i n g l e sweep modes. when the mechanical shutter ( o p t i c a l a x i s s h u t t e r , 3X. I l l e x O p t i c a l Co ) was opened i t t r i g g e r e d a pulse to open the shutte r of the o s c i l l o s c o p e camera; t h i s pulse was then passed to the D5 delay c i r c u i t , causing one of delayed t r i g g e r outputs - 60 -to t r i g g e r the o s c i l l o s c o p e . A l l cables which lead to camera were sh i e l d e d using s h i e l d i n g wire to prevent them from p i c k i n g up the r a d i a t i o n generated by the discharge of the photofl a s h lamps, which would i n t e r f e r e w i t h the operation of the camera. " P o l a r o i d " Land r o l l f i l m ( black and white ) type 47, with a speed of ASA3000 was used f o r most of work, but only one p i c t u r e ( 8,5 x 10 .5cm ) could be recorded on each u n i t of f i l m . ( 1 5 ) The o p t i c a l s h u t t e r . An I l l e x 3X ( I l l e x O p t i c a l Co ) o p t i c a l shutter- was used. This shu t t e r was placed on the o p t i c a l a x i s and was mounted wit h the beam s p l i t t e r assembly on the xenon housing base w i t h a heavy weight made of s o l i d lead. The opening of the shu t t e r t r i g g e r e d a pulse which was used to s t a r t a l l the delayed pulses i n the delay c o n t r o l u n i t . The D5 c i r c u i t a l l o w o s c i l l o s c o p e camera open f u l l y before r e s t of sequences i n i t i a t e d . A l l c ables which lead to the shutter were a l s o s h i e l d e d completely to prevent the p i c k i n g up of e l e c t r i c a l noise. (16) The spectrometer. Most of work were done using a J a r r e l l Ash model 78-^ -20, Ebert Mounting Vacuum Scanning Spectrometer. This instrument i s a p r e c i s e , plane c i r c u l a r g r a t i n g , vacuum spectrometer, which i s capable of d i r e c t p h o t o e l e c t r i c measurement of - 61 -l i n e i n t e n s i t i e s . The 1.0 Meter Ebert Mounting, using a g r a t i n g w i t h Il8'0 grooves/mm, produces a spectrum from 1 6 0 to 1 3 0 0 n m , with a r e s o l u t i o n of O.Olnm at 310nm i n the f i r s t order, and a. r e c i p r o c a l l i n e a r d i s p e r s i o n of 0.82nm/mm. The g r a t i n g angle could be adjusted e l e c t r i c a l l y to give the d e s i r e d wavelength e x a c t l y , using the automatic scan d r i v e w i t h a gear change device. This method d i d not cover a wide range of the spectrum at one f l a s h , but gave i n f o r m a t i o n at one wavelength only. However, t h i s method was w e l l s u i t e d to the measurement of the v a r i a t i o n of absorbance with time at each of a s e r i e s of wavelengths, and ther e f o r e to k i n e t i c s t u d i e s . The p h o t o m u l t i p l i e r housing was s i t u a t e d behind the e x i t s l i t , and was equipped w i t h m i r r o r s which were i n c l i n e d at a 4 5 degree angle to the o p t i c a l a x i s to r e f l e c t the l i g h t i n t o the p h o t o m u l t i p l i e r s . ( 1 7 ) Wavelength c a l i b r a t i o n . The f i n e tuning of the wavelength scale of the J a r r e l l Ash model 78-420 spectrometer was performed wi t h a v e r n i e r d i a l made by the Departmental mechanical shop. The c a l i b r a t i o n of t h i s v e r n i e r d i a l was c a r r i e d out using the emission l i n e s from a hollow cathode lamp ( Westinghouse, max-current 12mA, Ne gas f i l l e d ) which contains Zn, Ag, Pb and Cd i n the cathode metal. Table-2.2 l i s t s the emission l i n e s used to c a l i b r a t e the v e r n i e r d i a l . Most of the absorption spectra of the t r a n s i e n t s of i n t e r e s t l i e w i t h i n the range from 210 to 340nm. - 62 - i Table-2.1 Emission l i n e s used f o r the c a l i b r a t i o n of the wavelength scale of the spectrometer Elements Zn Ag Pb Wavelength ( nm ) 213.856 307.590 328.289 328.068 217.000 283.307 228.802 326.106 - 63 -(18) The photographic d e t e c t i o n system. (a) The photof l a s h lamp. The ph o t o f l a s h lamp was made of " S u p r a s i l " quartz and was 50cm i n length w i t h an 8mm i n s i d e diameter and a w a l l t h i c k n e s s of 1.5mm. I t d i f f e r e d from the previous design i n the use of a mechanical switch i n s t e a d of an e l e c t r o n i c a l s h u t t e r connected with spark gap. One t e r m i n a l was connected to the high voltage lead of a c a p a c i t o r ( D u b i l i e r 33>3joF ) by a mechanical switch, while the other was connected to ground. A pressure of ? t 2 t o r r of argon was used, and the h a l f peak width of the f l a s h was about 7JOS. (b) The spectroscopic lamp. A Lyman tube provided the photographic f l a s h from which an absorption spectrum could be recorded ( see Figure-2.13 ). The f l a s h was t r i g g e r e d at any d e s i r e d delay time a f t e r the p h o t o l y s i s f l a s h , thus r e c o r d i n g the ab s o r p t i o n spectrum of the r e a c t i n g system at that p a r t i c u l a r period r e a c t i o n . This spectroscopic lamp gave a continous spectrum with some s i l i c a a b s o r p t i o n and emission l i n e s on the back ground. The s i l i c a a b sorption and emission l i n e s can be used f o r the c a l i b r a t i o n of wavelength f o r the spectra. The discharge through the lamp was d i r e c t e d along a 5cm length of c a p i l l a r y quartz tubing which was o p t i c a l l y a l i g n e d with the r e a c t i o n v e s s e l and spectrograph. The l i g h t focussed down the r e a c t i o n v e s s e l onto the s l i t of the spectrograph. Argon at a pressure of 40 ± 10 t o r r was introduced i n t o the evacuated Lyman tube. The h a l f peak width f o r the lamp discharge was 2us. The el e c t r o d e s were made of tungsten, and were s o f t gure-2.13 The f l a s h p h o t o l y s i s apparatus with photographic d e t e c t i o n A : P h o t o l y s i s Lamp B : Reaction Vessel C : Brass Container D : C o l l i m a t o r Lens E : Focussing Lens F : Jarre1 Ash Spectrograph^ 3-4m) G : Tungsten E l e c t r o d e H : Spectroscopic Lamp Il»i2 : 2 / i F and 33-3/JF Capacitor r e s p e c t i v e l y J : E l e c t r o n i c Delay Unit K : Resistance L : Hydrogen Thyratron M : Induction C o i l Pick-up N : High Voltage Switch 0 : Reaction Mixture I n l e t P : Argon Gas I n l e t - 65 -soldered i n t o s t a i n l e s s s t e e l cones which were cemented wi t h black wax i n t o the B-10 sockets on the lamp. One t e r m i n a l was connected to the high voltage lead of the ca p a c i t o r ( D u b i l i e r 2.0yiF ) while the other was grounded through a t h y r a t r o n . When the t h y r a t r o n was t r i g g e r e d i t became conducting and allowed the lamp to f i r e . (c) The r e a c t i o n v e s s e l s . Most of work was done using a " Pyrex " r e a c t i o n v e s s e l which was 47cm i n length with an i n s i d e diameter of 20mm and a w a l l t h i c n e s s of 1mm. The quartz r e a c t i o n v e s s e l , made of " S u p r a s i l " quartz from Englehard I n d u s t r i e s , was n e c e s s a r i l y used when mercury dimethyl was used as a source of methyl r a d i c a l s . The design of the quartz r e a c t i o n v e s s e l was the same as that of the " Pyrex " r e a c t i o n v e s s e l . (d) The spectrograph . A J a r r e l l Ash 3'4m, Ebert Mounting g r a t i n g spectrograph, was used f o r photographic d e t e c t i o n . The 3«4m Ebert Mounting, usi n g a g r a t i n g w i t h 15000 grooves/inch, produces a high i n t e n s i t y spectrum i n the range 210 to 470nm i n the f i r s t order, with a r e c i p r o c a l l i n e a r d i s p e r s i o n of 0.51nm/mm. The e n t i r e s p e c t r a l range of t h i s spectrograph- was from 200 to 300°nm and the d e s i r e d wavelength r e g i o n could e a s i l y be obtained by changing the g r a t i n g i t s e l f and the g r a t i n g angle. A r a c k i n g mechanism allowed the photographic p l a t e to be advanced, exposing a f r e s h s t r i p of the p l a t e f o r each exposure. T y p i c a l l y , around 20 to 30 exposures were taken per p l a t e , depending on the s t r i p height. Although a number of b a f f l e s v/as used, s t r a y l i g h t and sc a t t e r e d l i g h t s t i l l entered and - 66 -i n t e r f e r e d with the spectrum, the seriousness of t h i s i n t e r f e r e n c e depending upon the wavelength r e g i o n observed. Therefore as the tra c e of abs o r p t i o n spectrum was drawn by using a microphotodensitometer (Model MK C, Joyce, Loebl & Co L t d ) , the i n t e r f e r i n g l i g h t had to be considered as a background i n each exposure s t r i p , and an appropriate c o r r e c t i o n was made, (e) Photographic p l a t e and p l a t e processing. I l f o r d p l a t e HP-3 ( Hypersensitive panchromatic p l a t e , 10.2 x 25.4cm ) was used f o r the photographic d e t e c t i o n system f o r the measurement at wavelength before 230 nm, the surface of HP-3 p l a t e was coated with sodium s a l i c y l a t e , which i s one of the common p h o t o s e n s i t i z e r s . A saturated s o l u t i o n of sodium s a l i c y l a t e i n methanol was used to deposit t h i s c oating onto the p l a t e . A standard procedure was adopted f o r the processing of the photographic p l a t e s to ensure that the r e s u l t s would be re p r o d u c i b l e . Aqueous s o l u t i o n s of Kodak D-19 Developer and of Kodak Rapid F i x e r were used to process the p l a t e s , and were prepared by the normal procedure. A exposed p l a t e was f i r s t immersed i n the developer s o l u t i o n f o r 5 minutes, w i t h constant a g i t a t i o n of the s o l u t i o n . Secondly, the plate was immersed i n d i l u t e a c e t i c a c i d ( about 1 or 2% ) f o r 2 minutes to i n h i b i t f u r t h e r development. T h i r d l y , the pl a t e was immersed i n the f i x e r s o l u t i o n f o r 3 minutes. The temperature of each s o l u t i o n was kept w i t h i n the range 18 to 20°C during the processing of the p l a t e . F i n a l l y the developed p l a t e was washed i n a stream of cl e a n c o l d water ( at about 15 ~ 20 °C ) f o r 20 —-30 minutes, and was d r i e d i n a stream of d r i e d a i r . - 67 -( f ) Wavelength c a l i b r a t i o n . A method to c a l i b r a t e the photographic was needed i n order to c h a r a c t e r i z e the absorption of a t r a n s i e n t species. Many absorption and emission l i n e s of SiO and Si02 are found i n the continuum of the spectroscopic f l a s h lamp, and these were mainly used f o r the range from 2 0 0 to 3 2 0 n m . (19) M a t e r i a l s and p u r i f i c a t i o n . (a) Azoalkanes Azomethane and azoethane, which were obtained from Merck Sharp, and Dohme ( Canada ) L t d , were used as cl e a n sources of the methyl r a d i c a l and of the e t h y l r a d i c a l , r e s p e c t i v e l y . Each azoalkane was proved by vapor-phase chromatography to be pure except f o r t r a c e s of n i t r o g e n , methane, ethane, and butane, which were removed by exhaustive degassing i n freeze-thaw c y c l e s . When f u r t h e r p u r i f i c a t i o n was needed, these azocompounds were p u r i f i e d by repeated bulb d i s t i l l a t i o n i n the vacuum l i n e system using d i f f e r e n t temperature baths, and were c a r e f u l l y f reed from contaminating water passing them e i t h e r through a P2O5 t r a p or through a t r a p c o n t a i n i n g potassium evaporated on the g l a s s w a l l s (b) I n e r t gases. Argon gas and n i t r o g e n gas, each of 99-9995% p u r i t y , and carbon d i o x i d e ( 99.995% pure ), were obtained from the Matheson Company arid were used as d i l u e n t s without f u r t h e r p u r i f i c a t i o n . n-Pentane was used as an organic i n e r t gas and was obtained from the Matheson Coleman and B e l l Manufacturing Chemist ( M.C.B. ), but was only 98% pure. Therefore n-pentane was p u r i f i e d by two - 68 -successive d i s t i l l a t i o n s ; the f i r s t w i t h a 50cm long packed d i s t i l l a t i o n tower, and second w i t h a lm long packed d i s t i l l a t i o n tower i n a stream of n i t r o g e n gas. A n a l y s i s of i m p u r i t i e s i n p u r i f i e d n-pentane was done by gas chromatography. P u r i f i e d n-pentane was stored over d r i e d " Molecular Sieve 4A " ( F i s h e r S c i e n t i f i c Company ), a m a t e r i a l having 4A holes. (c) Reactants. Oxygen ( 99'9995% pure. Matheson Company ) was used as a reactant without f u r t h e r p u r i f i c a t i o n . Acetone, which v/as of spectrophotometric grade ( 99.95% pure ) from M.C.B. chemists, was used as a source of the a c e t y l r a d i c a l without f u r t h e r p u r i f i c a t i o n . Acetone-d^ (D atom 100%, 99-% pure, from the A l d r i c h Chemical Co ) was used as a source of the CD3 r a d i c a l without f u r t h e r p u r i f i c a t i o n . Methyl e t h y l ketone ( a n a l y t i c a l reagent 99-9~% pure, from the M a l l i n c k r o d t Chemical Works ) was a l s o used as a source of the a c e t y l r a d i c a l without f u r t h e r p u r i f i c a t i o n . B i a c e t y l was obtained from the F i s h e r S c i e n t i f i c Company and was p u r i f i e d two successive d i s t i l l a t i o n s ; the f i r s t by a conventional d i s t i l l a t i o n method i n a stream of n i t r g e n gas, and the second at 20torr pressure using 30cm long packed d i s t i l l a t i o n tower i n a stream of n i t r o g e n gas. The r e s i d u a l water i n the p u r i f i e d b i a c e t y l was removed by d r i e d " Molecular Sieve 3A ". The p u r i f i e d b i a c e t y l was analyzed by gas chromatography, and by IR and MR spectroscopy. Figures-2.14, 2.15 and 2.16 are t y p i c a l of the r e s u l t s of such a n a l y s i s . In the gas chromatography a n a l y s i s ( see F i g u r e - 2 . l 4 ), e t h y l ether v/as used as a d i l u e n t and solvent of b i a c e t y l , and an - 69 -OV-210 ( 5$ ) column which was coated polyethylene g l y c o l as a l i q u i d phase was used. The r e s u l t shows that b i a c e t y l was almost completely pure. The i n f r a r e d spectrum of b i a c e t y l i s shown i n Figure-2.15- The IR spectrum shows four t y p i c a l a b s o r p t i o n bands of b i a c e t y l . The f i r s t intense band at 1120cm''" represents the antisymmetric v i b r a t i o n of C-C-C group, and the second and f o u r t h bands, at 1360cm"1' and 1430cm1" r e p e c t i v e l y , represent the bending v i b r a t i o n of CH 3 groups, while the C-0 s t r e t c h i n g band appears at 1720cm"1" as the t h i r d band. The MR spectrum of b i a c e t y l ( see Figure-2.l6 ) shows only one peak which corresponds to -CO-CH3. The NMR spectrum of b i a c e t y l i s s i m i l a r to that of acetone, as both molecules c o n t a i n t h i s group. Figure-2.14 The a n a l y s i s of p u r i f i e d b i a c e t y l by gas chromatography ^3 O If tS li'.' i i " r-1>J 01 B O D if. ra IT- If • f - If' OJ W Oi 7 E a l l . I i i E • r- r-EJ IT' CI «" 13 El • (•J l \ . i I 1' •-. il I- it In I- l u fi-l l f-i i i I- I r - r -- I 0" —i * • '£ 2 Ui i i ix. u r-.i I." n, ii U </> -' l l i j 2 i - i i -I I t^ . u U* O C I- • . . J I ..- Ii .-I Ii Ii l T . I» ' i i - 'i i i u c-If u.ij.-.i CO a • a a (S LU tf: (t -IT S) r- LU a £ j u* 1— . r CO F i g u r e - 2 . 1 5 The i n f r a r e d spectrum of p u r i f i e d b i a c e t y l Figure-2.16 The MR spectrum of p u r i f i e d b i a c e t y l 7.0 6 ^ 5J0 »»<» 4.0 — — 3j0. — — J O 1 1 1 ' 1 1 1 1 I I I I 8 0 7.0 1 1 1 ' 1 1 1 F' 1 • I I I 0 Hi 1.0 J—I I I ^0 - 73 -CHAPTER 3 MUTUAL COMBINATION OF METHYL RADICALS A, Introduction (1) Absorption spectrum of the methyl radical The resonance transitions of almost a l l known diatomic and polyatomic radicals l i e in the visible and near ultraviolet ( 20-23 )• Accordingly, the f i r s t attempts to find a spectrum of the methyl radical ( CEy ) were made in this region; indeed since C E j has the same number of electrons as NH2 ( 24 ), which does exhibit a strong spectrum in the red, i t appeared l i k e l y that C E j would have a transition in this region. The failure of these attempts, however, caused a reconsideration of the theory. From molecular orbital theory one does indeed expect a transition of CH^ in the visible region corresponding to that of NH2; but i f CH^ were planar and symmetrical this transition would be forbidden, the selection rules being much more restrictive for a molecule of point group D^n than for one of point group C2v» It was for this reason that an attempt was made to find a - 74 -Rydberg spectrum of CH^ in the vacuum ultaviolet. For this purpose a flash photolysis apparatus as f i r s t described by Norrish and Porter in 1949 ( 14 ) was used. Herzberg and Shoosmith characterized the absorption spectra of the CH^ and CD^ radicals in 1956, and f i t t e d a Rydberg series to each set of data ( 23 ). In the I n i t i a l study Hg(CH 3) 2 was used as the photolytic source of the methyl radical. The assignment of the observed spectrum to the methyl radical was supported by the results of experiments with CH3N2CH3, CH^ CHO, (CH^CO, CH^I and CH^Cl as radical sources. The same bands were observed in each case, except when the absorption was obscured by the absorption of the parent compound. The assignment was confirmed when the limi t of the Rydberg series was determined to be equivalent to 9.843 ev, which i s in good agreement with the value of the ionization energy of the methyl radical determined by mass spectrometry ( 25 )• A f u l l account of the characterization of the spectrum of the methyl radical, and a discussion of Its' structure was given by Herzberg in 1961. He concluded that the methyl radical in the ground state, ckz » had been shown to be planar or nearly planar with a CH distance of 1.08 A ( and therefore with a HCH bond angle equal or close to 120° ). Both the ground state and the observed excited states were shown to be consistent with elementary molecular orbital theory. Herzberg anticipated the application of the absorption in the 216 nm band to the kinetic study of methyl radical reactions, and resolved two maxima at 215.76 and 216.36 nm respectively. The absorption spectrum of the methyl radical in the gas - 75 -phase has also been observed by the pulse radiolysis of methane gas. Bosnali and Pernor ( 26 ) confirmed the positions of the two maxima in the 216 nm band using 1 atm of methane. Hickel (2b) used 30 atm of methane and obtained a complete absolute absorption spectrum between 212 and 219 nm, but failed to resolve the double peak. The spectrum, reproduced from Figure-2 of his paper, is shown as Figure-3.1. The value of the extinction coefficient at 3 -1 -1 the maximum is only 2.4 x 10"^ 1 mole cm , one quarter of the 4 -1 -1 accepted value of 1.0 x 10 1 mole cm obtained by Basco, James and Suart in 1971* and supported by Callear and Metcalfe in a review of values in 1976 ( 27 )• The positions of maxima i n the aqueous phase and gaseous phase are remarkably close. The plotting of the absolute absorption spectrum of the methyl radical from 215.8 to 216.4 nm has accordingly been undertaken in this work to supplement the data reported above. (2) The measurement of the rate constant for mutual combination  (a) An assessment of published work The characterization of the absorption spectrum of the methyl radical near 216 nm, which i s the band of the B 2 A J - X 2 A 2 transition, has provided the basis of the experimental method used for kinetic measurements in most recent kinetic studies of the rapid reactions of the methyl radical. The concentration of the methyl radical was calculated from the corresponding absorbance in the ultraviolet region, and i t s variation with time was observed by the methods of kinetic spectroscopy. The principal experimental values of the rate constant for the mutual combination of methyl radicals ( k ) were discussed by Callear and Metcalfe In 1976 ( 27 ). These result are - 76 -Figure-3-1 Absorption spectrum of the methyl radical according to Hickel, 1975 ( 28 ) Wovltngth (nm) R p u r * I. Spectrum of Ihe methyl radical (+) gas phase P o u * 30 •ton; (O) water (this work); (A) water <ref 3); (11) position ot the B bands of O k j Irt pas phase at low pressure (ret 12). Figure-3.2 Values of the rate constant for the mutual combination of methyl radicals mn &w. &rp mall -r 1 ' OH, mjwtMtlKn •V*/oK,HBMc",t" F j | 6. Tabulation or jpectroscopicall) determined rate coef-ficient* forCHj recombination. The width of each rectangle fc 2 ftandard deviations, and they hive • common area. - 77 -Table-3-1 Experimental values of the rate constant for the mutual combination of methyl radicals Measuement technique Temp 10- 1 0 k Ref. • K 1 mole-'1" s e c - 1 Rotating sector 398 - 408 2.41 29 406 3.2 t 0.3 30 Pulsed photolysis 407 2.35 31 Flash photolysis and 293 2.43 • 0.24 32 kinetic spectroscopy 298 2.6 t 0.3 (at 216.4 nm) 33 298 4.22 34 298 5.74 1 0.71 (at 150.4 nm) 35 298 5.72 (at 216.0 nm) 36 293 3.37 i 0.46 (at 216.4 nm) 37 295 3.17 i 0.38 27 This work 298 3.ia 2 0.50 (at 216.4 nm) Molecular modulation 298 1.81 38 spectroscopy 298 2.41 39 Flash photolysis and 313 2.4 • 0.18 40 mass spectroscopy - ?8 -l i s t e d with references in Table-3.1, and a clear insight into the measure of agreement between them is given by Figure-3.2, which i s adapted from Figure-6 of reference ( 27 ). The majority of the results l i e around 3 x 1 0 1 0 1 mole1 sec 1, and the group includes both recent values measured at high methyl radical concentrations, and earlier values measured at low methyl radical concentration by the rotating sector technique. The sole deviant result i s due to Bass and Laufer who obtained the much higher value of ( 5.7 - 0.7 ) x 1 0 1 0 1 mole1 sec 1 ( 35 )» using the method of flash photolysis and kinetic spectroscopy. (b) The previous work in this laboratory. The mutual combination of methyl radicals has already been studied in our group by kinetic spectroscopy; the decay of the absorbance of the methyl radical at 216.4 nm was recorded photographically and followed by plate densitometry ( 33 )• The value of ( 2.6 + 0.3 ) x 1 0 1 0 1 mole1 sec 1 is in broad agreement with the majority of results in Table-3»1» However, two of these results are based upon a modified form of the Beer-Lambert Law for the absorbance of the methyl radical, whereas the remainder have been calculated using the simple form of the law. Accordingly, a new investigation, employing an improved exerimental technique, was undertaken in an attempt to resolve such discrepancies. - 79 -B, Experimental. (1) Apparatus. The new investigation employed the new detection system, incorporating the pulsed xenon arc, dual beam system and balanced photomultipliers described in Section C of Chapter 2. The reaction vessel and reference vessel were both illuminated by the photoflash, which generated methyl radicals only in the reaction vessel. An intense pulse of analyzing light from the xenon arc was collimated and then s p l i t into two beams of almost equal intensity by the beam sp l i t t e r . Each beam was passed along the axis of one of the vessels; the beam energing from the reaction vessel was relatively attenuated at 216.4 nm by the methyl radicals present in that vessel. The difference in the absorbance of the two vessels at 216.4 nm was monitored by the balanced photomultipliers. The concentration of the methyl radicals was calculated from the absorbance at 216.4 nm using the simple Beer-Lambert relationship : Each estimate of the absolute value of <=^^ was derived from the measured value of the yield of the stable products ethane and nitrogen and the corresponding extrapolated value of the absorbance that would have been observed i f a l l the methyl radicals generated by the flash had been simultaneously present In the reaction vessel. The method of extrapolation w i l l be described later. The va l i d i t y of the simple relationship has been challenged ( 37»4l ) but we shall present evidence later - 80 -that the law is valid when a band pass of 0.6 to 0.16 nm centred on 216.4 nm i s used under normal operating conditions in the present apparatus. (2) Method. (a) General principles. The mutual combination of methyl radicals i s a reaction of the second order, and has been studied by following the deoay of the absorbance A(X) of the methyl radicals at chosen wavelength A. It w i l l be shown later that the kinetic analysis of the results yields a value for the ratio k/£(A)» where E(A) i s the value of the extinction cofficient at the wavelength A. If a set of experiments i s performed at a series of values of A, and the resulting values of £(A)/k are plotted against A, the graph w i l l represent an absorption spectrum of the methyl radical plotted in arbitary units. Absolute values of E(A) can be obtained from the relationship A(A) = E(A) [ C H 3 ] 1 i f a method can be found to determine the absolute value of the concentration of methyl radicals [CH3] • It w i l l be shown later that such a method may be based upon an estimation of the yield of the stable products, ethane and nitrogen. Clearly, i f both k/£(A) and £(A) are measured for a single reacting system, the value of k i s obtained from their product. A detailed account of each measurement follows. (b) The measurement of k/£(A). The statement that the combination of methyl radicals is of the second order may be represented by the equation: and, i f C i s : - dC / dt = 2 k C 2 = Co when t » 0, the integrated form of this equation 1 / C - 1 / C 0 = 2 k t Consider a vessel of optical length 1 containing a set of absorbing species i , each having an extinction coefficient £(A) at the wavelength A. Then the simple Beer-Lambert Law relates the absorbance A(A) of the species to the concentrations according to the equations : If the methyl radical i s the only absorbing species, the rate equation becomes: so that a plot of 1 / A(A) against time should be linear, with a gradient equal to 2k / 6(A) 1 • The method of least squares was used to f i t a straight line to a set of data and to evaluate the value of k / £(A) and Its standard deviation. A (A) = l o g 1 0 I 0(A) / I (A) = £ C± 1 1 / C = E(A) 1 / A( A) = 1 / C 0 + 2 k t A (A) E(A)Col I E(A) 3 — 1 . J l i i - 82 -(c) The measurement of the extinction coefficient, £» Each estimate of the absolute value of E was derived from the measured value of the yield of the stable products ethane and nitrogen and the corresponding extrapolated value of the extr absorbance Ao© that would have been observed i f a l l the methyl radicals generated by the flash had been simultaneously present in the reaction vessel at concentration C0• Since, AB£tT = E.Co.l, i t follows that, £ = A**** / Col. The extinction coefficient can therefore be evaluated i f both C0 and extr Aoo can be estimated. The estimation of Co i s based upon f i n a l product analysis. Let n(N 2) and n(C 2H£) b e t h e t o t a l molar yields of nitrogen and ethane repectively, then Co = {n(N 2) + n(C2H£)} / V where V i s the illuminated volume of the reaction c e l l . The stoichiometry of the photodecomposition of azomethane gives n(N2) = n(C2H6) when metathetical reactions are negligible, so that Co = 2n(N2) / V. The product nitrogen was isolated by condensing the remaining constituents of the reaction mixture after photolysis in a series of traps immersed in l i q u i d nitrogen which was further cooled by a stream of precooled helium gas. This nitrogen was transferred to a calibrated volume Vo at a known temperature To» the nitrogen pressure P0 was measured with a McLeod gauge, the number of moles of nitrogen was calculated by the gas equation t n(N 2) » PeVo / RT, and Co was obtained from the equation above • The principle underlying the estimation of the total extrapolated absorbance i s illustrated by Figure-3.3. The solid line represents the observed absorbance A t. This - 8 3 -increases from zero upon the f i r i n g of the photoflash, passes through a maximum Just after the intensity of the photoflash passes though i t s maximum, and thereafter declines as the rate of consumption of methyl radicals by mutual combination exceeds the rate of generation by the flash. If the consumption of methyl radicals could be neglected, the absorbance would follow the broken curve, increasing continually towards an asymptotic limi t equal to A « > . This limit i s effectively achieved within 2? usee after the f i r i n g of the photoflash. The trace of the photoflash output shows that 9 8 % of the light was emitted in the f i r s t 2k y^sec, and beyond this delay the second-order plot of the methyl radical absorbance was always linear. A computer programme was written to simulate the generation of the methyl radical by the photoflash, and revealed that generation was 99 % complete after 27 jxsec. It i s convenient to define the partial extrapolated value extr of the absorbance at a time t, A T , as the absorbance that would have been observed i f a l l the methyl radicals generated by the flash up to the time t had been simultaneously present in the reaction vessel. Clearly, the broken curve represents extr the partial extrapolated absorbance At with i t s asymptotic extr limiting value of A ^ 0 • The value of the partial extrapolated , extr absorbance after 16 jjsec, , i s also shown in the Figure. The difference between the partial extrapolated absorbance and the observed absorbance is represented by AA t = A t - A^, and the values of AA^£ and A A ^ Q are shown in the Figure. The estimation of AAX. i s clearly an essential process in the evaluation of the extinction coefficient, and w i l l be - 84 -described next* First, the region of the absorbance curve between 0 and 60 jasec was divided into four-microsecond Intervals, and the mean absorbance, <A^ > , was calculated for each Interval from the smoothed curve. The decrease in absorbance due to mutual combination during the interval i i s given to a good approximation by: = At ( -dA / dt ) = 4 x 10 6 <A1>2 G where G = d(l/A) / dt is the gradient of the second-order plot for the mutual combination of methyl radicals during the dark period after the photoflash. Consequently, the total decrease in absorbance due to mutual combination during the 60 jjsec period following the f i r i n g of the photoflash was obtained by summation over the 15 4-psec intervals: * A 6 o = i f UL = 4 x l o V ^ < A . V 1=1 i=l x 1 ' Finally, the total extrapolated absorbance at 60 usee was obtained from the equation: extr 15 . A A 6 0 = A60 + A A60 = A60 + ^ t> Ai where A^ Q i s the observed absorbance at 60jjsec. Each partial extrapolated value of the absorbance can be calculated from the corresponding partial summation: .extr . . . 1. A t = A t + A A t 3 5 A t + fa <>Ai - 85 -Figure-3.3 A diagram i l l u s t r a t i n g the extrapolation of absorbance CP o c o X ! 3 < •-*>--{J--0--0--o- _D C _ _ .extr ^ 0 " Amax * .extr s A16 A 4 A A ^ Z S A 0 k 8 12 16 20 24 Time ( jjsec) The solid line represents the observed absorbance At, and the broken line represents the extrapolated value A| x^ r of the absorbance, defined by the equation: .extr A t * A A T = A t 1=1 1 Two values of A ^ are illustrated: (i) when t = 60 usee ax = A 6 0 t r = A 6 0 * A A 6 0 = A 6 0 • h A . i=l 1 ( i i ) when t = 16 jAsec ( on the shoulder of the curve ) Aextr * j. A.A A A 1 6 s A 1 6 + * A l 6 * A 1 6 i=l 1 Note i This diagram has been distorted to show the details clearly. - 86 -extr extr The evaluation of the and Aj^ i s illustrated in Pigure-3.3. The total extrapolated absorbance A| J t r is called the maximum absorbance A g ^ for brevity in the following pages, - 87 -C. Results and Discussion. (1) The values of k/£(7Q and of £(>Q measured at 216.4 nm. The experimental results are shown in Table-3.2. The value of k/£(X) was measured at the absorption maximum at 216.4 nm . Our new value i s : k/E(2l6.4) « ( 3 . 3 i 0 . 5 ) x 10^ cm sec 1, and is based upon 24 results from 33 measurements. In addition our new value of the extinction coefficient of the methyl radical i s : £(216.4) - ( 9 . 5 t 0.4 ) x lO^ l mole1 cm1 at 216.4 nm, and i s based upon 33 measurements. This i s in excellent agreement with the results reviewed by Callear and Metcalfe, which range from 9.6 x 10 3 to 1.02 x 10^ 1 mole1 cm1 ( 2? ). Using this value of the extinction coefficient, the rate constant of the mutual combination of methyl radical was calculated to be ( 3»l4 t 0 .51 ) x 10 1 0 1 mole1 sec 1, which i s also based upon 33 measurements. The value for the rate constant f a l l s into the middle of " low " values in Table - 3 . 1 and Flgure - 3 . 2 , supporting them against the M high w value of Bass and Laufer ( 35 ) . Remarkable good agreement is observed between our value and the value of ( 3 . 3 7 t 0.46 ) x 10 1 0 1 mole1 sec 1 reported by James and Simons. It may be argued that the significance of this agreement is diminished as these authors expressed the absorbance of the methyl radical in the form A = E ( C 1 ) 0 * ^ , whereas the present results were calculated using the relationship A = £ C 1 . However, i t is more probable that each relationship i s appropriate for the respective apparatus, that the difference in the values of the exponent i s irrelevant as i t s effect vanishes by a self-cancelling process in the calculation, and therefore - 88 -Table - 3 . 2 Values of k / e ( 2 l 6 . 4 ) and k measured for the mutual combination of methyl radicals at 2 1 6 . 4 nm Photoflash energy i 360 J ( 12 kV, 2 . 5 J J F ) Exp No. Mixture CH-j / one flash S^nax i o - 3 E at 216.4 nm 1 mole^cm - 1 10 - 6 k/6 at 216.4 nm cm sec -* IO" 1 0 k 1 mole'^sec-'1' H-112-A 0.226 9-93 3.^ 5 3-42 Me2N2 « n-C^H^g 0.204 8.96 3.50 3.14 = 2.7 « 120 0.193 8.4« 3.28 2.78 [CH.j3 = 2.5xl0"7 K 0.211 9.27 3-85 3-57 0.218 9-58 3.71 3.55 0.212 9.31 3-80 3.54 H-115-A 0.267 9.72 3.25 3.16 Me2N2 » n - C 5 ^ l 2 0.272 9.91 3-23 3.20 « 3-0 « 33 0.256 9.32 2.53 2.35 [CH3]= 3-OxlO"7 M 0.276 10.05 4.00 4.02 0.262 9.54 3.05 2.91 0.284 10.34 3-77 3.90 0.242 8.81 2.14 1.89 * 0.258 9.40 3.35 3.15 0.264 9.61 3.24 3-11 0.264 9-61 3-14 3.02 0.271 9-87 3.38 3.34 0.272 9.91 3-76 3.72 continued - 59 -H-116-A 0,270 9-36 3.57 3.34 Me2N2 i n-C^H12 0.265 9.16 3.69 3-39 = 3-0 : 42 0.257 8.91 2.60 2.32 CH3]= 3 . 1 X 1 0 " 7 11 0.279 9.67 3.23 3.13 0.267 9.25 2.61 2.41 0.264 9.15 3.24 2.97 Mean values » k/£(2l6.4) = ( 3.3 ± 0.5 ) x 10 6 cm sec' 1 of 24 measurements above, E(216.4) = ( 9.5 ± 0.4 ) x 10 3 1 mole^cm" 1 of 33 measurements, and k = ( 3.18 ± O.50 ) x 10 1 0 1 mole" 1sec" 1 of 32 measurements. Note 1 (1 ) The concentration of azomethane at time 0. Exp No. [Me 2N 2 ]t-0 m o l e 1 " 1 H-112-A 1.47 x 10"^ H-115-A 1.64 x 10 - 4 H-116-A 1.64 x 10"^ (2) The band pass i s 0.06 nm (3) [CH 3]« C 0 = A B a x /£(A) 1 (4) * this value was neglected - 90 -that comparison of the two results Is valid and the agreement is significant. Accordingly we may conclude that the values of k 2 & a^ L £ ( 2 1 6 . 4 ) found in this work are in f u l l agreement with the most preoise literature values. ( 2 ) The absorption spectrum of the methyl radical in the range  from 215 to 217 nm. In the preliminary survey of the absorption spectrum of a transient species by the photoelectric detection system, the value of £(X)/k ( which i s the reciprocal of the value of k/E(A) given by the second-order procedure of data analysis ) i s used to trace the absorption spectrum of the transient species when the concentration of the transient species i s not known. A plot of the value of £(?0/k against wavelength represents the absorption spectrum of the transient species in arbltary units. The values of £(X)/k at different wavelengths are shown in Table - 3 . 3 , and the absorption spectrum of the methyl radical obtained by this method i s shown in Figure - 3 . 4 . In addition, a microphotodensitometer trace of the absorption of the methyl radical by the photographic detection system is shown in Figure-3 . 5 . The exposure of each successive strip follows a single time sequence. The calibration of the spectra was done by using the absorption lines of s i l i c a . The relative absorption spectrum of the methyl radical i s represented in complementary ways by the values of e(X)/k in Figure - 3 . 4 and by the trace of Figure - 3 . 5 . Both spectra show resolved maxima at wavelengths close to the values of 2 1 5 . 7 6 and - 91 -Table - 3 . 3 Values of £(A)/k at different wavelengths Photoflash energy i 360 J ( 12 kV, 2.5 uP) Exp No. « H-104-A Wavelength 10"6 k/£(A) 107 E(A)/k 10 - 3 &(A) nm cm sec -* sec cm-* 1 mole"* cm-* 215.2 7.98 1.25 4.31 a 3.93 b 215.4 8.66 1.15 3-97 3.62 215.6 6.98 1.43 4.93 4.50 215-7 4.01 2.49 8.57 7.83 215.8 3.72 2.69 9.25 8.44 215.9 3.43 2.92 10.03 9.16 216.0 3-37 2.97 10.20 9.31 216.1 3.94 2.54 8.74 7.98 216.2 3.72 2.69 9.25 8.44 216.3 3-^ 6 2.89 9.94 9.08 216.4 3-62 2.76 9.50 8.67 216.5 3.82 2.62 9.01 8.22 216.6 5.31 1.88 6.48 5.92 216.8 6.98 1.43 4.93 4.50 217.0 10.00 1.00 3.44 3.14 Note i (a) normalized to give E(2l6.4) = 9.5 x 10-5 1 mole" cm by multiplying each value of £/k by 3-44 x 10*° 1 mole"* s e c - 1 , (b) normalized by multiplying each value of by 3.18 x 10*° 1 mole -* sec -*, the experimental value of k given i n Table-3.2. - 92 -Pigure-3.4 Absorption spectrum of methyl radical by photoelectric detection •E o o <D LU O 15 ^ 10 215 216 217 A ( n m ) 218 0 •E o o E uu CO I o Note : the l e f t hand ordinate gives the values of 6(A)A derived from the second order ploti the right hand ordinate gives the corresponding absolute values of £(A) • - 93 -Figure-3•5 Absorption spectrum of methyl radical by photographic detection and the corre sponding microphotodensitometer trace _ 94 -2 1 6 . 3 6 nm found by Herzberg ( 42 ). The absolute absorption spectrum may be obtained by a normalization procedure corresponding to reading the right hand ordinate in Figure-3 . 4 . The simplest normalization procedure i s to multiply each value of E(A)A in Table - 3 . 3 by the experimental value k = 3.18 x 1 0 1 0 1 mole1 sec 1 quoted in Section C . l . An alternative procedure yields £= 9 . 5 x 10J 1 mole cm at 2 1 6 . 4 nm in agreement with the result quoted in Section C.l and requires a factor of 3 . 4 4 x 1 0 1 0 1 mole1 sec 1. The results of both procedures are l i s t e d in Table - 3 . 3 . The lat t e r procedure was adopted for the absolute spectrum of Figure - 3 . 4 . The absolute absorption spectrum shown in Figure - 3 . 4 i s quailtatitively and quantitatively supported by established work, and extends our knowledge of the spectrum appreciably. - 95 -D, Appendix; The Validity of the Beer-Lambert Law for Methyl Radical Absorption (1) Introduction The value of the rate constant for mutual combination of methyl radicals, and associated results presented in Section C of this Chapter, are calculated on the assumption that the absorbance of the methyl radical i s directly proportional to the product [CH^] 1, where 1 i s the optical path length; this assumption is the basis of the Beer-Lambert Law. Simons and coworkers have recently published two related studies of fast reactions of methyl radicals by kinetic spectroscopy (37»41). In each of these studies they used a band pass of 0.2 nm in order to obtain an adequate signal to noise ratio for the measurement of the absorbance of the methyl radical. For a f i n i t e band pass, they suggested that the Beer-Lambert Law should be modified to make the absorbance of the methyl radical proportional to the expressioni { [CH3] 1 } ° where the exponent n would depend upon the particular experimental conditions. This proposal implies that n should be measured afresh for every new system. They measured the exponent n by the variable path length method, and reported that n = 0.?2 t 0.07 for one set of experiments ( 41 ) , and that n = 0.59 ± 0.04 for another set ( 37 )• The difference between their values of n is not significant, which Is consistent - 96 -with the authors' statement that the baslo apparatus, the partial pressures of azomethane and argon, the energy of the photoflash, and the band pass were the same for both sets of experiments ( 37 )• The simple form of the Beer-Lambert Law corresponds to the value n =» 1 , and the deviation of n from unity for either of the sets of results i s too great to be dismissed without further investigation. Accordingly the new double beam kinetic spectrophotometer described in Chapter 2 was employed to determine the value of the exponent n under the experimental conditions used to determine the value of the rate constant for mutual combination of methyl radicals. Two distinct methods were used. In one method the effect of changing the band pass from 0 . 0 6 nm to 0 . 1 6 nm was observed. In the other method the effect of masking one half of the illuminated length of the reaction vessels with symmetrically placed sets of cylindrical masks of equal length was observed for several values of mask length. A l l experiments were carried out in " Pyrex '* reaction vessels, and a double gas f i l t e r containing C l 2 and Br 2 was placed between the reaction vessels and the spectrograph to prevent scattered li g h t from entering the spectrograph. Azomethane was used as the source of methyl radicals, and argon gas, carbon dioxide, and n-pentane gas were used successively as inert gases. The purification of these gases has been described in Chapter-2, Section - 2 0 . (2) The Variable Band Pass Method. (a) Experimental procedure and results. The validi t y of the Beer-Lambert Law in this system has been - 97 -examined by making sets of measurements of k /£ for two values of the band pass ( 0.06 nm and 0.16 nm, each centred upon 216.4 nm ) under otherwise closely similar conditions. The increase in band pass was achieved by increasing the width of the spectrograph s l i t from 75 nm to 200 nm, but this alone would lead to an increase in the signal-to-noise ratio. Accordingly, the intensity of the monitoring light from the pulsed xenon arc was reduced appropriately from Set 2 to Set 3 to allow both sets of measurements to be made at similar levels of the signal-to-noise ratio. Set 1 comprises measurements made at a higher slgnal-to-nolse ratio, and i s Included for comparison. The scope of some of these experiments was extended to Include the measurement of Ajjjg^ and of the yield of nitrogen, so that the extinction coefficient could be estimated. The comparison of the mean values of s obtained from the partial Sets 2 and 3 allows an alternative test of the validit y of the Beer-Lambert Law. (b) Discussion The value of the extinction coefficient of the methyl radical i s a maximum at 216.4 nm, and declines rapidly as the wavelength is Increased or decreased in the immediate neighbourhood of this maximum. Accordingly, i f a series of experiments in conducted, each with a band pass centred on 216.4 nm, but with the magnitude of the band pass successively increased, we may expect the effective value of the extinction coefficient to show a corresponding progressive decrease, and the value of k / £ to show a commensurate progressive increase. The mathematical interpretation of any increase in the - 98 -Table-3.4 Values of k / £ for the mutual combination of methyl radicals measured for two s l i t widths and two xenon arc energies at 216,4 nm Photoflash energy: 1080 J ( 12 kV, 7.5 MP ) Set-1, 200 nm s l i t width and 140 V Xe-pulse Szp No. Gas Mixture Photo No. 10"6 k / e cm see"* H-175-A MegHj t n-C^Hi2 1424 3-59 t 0.17 - 3.5 t 35 1425 1426 4.07 + 0.10 3.88 t 0.13 •7 1427 1428 1429 1430 3.86 + 0.10 3.80 t 0.08 3.72 + 0.04 3.97 t 0.21 H-176-A ltejjlr, t n-C^H12 1443 3.89 3 0.14 - 3.5 i 50 1444 1445 1446 3.84 + 0.21 3.73 + 0.27 4.08 + 0.27 H-177-A Ma2N2 t n-C^H12 1453 3.92 + 0.13 - 3.0 * 4? 1455 1456 1457 3.62 + 0.19 3.63 ± 0.05 3.82 t 0.04 mean value j 3.83 t 0.15 - 99 -Set-2, 75 nm s l i t width and 140 V Xe-pulse io- 6 k /S Exp No. Gas Mixture Photo No. cm sec H-175-A M e t n—C^Hj^ 14-31 4.10 t 0.09 - 3.5 i 35 1432 3.18 i 0.07 1433 3.32 ± 0.08 1434 3.34 t 0.20 1*35 4.10 + 0.22 1436 3.46 + 0.21 H-176-A Me2N2 t n-C^Hi2 1447 2.81 + 0.14 - 3.5 t 50 1448 2.84 t 0.13 1450 3.71 ± 0.15 H-177-A 1458 3-58 + 0.21 » 3.0 i *7 1461 3.53 t o.21 mean value 1 3.^ 5 ± 0.43 - 100 -Set - 3 , 200 nm s l i t width and 60 V Xe-pulse Ezp No. Gas Mixture Photo No. 10"6 k / £ cm see"* H-175-A MegNj t n-C^H12 - 3.5 « 35 1437 1438 1442 3.54 ± 0.02 3.26 ± 0.13 3.29 + 0.13 H-176-A Me2N2 t n-C^H12 - 3.5 t 50 1451 1452 2.99 + 0.09 3.48 + 0.09 H-177-A Me2N2 t XJ-C5H12 - 3.0 t 47 1462 1463 1464 mean value 3.90 + 0.14 4.08 ± 0.31 3.81 t 0.18 » 1 3.54 t 0.37 Mean value of k /£ with an overall standard deviation based upon the 34 measurements of 1, 2 and 3 t k /£ « ( 3.64 ± 0.35 ) x 106 cm seo - 1 Note (1) the oonoentration of azomethane at time 0. Exp No. [CH3N2CH. 3  t-o B O l e 1 - 1 H-175-A 1.91 X 10-* H-176-A 1.91 z 10- 4 H-177-A 1.64 X 10- 4 - 101 -Table-3«5 Values of E for the methyl radical at 216.4 nm, based upon experiments liste d i n Table-3.4 1, 200 na s l i t width, 140 v - Xenon pulse. Exp No. Photo No. 10"6 k / E -1 om see *aax <*»«> £216.4 1 mole"* ca H-175-A 1424 1425 1426 3.59 t 0.17 4.07 t 0.10 3.88 t 0.13 0.284 0.299 0.303 1427 3.86 + 0.10 0.294 0.3006 1.08 x 10* 1428 3.80 • 0.08 0.309 1429 3.72 + 0.04 0.302 1430 3.97 t 0.02 0.286 2, 75 na s l i t width, 140 T - Xenon pulse. H-175-A 1431 1432 4.10 t 0.09 3.32 ± 0.08 0.318 0.292 1433 3.18 • 0.07 0.307 0.2925 1.05 x 10* 1434 3.34 ± 0.20 0.275 1435 4.10 * 0.22 0.274 1436 3.46 I 0.21 0.289 3, 200 na s i l t width, 60 v - Xenon pulse. H-175-A 1437 3.54 * 0.02 0.280 1438 3.26 • 0.13 0.269 0.274 9.87 x 103 1442 3.29 i 0.13 0.273 - 102 -apparent value of k / s with an increase in band pass may follow either of two alternative procedures. The f i r s t procedure i s to retain the value of the extinction coefficient at the absorption maximum as a hypothetical value for the whole band pass, and express the decline In i t s effective value by placing the exponent n less than unity in the expression for the absorbance: A - £ ( C 1 ) n This expression is best suited to the treatment of the variable path length method, and is used in Section 3» The alternative mathmatlcal procedure Is to retain the form: A = E C l o f the Beer-Lambert Law, but to use an effective value for £ which in general w i l l be less than the value for the absorption maximum and w i l l decline progressively as the band pass i s increased. However, there w i l l be a c r i t i c a l magnitude of the band pass within which the effective value of £ w i l l not be significantly lower than the true value at the absorption maximum. This i s the basis of the test employed in the variable band pass method. If the effective value of £ is the same for two significantly different magnitudes of the band pass, then neither magnitude i s greater than the c r i t i c a l magnitude defined above, and the absorbance is given by the expression A =* £ (C 1) n , both with n equal to unity and with £ equal to i t s value at the absorption maximum. Table - 3 . 6 l i s t s values of k / £ calculated on the assumption that £ = C 1 / A , as required by the Beer-Lambert Law. The comparison of values of k / £ for band passes of 0 . 0 6 - 103 -and 0.16 nm at similar levels of signal-to-noise ratio can be made with the results of Sets 2 and 3 . The respective mean values of k / £ are t k / £ a ( 3 . 4 5 + 0.4-3 ) x 10 6 cm sec 1 for Set 2 ; k / £ = ( 3 . 5 4 ± 0 . 3 8 ) x 10 6 cm sec 1 for Set 3 • There Is no significant difference between these mean values, in fact the agreement is remarkable close. On this basis there is no s t a t i s t i c a l evidence that the effective value of £ differs from the true maximum value. Set 1 comprises measurements for which the signal-to-nolse ratio should be greater than in Sets 2 or 3 ; the mean values of k /£ are: k / £ = ( 3*83 ± 0 . 1 5 ) x 10 6 cm sec 1 for Set 1 ; k / £ = ( 3 . 6 5 t O.35 ) x 10^ cm sec 1 for a l l three sets. This overall value of k / £ » ( 3 . 6 5 ± 0 . 3 5 ) x 10^ cm sec 1 i s close to the similar value of ( 3 . 3 1 t 0.46 ) x 1 0 6 cm sec 1 obtained previously in this work, which was based upon the 24 measurements reported in Section C of this Chapter. Table - 3 . 6 also l i s t s the effective values of the extinction coefficient obtained for band passes of 0.06 nm and 0.16 nm centred on 216.4 nm. These values are respectively 10.5 x 10 3 -1 -1 and 9*9 x 10^ 1 mole cm for the comparable Sets 2 and 3 . These values do not differ significantly from one another even i f the ratios of the standard deviations to the mean values are as low as 0 . 0 3 . These values are also in reasonable agreement Table-3.6 A summary of the results calculated assuming that A = £[CH'] 1 Set number s l i t width nm pulse voltage V value of k/6 extinction coefficient 10 - 6 k/e cm sec"* number of experiments io"*e 1 mole~1cm~* number of experiments 1 200 140 3.83 i 0.15 15 1.0b a 2* 75 140 3-45 i 0.43 11 1.05 6 3* 200 60 3.54 I 0.37 0 0.99 3 mean of the three sets 3.64 * O.35 34 * Sets 2 and 3 are the pair with a similar signal-to-noise ratio. - 105 -with the value of ( 9 . 5 * 0 . 4 ) x 1QJ 1 mole cm obtained previously in this work and reported in Section C, and with the most precise literature values reviewed by Callear and Metcalfe, -a i - l - l which range from 9 . 6 x 1 0 J to 1 0 . 2 x 10-* 1 mole cm ( 27 ) . We may therefore conclude from both classes of experiment in this section that the Beer-Lambert Law i s valid for the methyl radical under the chosen experimental conditions. (3) The Variable Path Length Method. (a) Experimental procedure. The validity of the Beer-Lambert Law has been Investigated by comparing the values of absorbance at 2 1 6 . 4 nm obtained when the whole length and when one half of the length of the reaction c e l l were exposed to illumination by the photoflash under otherwise identical conditions. The path length was halved by masking one half of illuminated length of the reaction vessel by symmetrically placed sets of cylindrical masks of equal length, with an appropriate correction for asymmetry. Three masking patterns were adopted to mask 50 % of the 914 mm long reaction vessel from photoflash lightz (1) one half of the reaction vessel was covered with a single black cylindrical mask 457 mm long. ( i i ) one half of the reaction vessel was covered with three equally spaced cylindrical masks, each 1 5 2 . 3 mm long, formed by cutting the mask above into three equal parts. ( i l l ) one half of the reaction vessel was covered with fifteen equally spaced cylindrical masks, each 3 0 . 5 mm long, formed by cutting each of three masks above into five equal - 106 -parts. (b) Theory Asymmetry in the irradiation of the reaction vessel may arise from departures from uniformity in the emission of radiation along the length of the photoflash tube, especially near the electrodes. Such asymmetry may be compensated by conducting two sets of experiments, in which the illuminated and masked regions of the reaction vessels are Interchanged. For example, in pattern (1) the two halves of the vessel were alternately masked. The whole series of measurements was repeated by using as the reaction vessel the vessel which had been used as the reference vessel, and as the reference vessel the vessel which had been used as the reaction vessel. These vessels are of the same length, but d i f f e r in volume by 9.5 %, and this difference was compensated by an appropriate correction. The relationship between absorbance and the exponent n is assumed to be : A = £{[CH 3] 1} n ( 1 ) Let A 1 be the absorbance observed in the absence of masks, then: A± - E ( C 1 ) n ( 2 ) where C =* [CH^] . Let A^ be the absorbance observed when one half of the length of the reaction vessel i s masked, then: A i = £ ( C l / 2 ) n ( 3 ) i f the illumination of the vessel i s completely uniform in the absence of the mask. Here C «= n ( CH3 ) / V ( where V i s the - 107 -total volume of the vessel ) and i s , of course, not uniform throughout the vessel. Combination of equations ( 2 ) and ( 3 ) yields the ratio: The experiment in part ( 1 ), where only a single black cylindrical mask was used, i s most l i k e l y to be affected by deviations from uniformity in illumination due to a difference in light emission from the two ends of the photoflash tube. Accordingly, we adopt two complementary equations : A| = E ( C + 1 / 2 ) n ( 5 ) and A^ =* E ( c" 1 / 2 ) n ( 6 ) where A^ i s the absorbance observed when one half of the length of the reaction vessel i s masked at the anode side, and A ^ i s the absorbance observed when one half of the length of the reaction vessel i s masked at cathode side, and C + and c" are the respective concentrations. The effective value of C for f u l l illumination i s ( C + + C* ), so that the ratio A J / A1 becomes : 4 / A 1 * ( C + / ( C + + C" ) ) n ( 7 ) i f C + =* C*" , this ratio becomes : A | / Ax » ( 1 / 2 ) n ( 8 ) and - 10b -Ai / 2 n therefore At + Al - 2 A t / 2 n = 2 1" 1 1 A ] so that absorbances are not simply additive in general. Only in the special case, when n = 1 and the simple Beer-Lambert Law i s obeyed, are absorbances additive : A £ + H s A l ( 10 ) In general, equations ( 5 ) and ( 6 ) may be rewritten as A | / A£ = ( c + / c" ) n so that : 0" = C + ( A ^ / A J ) V N ( 11 ) then, substituting equation ( 11 ) into equation ( 7 ) : 4 n V c + + c + l/n ( 12 ) and A f H 1 i 1 + \ 1 A * l/n ^ n ( 13 ) The complementary equation ( 13* ) for A A / A^ i s given in Table-Table-3.7 Summary of equations used to evaluate n for different masking patterns and the correction for asymmetry Masks Equations used to evaluate n Correction for asymmetry masked and unmasked regions interchanged reaction and reference vessel interchanged number length mm 1 457 A l 1 = 1 + 4 i A l f = I 1 + f A * (13) \ H I ) 1 A J 1 / N " ) N " — r - J (13') \ A i / ) yes yes 3 152.3 A l n = 2 n (4) no no 15 30.1 no no - 110 -3 . 7 . Equation ( 13 ) or ( 1 3 ' ) was used to calculate the corresponding estimate ( n + or n" ) of the value of n at different periods of reaotlon following the photoflash. In equation ( 13 ), ( / ) i s the correction term and the ratio of ( A ^ / A £ ) i s nearly unity. The term : ( A ^ / A ^ J 1 ^ 1 1 has a very small influence on the value of A ^ / A ^ . For example, i f ( A ^ 7 A J ) - 1 . 1 0 0 , then ( A ^ / A | ) 1 / / n has the value 1 .127 and 1 . 0 8 3 for n = 0 . 8 and 1 .2 respectively. The value of n was calculated from the experimental results by an iterative procedure based upon the revised equation : A = Ay2 The process of iteration w i l l be described. Fi r s t , place n* = 1 and calculate n£, the f i r s t estimate of n". Secondly, place n' = n^ and calculate n 2» the second estimate of n". Thirdly, iterate until two successive estimates of n" agree within the desired limits of precision; then n' = n" = n. The val i d i t y of the f i n a l value was estimated at each delay time using the iterative procedure with two different I n i t i a l values of n' : n' = 1 and n* =* 0 . 7 . The limiting values of n" at each delay time from both i n i t i a l values of n* were exactly the same, and the mean value of n" was calculated to be 0*9^7 - 0 . 0 2 2 . The only difference resulting from a choice of n' = 1 or n' = 0 . 7 in the calculation for estimating the values of n" was found in the number of iterations required to achieve a constant value of n" ; two or three iterations were required when n' =« 1 i n i t i a l l y , whereas three or four iterations were needed with - I l l -n' a 0 . 7 . The volumes of the reaction vessels di f f e r by 9 . 5 % and a corresponding correction was made in the calculation of the ratio of / A^. (C) Results The results are shown in Table - 3 . 8 and in Figure - 3 . 6 . At this point i t should be recognized that the valid i t y of equations ( 4 ) , ( 13 ) and ( 1 3 ' ) i s limited to short delay times* The concentration terms : C, C + and C are each of the form n [CH3 ] / V, and are therefore not uniform throughout a masked vessel of total volume V. The derived equations ( 4 ) , ( 13 ) and ( 1 3 ' ), which are quoted in Table-3.7 and are used to calculate n, are therefore s t r i c t l y valid only immediately after an instantaneous flash, or at the hypothetical " zero time " of the actual flash. As the delay following the f i r i n g of the flash i s increased, the deviation of the system from the appropriate equation of Table-3.7 also increases and the estimate of n obtained from that equation becomes increasingly inaccurate. This behaviour is apparent in curves 2 and 3 of Pigure - 3 . 6 , and w i l l be discussed f u l l y in Section-d. (d) Discussion The results of the variable path method are given in Table - 3 . 8 and Pigure - 3 . 6 . The apparent values of the exponent n were measured for three patterns of masking at increasing values of the delay between f i r i n g the photoflash and recording the absorbance. Two main characteristics emerge. Fi r s t , each curve may be extrapolated to a value of n very close to unity for a zero delay time ; the direct measurement at this time is impossible. Table -3 .8 The relationship between the time of reaction and n \ Masks Exponent n 1 x 457 mm mask 3 x 152*3 mm 15 x 30.1 mm Time \ ( H-184-A ) masks masks ( seo ) \ n" n+ ( H-178-A ) ( H-I83-A ) 46 0.949 0.949 0.940 0.888 66 0.936 0.936 0.902 0.757 86 0.921 0.921 0.879 0.660 106 0.942 0.942 0.854 0.580 126 0.943 0.943 0.855 0.516 146 0.989 0.989 0.840 0.483 Relationship random fluctuation about a mean ( 0.947 t 0.022 ) monotonio monotonio - 113 -Figure-3-6 The r e l a t i o n s h i p between the value of the exponent n and the time delay between f i r i n g the photoflash and r e c o r d i n g the absorbance. 0.2 \-01— 1 > 1 1 i i i i 20 40 60 80 100 120 U0 160 Time ( \xsec) No. of the curve M a s k s F i t t e d curve 1 2 3 1 x 457 mm 3 x 153.2 mm 15 x 30 mm S t r a i g h t l i n e , n =0.95 Smoothed curve Smoothed curve - 114 -Secondly, each pattern of masking has Its own curve, and the more the masking cylinder is subdivided, the greater is the deviation of n from unity. Figure - 3 . 6 i s consistent with a true value of n which does not di f f e r significantly from unity. The observed deviation of the measured values of n from unity are due to two causes. Fir s t the penumbra effect, which causes partial illumination of those regions of tube that would be completely shielded by the masks i f the illuminating l i g h t were s t r i c t l y collimated, and therefore causes methyl radicals to be generated in those regions. This effect alters neither the number of methyl radicals generated nor the consequent i n i t i a l absorbance of the whole vessel, but i t does make the i n i t i a l concentration in the illuminated zones s l i g h t l y lower than i t would have been in i t s absence. The penumbra effect increases in importance with the subdivision of the masking cylinder and the consequent increase in the number of boundaries between the zones. Secondly the diffusion of methyl radicals from the sites where they were formed within the illuminated zones w i l l cause a net d r i f t of radicals into the dark zones, and the depletion of the methyl radical concentration in the illuminated zones w i l l increase with the time lapse following the f i r i n g of the photoflash. The diffusion effect w i l l likewise increase in importance with the subdivision of the masking cylinder and the consequent increase in accessibility of the dark regions. The concentration of methyl radicals in the illuminated zones is therefore I n i t i a l l y depleted by the penumbra effect and thereafter progressively depleted by the diffusion effeot at - 115 -a rate proportional to the f i r s t power of their concentration. These effects are absent in the unmasked reaction vessel,where the only significant depletion is by second order mutual combination at the time dependent rate R(t). In the Illuminated zones of the partially masked vessels both the penumbra effect and the f i r s t order process of depletion of methyl radical concentration by diffusion w i l l lower the rate of second order depletion by mutual combination significantly below R(t), so that the f a l l in the concentration of methyl radicals after a lapse of time t beoomes progressively less than in the unmasked vessels. The mathematical analysis is based upon two relationships of the type: ( A£ / Aj ) » { c + / ( c + + c" )} n , with no correction for the penumbra and diffusion effects. Since these effects have the result of progressively raising the value of C + in the numerator above the values of C + and c" in the denominator of the equation above, the mathematical method responds by a compensating reduotion in the apparent value of n. The reduction in the apparent value of n w i l l be greatest under the conditions which develop the penumbra and diffusion effects most completely: high subdivision of the masking cylinder and a long delay after the f i r i n g of the photoflash respectively, as Pigure - 3 . 6 shows. We may conclude that the results obtained by the variable path length method are f u l l y consistent with a value of unity for n in the equation: A = £ ( C 1 ) n , when i t i s applied to the study of reactions of the methyl radical by kinetic spectroscopy under normal conditions in,the present apparatus. - 116 -(4) Conclusion The results of both the variable band pass experiments and of the variable path length experiments f u l l y support the val i d i t y of the Beer-Lambert Law expression : A • E C 1 when i t i s applied to the study of reactions of the methyl radical by kinetic spectroscopy under normal conditions in the present apparatus* - 117 -CHAPTER 4 MUTUAL INTERACTION OF ETHYL RADICALS A, Introduction (1) Absorption spectrum of the ethyl r a d i c a l The ethyl r a d i c a l i s the second member of the homologous series of n-alkyl r a d i c a l s . It resembles the methyl r a d i c a l i n many of i t s reactions with other r a d i c a l s , but d i f f e r s i n i t s capacity to undergo disproportionation to y i e l d the corresponding alkene, ethene. Furthermore, the ethyl r a d i c a l does not possess an Intense, narrow and structured absorption spectrum l i k e that of the methyl r a d i c a l . The absorption spectrum of the ethyl r a d i c a l has not previously been characterized with any certainty. The l i t e r a t u r e contains only four reports of t h i s spectrum (28,39,43,44) Each describes a very weak absorption i n the u l t r a v i o l e t , but the assignments are both tentative and c o n f l i c t i n g . Gaydon, Spokes and Suchtelen looked for the absorption spectra of a l k y l r a d i c a l s i n the flames of corresponding - 1 1 8 -a l k y l derivatives (43)• They detected the known absorption spectrum of the methyl r a d i c a l i n flames of dimethyl ether, acetone, acetaldehyde and methane, but not of methanol. Accordingly, they looked for the absorption spectrum of the ethyl r a d i c a l i n the flames of d i e t h y l ether and ethane. They found a weak but f a i r l y d e f i n i t e band with maxima at about 222.8 and 224.2nm, the maxima being about 0.5nm wide, i n the flames of both compounds. They considered that t h i s absorption band i s similar in character to the absorption band of the methyl r a d i c a l . They assigned t h i s band to the ethyl r a d i c a l by analogy, but claimed no conclusive proof of t h i s assignment. Wendt, Wyrsch and Hunziker ( 44 ) examined the absorption spectra of four gaseous reacting systems which were known to generate the ethyl r a d i c a l : 1 . Hg ( 3P) + C 2H6 * Hg ( 1S) + C 2Hj + H-2. Hg ( 3P) + ( C 2H 5 ) 2 C 0 ^ Hg ( 1S) + C2H3 + C 2H^C0 3. Hg ( 3P) + H 2 > Hg ( i s ) + 2H-H + C 2Hj^ * > C 2H J 4. Hg ( 3P) + N 20 * Hg ( XS) + N 2 + 0 0 + C 2H 6 *• 0H'+ C 2RJ 0H*+ C 2H 6 *• H 20 + C 2H£ The absorption spectrum of each system included a similar broad band at 206+lnm, which was t e n t a t i v e l y attributed to the ethyl r a d i c a l ; no prominent and / or persistent bands were found - 119 -at 222 or 224nm. Hlckel ( 2 8 ) examined the absorption spectra of the methyl and ethyl r a d i c a l s in water, which were generated by pulse r a d i o l y s i s . Pulse r a d i o l y s i s of pure water generates both the hydroxyl r a d i c a l and the hydrated electron: If ethane i s dissolved i n water, r a d i o l y s i s w i l l y i e l d ethyl r a d i c a l s by metathesis between the hydroxyl r a d i c a l s and the ethane molecules: Unfortunately the hydrated electron absorbs i n the u l t r a v i o l e t and hinders the search for the absorption of the ethyl r a d i c a l . A scavenger must therefore be added to the solution to remove the hydrated electrons. Either nitrous oxide or ethyl chloride i s e f f e c t i v e : N 20 (aq ) + e~ (aq ) »• N 2 ( aq ) + 0H~ ( aq ) + OH' (aq ) C2H5CI ( aq ) + e" ( aq ) > C 2Hj ( aq ) + C l " ( aq ) Accordingly, the absorption spectrum of the ethyl r a d i c a l -2 -1 in aqueous solution was detected i n a 5 x 10 mole 1 aqueous solution of ethane, containing either nitrous oxide or ethyl chloride, which was subjected to pulse r a d i o l y s i s . The absorption spectrum of the ethyl r a d i c a l i n water was observed to increase s t e a d i l y i n i n t e n s i t y when the wavelength was decreased from 270 to 200nm without passing through a maximum. OH' ( aq ) + e" ( aq ) C 2H 6 ( aq ) + 0H'( aq ) C 2 H5 ( aq ) + H 20 ( 1 ) - 1 2 0 -The decay of the r a d i c a l s was foll o w e d s p e c t r o p h o t o m e t r i c a l l y , and f o l l o w e d second order k i n e t i c s w i t h a r a t e constant of k = ( 1.2 ± 0.2 ) x 10 9 1 mole""1 s e c " 1 , i n d i c a t i n g a d i f f u s i o n c o n t r o l l e d r e a c t i o n . The absorption spectrum of the methyl r a d i c a l i n water was als o d e s c r i b e d , and was reported to be much broader than the spectrum of the methyl r a d i c a l i n the gas phase, extending over the range from 230 to below 200nm. The p o s i t i o n of the maximum i s approximately the same i n each phase: 2l6.4nm i n the gas phase compared to 213±2nm i n water. The s i m i l a r i t i e s and d i f f e r e n c e s i n the sp e c t r a of the methyl r a d i c a l i n the gas phase and i n s o l u t i o n were not discussed i n d e t a i l by H i c k e l . Parkes and Quinn ( 39 ) used t h e i r molecular modulation spectrometer to examine the absorption spectrum of a mixture of 15»7torr azoethane and 600torr n i t r o g e n immediately a f t e r f l a s h p h o t o l y s i s . They discovered a weak absorption band extending from 240 to 260nm, w i t h a maximum at 250nm. The decay of the absorption a t 250nm followed second order k i n e t i c s , w i t h a r a t e constant of about 8.0 x 10? l m o l e - 1 s e c - 1 . This r e s u l t i s co n s i s t e n t w i t h the assignment of the spectrum t o the e t h y l r a d i c a l which would be consumed by blmolecular mutual i n t e r a c t i o n ; i t i s not c o n s i s t e n t w i t h an assignment to an e x c i t e d s t a t e of azoethane that would decay by a unimolecular process. Absorption by azoethane was too strong below 230nm to al l o w a search f o r bands at 224, 223 or 206nm i n t h i s system. The magnitude of the r a t e constant assigned by Parkes and Quinn to the mutual i n t e r a c t i o n of e t h y l r a d i c a l s l i e s between the values f o r the corresponding i n t e r a c t i o n s of methyl and i s o p r o p y l Table-4.1 The characterization of the absorption spectrum of the ethyl radical Authors Year Method and Radical Source A max nm nm Cmax i -,-1 - 1 1 mole cm Remarks Ref. Gaydon, Spokes and van Suchtelen I960 Flames of Diethyl Ether and of Ethane 222.8 224.2 -v-0.5 ~0.5 43 Wendt, Wyrsch and Hunziker 1974 Modulated Excitation of Mercury Photosensitized Reactions 206±1 no bands at 222 or 224 nm 44 Hickel 1975 Pulse Radiolysis of Ethane i n Water no maxima absorbs i n the range 270 to below 200 nm 28 Parkes and Quinn 1976 Photolysis of Azoethanei Observation by Molecular Modulation Spectroscopy 248 20 3.3 x 10' observation impossible for A<225 nm 39 This work 1978 Plash Photolysis of Azomethanej Observation by Kinetic Spectroscopy 247 25 4.8 x 102 no bands at 223 or 224 nm Note IAX is the width of the absorption peak when \= i \ max - 122 -r a d i c a l s , and thus forms a c o n s i s t e n t p a t t e r n of r e a c t i v i t y . However, the assignment of the e t h y l r a d i c a l spectrum r e s t s upon one s e r i e s of experiments w i t h e t h y l r a d i c a l s derived from onl y a s i n g l e source. This assignment i s th e r e f o r e l e s s c e r t a i n than the assignments of the spectra of the methyl, i s o p r o p y l and t e r t - b u t y l r a d i c a l s ; each of these species was generated from seve r a l d i s t i n c t r a d i c a l sources, and gave a much more intense a b s o r p t i o n . An Independent study of the spectrum of the e t h y l r a d i c a l was c l e a r l y d e s i r a b l e , and t h i s was performed and i s described i n t h i s chapter. The r e s u l t s of these s t u d i e s are included i n Table-4.1. (2) The r a t e constant f o r mutual i n t e r a c t i o n of e t h y l r a d i c a l s . (a) Absolute measurements Four absolute measurements of the r a t e constant f o r the mutual combination of e t h y l r a d i c a l s have been reported i n the l i t e r a t u r e : by Shepp and Kutschke i n 1957 ( 45 ), by H i c k e l i n 1975 ( 28 ), by Golden, Choo, Perona and p i s k i e w i c z i n 1976 ( 46 )i and by Parkes and Quinn i n 1976 ( 39 ). The r e s u l t s of these studi e s are included i n Table-4.2, and c o n s t i t u t e the set of " high " values f o r t h i s r a t e constant. ( i ) The r o t a t i n g sector method Shepp and Kutschke a p p l i e d the r o t a t i n g s e c t o r method to the study of the mutual combination of e t h y l r a d i c a l s formed by the low i n t e n s i t y p h o t o l y s i s of d i e t h y l ketone. They reported values of the r a t e constant of ( 1.5 ± 1 ) x 10 1 0, ( 2.0+0.5 ) x 10 1 0, and ( 4.2 + 0.8 ) x 10 1 0 1 mole 1 s e c 1 a t 323, 373 and 423 K r e s p e c t i v e l y . These values imply an energy of a c t i v a t i o n - 1 2 3 -of (2 ± 1) kcal mole 1, but such a high value seems un l i k e l y for the mutual combination of a l k y l r a d i c a l s (47 ). The exact app l i c a t i o n of the theory of the r o t a t i n g sector i s r e s t r i c t e d to a simple mechanism comprising reactions l ( i - v ) of reference ( 45 )» and the authors assumed that they could neglect reactions l ( v i ) and l ( v i i ) : 2 C 2H 5C0C 2R4 > C^COC^HgCOCgH^ l ( v i ) C2H^COC2H4 »• C 2H^ + CO + CgH^ l ( v i i ) These are reactions of the r a d i c a l C2H^C0C2H^, which i s formed by metathesis between the ethyl r a d i c a l and d i e t h y l ketone. Consequently these reactions become increasingly important as the reaction temperature i s raised; moreover, p a r t i c i p a t i o n of reaction l ( v i i ) leads to a chain reaction. The magnitude of the apparent a c t i v a t i o n energy f o r combination may be a spurious consequence of the increasing p a r t i c i p a t i o n of reactions l ( v i ) and l ( v i i ) at higher temperatures. (11) The technique of pulse r a d i o l y s i s . Hickel applied the technique of pulse r a d i o l y s i s to the study of the combination of ethyl r a d i c a l s i n aqueous solution ( 28 ). The ethyl r a d i c a l was formed by the abstraction of a hydrogen atom from an ethane molecule by a hydroxyl r a d i c a l which had been generated i n water by pulse r a d i o l y s i s . He reported that the disappearance of ethyl r a d i c a l s followed second order k i n e t i c s . His value of the rate constant for combination was ( 1 . 2 I 0 . 2 ) x 1 0 7 1 mole sec at 2 9 8 K, and an apparent ac t i v a t i o n energy for the combination of - 124 -( 3*9 t 0.4 ) k c a l mole 1 was derived from the e f f e c t of temperature upon the r a t e . A p a r a l l e l study of the combination Q of methyl r a d i c a l s i n water y i e l d e d a r a t e constant of 1.6 x 10 -1 -1 1 mole sec w i t h an apparent a c t i v a t i o n energy of ( 3.9 ± 0.4 ) k c a l mole 1. These a c t i v a t i o n energies are a l i t t l e higher than the a c t i v a t i o n energy of 2.9 k c a l mole 1 f o r the d i f f u s i o n of the both methane and ethane molecules i n water. However, there i s evidence that an a l k y l r a d i c a l may d i f f u s e more slow l y than i t s parent hydrocarbon i n s o l u t i o n ( 48 ). A c c o r d i n g l y i t seems probable that the combination of both methyl and e t h y l r a d i c a l s i s d i f f u s i o n - c o n t r o l l e d i n aqueous s o l u t i o n . ( i i i ) The technique of very low pressure p h o t o l y s i s . Golden et a l . ( 46 ) a p p l i e d the technique of very low pressure p h o t o l y s i s to the absolute measurement of the r a t e constant of the mutual combination of e t h y l r a d i c a l s . They generated the e t h y l r a d i c a l by the p y r o l y s i s of azoethane, and monitored azoethane, the e t h y l r a d i c a l and n-butane by mass spectrometry. They es t a b l i s h e d ' that the n-butane was formed only i n a second order r e a c t i o n of e t h y l r a d i c a l s . Q T h e i r value of r a t e constant f o r combination was 4.5 x 10 1 mole 1 s e c 1 at 860 t 17 K under very low pressure c o n d i t i o n s , but f o r comparison w i t h other work the value at high pressures, k00, i s r e q u i r e d . They claimed that k/k 0 0 should be about 1/2 f o r t h e i r c o n d i t i o n s , u s i n g " almost any model of the t r a n s i t i o n s t a t e which i s compatible w i t h butane decomposition ". This gives k°° = 1 x 10 1 0 1 mole 1 s e c 1 a t high pressure at 860 K . - 125 -( i v ) The technique of molecular modulation spectrometry. Parkes and Quinn used the technique of molecular modulation spectrometry to monitor d i r e c t l y the e t h y l r a d i c a l s formed by the p e r i o d i c a l l y i n t e r r u p t e d p h o t o l y s i s of azoethane. Their method depends upon the d e t e c t i o n of an absorption which can be assigned u n e q u i v o c a l l y to the r a d i c a l of i n t e r e s t , but they admitted that t h e i r assignment of a spectrum to the e t h y l r a d i c a l i s t e n t a t i v e o n l y , and that the consequent value f o r the r a t e constant i s the l e a s t c e r t a i n of the four a l k y l r a d i c a l combination r a t e constants t h a t they have determined. Their r e s u l t , ( 8 . 0 1 2.0 ) x 10? 1 mole sec , measured a t room temperature, i s not s i g n i f i c a n t l y d i f f e r e n t from the value obtained at 860 K by very low pressure p y r o l y s i s . This I n d i c a t e s that the energy of a c t i v a t i o n i s very s m a l l , i n co n t r a s t to the co n c l u s i o n of Shepp and Kutschke. (v) The thermodynamic c r i t e r i o n . The r e s u l t s of the four absolute methods are i n broad agreement i n p r e d i c t i n g a value of ~ 1 x 1 0 1 0 1 mole 1 s e c 1 f o r the r a t e constant of mutual combination of e t h y l r a d i c a l s . In i s o l a t i o n , t h i s would appear to be a s a t i s f a c t o r y s o l u t i o n 10 -1 to the problem. Unfortunately, the value of 1 x 10 1 mole s e c 1 seems to be a f a c t o r of from 2 to 5 too high to be compatible w i t h accepted thermodynamic values i n conjunction w i t h extensive k i n e t i c data on the reverse r e a c t i o n , the d i s s o c i a t i o n of the n-butane molecule to two e t h y l r a d i c a l s . The d i f f i c u l t y a r i s e s because the system* CH^CHg - CH 2CH 3 5 = t 2 CH^CHg* ; K = k f / k r Table -4.2 Values of the rate constant for the gas phase reaction: 2 C 2 H 5 " C 4 H 1 0 » k 2 Part-A, Direct methods Authors Year Method Temp K k 2 1 mole* sec* Shepp and Kutschke 1957 Rotating Sector 323 373 423 ( 1.5 ± 1 ) x i o 1 0 ( 2.0±0.5 ) x 1 0 1 0 ( 4.2 + 0.8 ) x 1 0 1 0 E 2 = 2 ± l kcal mole"1" Golden, Choo, Perona and Pisz k i e w i c z 1976 Very Low Pressure F y r o l y s i s of Azoethane 860 ± 17 4.5 x 10 9 at low pressure 1.0 x 10*°at high pressure Parkes and Quinn 1976 Molecular Modulation Spectrometry ~298 ( 8 + 2 ) x 10 9 This work 1978 Flash P h o t o l y s i s and K i n e t i c Spectroscopy ~298 ( 1.4 ± 0.3 ) x 1 0 1 0 - 12? -i s overdetermined i f k f ) ky, A H ° and A S ° are a l l known at a common temperature T. Overdetermination i s due to the r e l a t i o n s h i p of K both t o k f and kp and to A H ° and A S ° , as expressed by the equation: k f / k r = K = exp ( A S ° / R - AH 0/ RT ) Yet another r e s t r a i n t i s placed on t h i s system by the requirement t h a t the energy of a c t i v a t i o n f o r combination of e t h y l r a d i c a l s : Ep = 0 . Golden et a l i a ( 46 ) have discussed t h i s c o n t r a d i c t i o n between the k i n e t i c and thermodynamic r e s u l t s and have attempted a r e c o n c i l i a t i o n by a d j u s t i n g the entropy and the heat of formation of the e t h y l r a d i c a l . U n f o r t u n a t e l y, the p e r m i s s i b l e changes i n the thermodynamic values f o r the e t h y l r a d i c a l were i n s u f f i c i e n t i n r e l a t i o n to the value of the r a t e constant f o r the mutual combination of e t h y l r a d i c a l s derived from the work of H i a t t and Benson ( 49 ). These authors d e r i v e d a value f o r t h i s r a t e constant r e l a t i v e to the e s t a b l i s h e d value of the r a t e constant f o r combination of methyl r a d i c a l s and the thermochemistry of the b u f f e r r e a c t i o n : CHj + C2H^I ~.—" CH^I + C2H^ Using the r e v i s e d thermodynamic values , the r a t e constant f o r the combination of e t h y l r a d i c a l s was r a i s e d from 4 x 10 9 -1 -1 to 2 x 10 1 mole sec , but the d i f f e r e n c e between the r e v i s e d 10 -1 _ i value and 1 x 10 1 mole sec , r e p r e s e n t a t i v e of the r e s u l t s of absolute methods, remains f a r too great to be disregarded. - 128 -This system i s discussed i n greater d e t a i l i n the next s e c t i o n , (b) Methods i n v o l v i n g the thermochemistry of the e t h y l r a d i c a l The c o n t r i b u t i o n of such i n d i r e c t methods to the corpus of values of the r a t e constant f o r the combination of e t h y l r a d i c a l s has been s u b s t a n t i a l . The r e s u l t s of these methods are i n s u b t a n t i a l agreement, and c o n s t i t u t e the set of " low " values f o r the r a t e constant, i n c o n t r a s t the r e s u l t s of the absolute methods, which provide the c o n s i s t e n t set of " high " v a l u e s . These methods f a l l i n t o three c l a s s e s : ( i ) product a n a l y s i s of r a d i c a l b u f f e r systems. ( i i ) r a t e s t u d i e s of the p y r o l y s i s of n-butane ( i i i ) r a t e s t u d i e s of r e a c t i o n s of the e t h y l r a d i c a l , i n c l u d i n g metathesis and dismutation. Hughes, Ma r s h a l l and P u r n e l l reviewed the r e s u l t s obtained by these methods i n 1974 ( 50 )• They recorded t h a t H i a t t and 8 —1 1 Benson had found a value of 4 x 10 1 mole sec at 354 K and at 415 K by r a d i c a l b u f f e r technique ( 49 ), w h i l e Hase, Johnston and Simons had placed the r a t e constant i n the upper end of the 8 8 —1 —1 range 1 x 10 to 6 x 10 1 mole sec by a p p l y i n g unlmolecular decomposition theory to the r e s u l t s obtained f o r the decomposition of c h e m i c a l l y a c t i v a t e d n-butane ( 52 )• They continued by s t a t i n g t h a t Pacey and P u r n e l l had 8 1 1 obtained a value of 3 x 10 1 mole sec at 951 K from a study of the thermal decomposition of n-butane ( 53 ) and that Marshall and P u r n e l l had shown th a t l i t e r a t u r e data f o r r e a c t i o n s of 8 " m 1 e t h y l r a d i c a l s a l s o l e d to values c l o s e to 2.5 x 10 1 mole s e c 1 f o r temperatures near 500 K ( 54 ). They added t h e i r own Table-4.2 Values of the rate constant f o r the gas phase reactioni 2 C 2HJ - 0kHiO ' k2 Part-B, Indirect methods Authors Year Method Temp K k2 1 mole 1 s e c 1 H i a t t and Benson 1972 Radical Buffer 354 415 4 x 108 ( E 2 = 0 ) P u r n e l l and Quinn r e c a l c u l a t e d by Hughes and Marshall 1962 Thermal P y r o l y s i s of n-Butane near Atmospheric Pressure 693 803 2.5 x 108 Pacey and P u r n e l l 1972 the same as the above 951 3 x 108 Hughes, Marshall and Pu r n e l l 1974 the same as the above 895 981 4 x.108 Golden, A l f a s s i and Beadle 1974 Very Low Pressure P y r o l y s i s of n-Butane — 1100 estimates of k 2 at 400 K 3 x 108, 6 x 108 and 8 x 108. Hase, Johnson and Simons 1972 Chemically Activated P y r o l y s i s of n-Butane ^-298 estimates of k 2 at 400 K from 8.5 x 10? to 1.1 x 10*. Marshall and Purne11 1972 C 2 H 5 + " 2 ^ C 2 H 6 + H* C2 H5 = C 2 \ + H ' —550 ~-500 1 x 108 2.5 x 108 - 130 -8 —1 —1 value of 4 x 1 0 1 mole sec In the range of temperature from 8 9 5 to 9 8 1 K, obtained from a study of the thermal decomposition of n-butane. They concluded that the strong measure of agreement between a l l these values , which had been obtained over a wide range of temperature, was the more impressive as the r e s u l t s had been derived by using a wide v a r i e t y of techniques. They also emphasised that a l l these values are based upon the c u r r e n t l y accepted thermochemistry of the e t h y l r a d i c a l . A more d e t a i l e d d i s c u s s i o n of the r e s u l t s of the three c l a s s e s of methods f o l l o w s . ( i ) The r a d i c a l b u f f e r method. H i a t t and Benson ( 49 , 51 ) studied a r e a c t i n g system governed by the r a d i c a l b u f f e r e q u i l i b r i u m : CHj + GgH^I « CH3I + C 2H£ ; K m Q which y i e l d s alkanes by the mutual combination r e a c t i o n s : C H 3 + CH^ • C 2H 6 ; k^ CH3 + C 2H^ *• C 3Hg C 2HJ + C 2H^ > C^Hg The symbols used above are taken from t h e i r papers. These authors measured the y i e l d s of propane and n-butane and deriv e d a value of k g from the equations: dfoHttJ_ k e CC2H5) k e (C0H5I] d t e H o j " k m e ( C H 3 ] " k m e m e (CH3I) Kme *e 2 me * m e ' - 131 -km/ [CH3I] The e v a l u a t i o n r e q u i r e s a value f o r 1^, which may be regarded as an e s t a b l i s h e d q u a n t i t y from the d i s c u s s i o n of Chapter-3. I t als o r e q u i r e s a value f o r K^, which i m p l i e s values of ^H^^g , S298 a n d Cp°rp f o r each of the species i n the r a d i c a l b u f f e r equation. Such values are known w i t h s u f f i c i e n t accuracy f o r C H 3 I , C 2H^I and C H 3 . The thermodynamic values f o r the e t h y l r a d i c a l are known w i t h l e s s accuracy. For example, i f an energy b a r r i e r of 2 k c a l mole 1 i s assigned to the i n t e r n a l r o t a t i o n of _1 the e t h y l r a d i c a l , the value of S° i s changed by 1 eu mole . o - -1 The value of AHf may a l s o be i n e r r o r by 1 k c a l mole . Changes i n the values which are greater than these are improbable on s t r u c t u r a l grounds ( 4 9 ) • g H i a t t and Benson ( 51 ) p r e f e r the value : k Q = 4 x 10 1 -1 -1 mole sec which i s a s s o c i a t e d w i t h a zero energy of a c t i v a t i o n f o r the combination of e t h y l r a d i c a l s , i . e . , E = 0.0 t 0.2 k c a l mole . They p o i n t out that an adjustment of the thermochemistry 4 of the b u f f e r r e a c t i o n which i s s u f f i c i e n t to r a i s e k e to 1 9 - 1 - 1 4 x 10 1 mole sec a l s o lowers the a c t i v a t i o n energy E to -2 -1 k c a l mole , which i s s u r e l y improbable. Golden et a l i a ( 46 )> using the changes i n s° and &H£ f o r the e t h y l r a d i c a l given i n 9 -1 -1 the previous paragraph, consider that k e = 2 x 1 0 ' 1 mole sec i s the maximum value that can be d e r i v e d from the r e s u l t s of H i a t t and 3enson. This i s s i g n i f i c a n t l y lower than the r e s u l t s of the - 132 -absolute measuements. ( i i ) Rate s t u d i e s of p y r o l y s i s of n-butane Both thermal and chemical a c t i v a t i o n have been used to accomplish the p y r o l y s i s of n-butane, and s t u d i e s have been made both at pressures near to atmospheric pressure, and under very low pressure c o n d i t i o n s . The most e a s i l y i n t e r p r e t e d r e s u l t s were obtained by thermal p y r o l y s i s near atmospheric pressure at high temperatures. Recent values are i n c l o s e agreement: Pacey and P u r n e l l obtained a value of 3 x 10 1 mole sec at 951 K i n 1972 ( 53 ), whereas Hughes, Marshall and P u r n e l l obtained the value of 4 x 10 1 mole 1 s e c 1 f o r the range from 895 to 981 K i n 1974 ( 50 ). Furthermore, Hughes and Marshall r e c a l c u l a t e d i n 1975 the r e s u l t s obtained by P u r n e l l and Quinn i n I962 and obtained a 3 1 1 value of 2.5 x 10 1 mole sec f o r the range from 693 t o 803 K. The set of r e s u l t s obtained from t h i s technique i s thus compatible w i t h a zero energy of a c t i v a t i o n . The i n t e r p r e t a t i o n of the r e s u l t s of the very low pressure p y r o l y s i s of n-butane r e q u i r e s a d e t a i l e d model f o r the t r a n s i t i o n s t a t e . Golden, A l f a s s i and Beadle discussed the r e s u l t s of such a p y r o l y s i s at 1100 K i n 197^ ( 55 ). They s e l e c t e d the frequencies f o r t h e i r models to y i e l d three d i s t i n c t values f o r the A f a c t o r f o r the d i s s o c i a t i o n of butane which were compatible w i t h three chosen k i n e t i c c r i t e r i a . The f i r s t and second c r i t e r i a were that the energy of a c t i v a t i o n f o r the combination of e t h y l r a d i c a l s should be zero at 298 K and 1100 K r e s p e c t i v e l y . The t h i r d c r i t e r i o n was that l o g ( A / s e c 1 ) = 16.4 f o r each C-C - 133 -rupture. The corresponding values c a l c u l a t e d f o r the r a t e constant f o r the combination of e t h y l r a d i c a l s at 800 K were: 9 8 8 1 — 1 1.0 x 10 , 8 x 10 and 8 x 10 1 moli sec r e s p e c t i v e l y , i n reasonable agreement w i t h each other and w i t h the r e s u l t s obtained near atmospheric pressure. However, the longer e x t r a p o l a t i o n to 400 K y i e l d e d the c a l c u l a t e d v a l u e s : 3 x 10 , 6 x 10^ and 8 x 10^ 1 mole 1 s e c 1 r e s p e c t i v e l y , showing an i n c r e a s i n g s e n s i t i v i t y to the type of model used. The i n t e r p r e t a t i o n of the r e s u l t s of the c h e m i c a l l y a c t i v a t e d p y r o l y s i s of n-butane i s a l s o i n f l u e n c e d by the type of model chosen f o r the t r a n s i t i o n s t a t e , but the range of c a l c u l a t e d values of the r a t e constant i s g r e a t e r . Hase, Johnston and Simons used three d i s t i n c t models i n the a n a l y s i s of t h e i r r e s u l t s ( 52 ), and t h e i r c a l c u l a t e d values of the 7 9 - 1 - 1 r a t e constant ranged from 8.5 x 10 to 1.1 x 10 1 mole sec at 400 K. We may conclude that the study of the p y r o l y s i s of n-butane by three d i s t i n c t techniques y i e l d s values f o r the r a t e constant f o r the combination of e t h y l r a d i c a l s which are c o n s i s t e n t w i t h 8 a r e p r e s e n t a t i v e value of 2.5 x 10 . ( i i i ) Rate s t u d i e s of other r e a c t i o n s of the e t h y l r a d i c a l Marshall and P u r n e l l have de r i v e d estimates f o r the r a t e constant f o r the combination of e t h y l r a d i c a l s f o r two systems i n which t h i s r e a c t i o n i s i n competion w i t h e i t h e r a m e t a t h e t i c a l or a d i s m u t a t i o n a l r e a c t i o n of the e t h y l r a d i c a l . Using t h e i r system of numbering, the f i r s t system comprised the r e a c t i o n s : 2 Q2R'5 n-C^H 1 0 ( 1, - 1 ) - 1 3 4 -C 2 H £ + H 2 T=Z C 2 H 6 + H - ( 2 , - 2 ) I They used the known Arrhenius expressions f o r k_ 2 and f o r k 2 / k| in conjunction w i t h values of A H " 2 & N D ^ S " at 550 K to c a l c u l a t e the Arrhenius expression f o r the combination r a t e constant: kj_ = 10 9 * 2 exp ( -3000 / RT ) 1 mole 1 s e c 1 7 _1 _ i which has the value of 8 x 10 1 mole sec at 550 K . To allow f o r the u n c e r t a i n t y i n the thermochemistry and the Arrhenius 8 -1 -1 parameters, they rounded t h i s value o f f to 1 x 10 1 mole sec at 550 K . The second system comprised the r e a c t i o n s : 2 C 2 H ^ « CkE1Q ( 1, - 1 ) C 2 H ^ z=± C2\ + H - ( 3, - 3 ) The value of k ^ i s known at 2 9 8 K and the Arrhenius expression i f o r k" / k| has been evaluated from the corresponding values of k^ / k| over the range 670 - 770 K. Marshall and P u r n e l l evaluated the Arrhenius expression f o r k^ u s i n g the values of A H ^ and A a t 550 K , which i s an approximate mean between the two experimental ranges; f u r t h e r c a l c u l a t i o n y i e l d e d the value 8 — 1 1 of 2 . 5 x 10 1 mole sec f o r the r a t e constant f o r combination of e t h y l r a d i c a l s . Such r e s u l t s are i n good general agreement w i t h the r e s u l t s obtained by the technique of butane p y r o l y s i s and the r a d i c a l b u f f e r method; however the two l a t t e r techniques should have the higher p r e c i s i o n and t h e i r r e s u l t s should be regarded as d e f i n i t i v e f o r the methods which are not absolute. In c o n c l u s i o n t h e r e f o r e we f i n d a ba s i c discrepancy between - 135 -the two sets values of the r a t e constant f o r the combination of e t h y l r a d i c a l s : those which are measured by absolute methods, those which are not. (3) The combination and d i s p r o p o r t i o n a t i o n of e t h y l r a d i c a l s . (a) General p r i n c i p l e s The mutual i n t e r a c t i o n of e t h y l r a d i c a l s comprises both combination and d i s p r o p o r t i o n a t i o n : 2 CK^CHg - — * CH3CH 2CH 2CH 3 ( k c ) 2 CH 3CH£ * CH C H 3 + GHg = CH 2 ( k d ) The commonly accepted value f o r the r a t i o k^ / k c i s 0.14(56,57)» This value i s r e l a t i v e l y i n s e n s i t i v e to change of r e a c t i o n temperature, so that E^ - E c s= 0 ( 56 ). Moreover, i t i s g e n e r a l l y accepted that E C ~ 0 , as s t a t e d i n Section A . 2.a.v, and t h i s r e s t r a i n t has been widely used i n the i n t e r p r e t a t i o n of the r e s u l t s of the i n d i r e c t methods f o r the measurement of k c, discussed i n Section A . 2.b. Consequently E^ 0 a l s o . The value of k^ / k Q, and i t s v a r i a t i o n w i t h temperature, may be obtained by a n a l y z i n g the products. Such experiments are u s u a l l y conducted i n the gas phase, using gas chromatography as the a n a l y t i c a l method. (b) Energies of a c t i v a t i o n . The d e t a i l e d mechanism of combination and d i s p r o p o r t i o n a t i o n has been the subject of much controversy. One group of workers has proposed t h a t the t r a n s i t i o n s t a t e s f o r combination and d i s p r o p o r t i o n a t i o n must be very s i m i l a r , and t h a t the o v e r a l l i n t e r a c t i o n may be treated as a four-centre r e a c t i o n ( 43,58 )• - 136 -Another group has argued that the two transition states are not similar, but that both possess pronounced ionic character ( 59 )• However, no comprehensive Interpretation has yet arisen from these discussions ( 60 )• In the absence of a fundamental theory, a search i s made for an empirical relationship which w i l l satisfactorily correlate the f u l l range of experimental data in the f i e l d in question. The most promising empirical relationship in the f i e l d of the mutual interaction of alkyl radicals appears to be a linear dependence of log ( k d / k c ) upon S£ - S£, the difference in the entropies of the products of disproportlonation and combination respectively. If this relationship was s t r i c t l y obeyed, i t would follow that the corresponding difference in the energies of activation, - E c, should have a common value for a l l alkyl radicals. The points for most of alkyl radicals studied l i e close to the regression line drawn for this relationship, so that the difference E^ - E c has a common value for those radicals, and that common value may be zero ( 61 )• The ethyl radical belongs to this set. The value of E^ - E c could not be distinguished from zero in early studies conducted with small radicals, owing to three experimental d i f f i c u l t i e s : ( 1 ) a large degree of scatter among the data, ( i i ) a small temperature range of measurement, and ( i l l ) the d i f f i c u l t y of distinguishing a temperature dependence of k^ / k Q from concurrent changes in the reaction mechanism which may arise at higher temperature. These d i f f i c u l t i e s may be minimized by a careful choice of the - 137 -reacting system, and by extending the range of temperature well below room temperature. The ethyl radical has been the subject of successive studies which illustrate the remarks in the previous paragraph. The values of k d / k^ obtained by Kerr and Trotman-Dickenson from the photolysis of propionaldehyde showed no systematic variation over the range from 323 to 588 K ( 62 ). However, Held et a l i a , generating ethyl radicals by the mercury photosensitized decomposition of hydrogen in the presence of ethylene, reported that k d / k 0 increased with temperature in the higher temperature range from 513 to 593 K ( 63 ). Azoethane seemed to be a more satisfactory photochemical source for the generation of ethyl radicals, both in the gas phase and in solution. Dixon et a l i a used azoethane for experiments in the gas phase spanning the range from 208 to 317 K, and for experiments in a variety of solvents, spanning the range 82 to 358 K ( 64 ). They reported that the value of k^ / k c for the ethyl radical decreased as the temperature was increased, and that the results were consistent with the difference in energies of activation: E c - E d = 300 cal mole1. G l l l i s obtained the closely similar value: E c - E d = 290 t 30 cal mole1 from experiments with the |- radiolysis of ethylene-d^ in liquid methane over the range of temperature from 92 to 179 K ( 65 )• The most recent study, with the direct photolysis of ethylene followed by addition of hydrogen atoms to ethylene, was conducted by Hooper et a l i a ( 66 ), who reported that there was no systematic variation of the value of k d / k c over the range - 138 -_1 from 173 to 298 K, yielding the result E c - E d = 0 kcal mole . _ i We may conclude that E c - E^ < 0. 3 kcal mole . It seems very probable that E c = 0 for the mutual combination of ethyl radicals, so that E d ~ 0 for their mutual disproportlonation. Estimates of the value of k d / k c for the ethyl radical have been very numerous, and range from 0.09 to 0.15 ( 6 7 - 7 2 ) . following a c r i t i c a l assessment of these results by Back et a l i a ( 67 ), the value : ^ / k c = 0.14 has been adopted as the representative value with which the estimate of the current work w i l l be compared. - 139 -B, Experimental Method (1) General P r i n c i p l e s The apparatus and method are s i m i l a r to those used f o r the study of the mutual combination of methyl r a d i c a l s , which has been described i n Section B of Chapter 3. The p r i n c i p a l changes i n method were d i c t a t e d by d i f f e r e n c e s i n the absorption s p e c t r a of the a l k y l r a d i c a l s and i n the nature of the s t a b l e products. A p r e l i m i n a r y study of the absorption spectrum of the e t h y l r a d i c a l revealed a broad, weak abso r p t i o n i n the range from 2 3 0 to 2 6 0 n m , w i t h a maximum at or near 2 4 5 n m . The d i f f e r e n c e between t h i s absorption curve and the intense, narrow, bimodal absorption curve of the methyl r a d i c a l l e d to two major d i f f e r e n c e s i n technique. F i r s t , there i s no reason to doubt that the Beer-Lambert Law w i l l be v a l i d f o r the e t h y l r a d i c a l w i t h a band pass of 0 . l 6 n m , and the form of expression f o r the absorbance, A = E(A) [ C 2 H ^ ] 1, has been used f o r the k i n e t i c a n a l y s i s without f u r t h e r I n v e s t i g a t i o n . Secondly, the k i n e t i c a n a l y s i s of each experiment y i e l d e d a value of £(A)/k, where k i s the r a t e constant f o r the mutual combination of e t h y l r a d i c a l s and Is independent of the wavelength A used. Consequently a set of experiments at a s e r i e s of values of A y i e l d e d a corresponding s e r i e s of values of E(A)/k, and a p l o t of these values against A gave the form of the absorption spectrum of the e t h y l r a d i c a l . The absolute spectrum was obtained a f t e r product a n a l y s i s . The r e a c t i o n and reference - 140 -ve s s e l s were made of " Pyrex " and f i t t e d w i t h end windows " S u p r a s i l " quartz to transmit monitoring l i g h t i n the re g i o n of the absorption of the e t h y l r a d i c a l . Stray l i g h t from the ph o t o f l a s h was removed by the double gas f i l t e r c o n t a i n i n g c h l o r i n e and bromine. The p u r i f i c a t i o n of the e t h y l r a d i c a l source, azoethane, and of the moderating gases, has been described i n Section C.20 of Chapter 2. (2) K i n e t i c Measurements. E t h y l r a d i c a l s were generated by the f l a s h p h o t o l y s i s of azoethane: C2H5-N=N-C2H5 + hV *- 2 C 2 H 5 + N 2 ( 1 ) Argon or n-pentane was added to act as a moderating gas i n s u f f i c i e n t q u a n t i t y to prevent the temperature of the r e a c t i n g system from r i s i n g more than a few degrees above room temperature. Under these c o n d i t i o n s the only s i g n i f i c a n t r e a c t i o n s of the e t h y l r a d i c a l were mutual combination and d i s p r o p o r t i o n a t i o n : 2 C 2H^ * C^H 1 0 ( 2 ) 2 C2H"5 * C 2H4 + C 2H6 ( 3 ) A c c o r d i n g l y , the only s i g n i f i c a n t s t a b l e products of the p h o t o l y s i s were n i t r o g e n , ethene, ethane and n-butane, and t h e i r y i e l d s were measured i n each experiment. The mutual i n t e r a c t i o n of e t h y l r a d i c a l s i s of the second order. F o l l o w i n g the form of k i n e t i c a n a l y s i s described f o r the methyl r a d i c a l i n Section B.2.b of Chapter 3> we o b t a i n the analogous expression f o r the - 141 -absorbance A(A) of the e t h y l r a d i c a l at a wavelength X: - i - g . 1 + A W E W C o l l | E U ) / T where k = k 2 + k^, and C 0 i s the h y p o t h e t i c a l c o n c e n t r a t i o n of the e t h y l r a d i c a l at time zero. This equation p r e d i c t s t h a t a p l o t of 1/A(A) agai n s t time should be l i n e a r w i t h a gradient equal to 2 k / £ ( A ) l . A c c o r d i n g l y , the method of l e a s t squares was used to f i t a s t r a i g h t l i n e to the appropriate data of each experiment, and to evaluate k/£(A) and i t s standard d e v i a t i o n . The r e s u l t s were used to p l o t the r e l a t i v e a b s o r p t i o n spectrum of the e t h y l r a d i c a l , Figure-4.1. ( 3 ) The measurement of absolute values of E(X) and k. Absolute values of 6(A) were c a l c u l a t e d by combining two sets of data from each experiment: ( i ) the y i e l d s of the s t a b l e products, and ( i i ) the h y p o t h e t i c a l value t h a t the absorbance of the e t h y l r a d i c a l would have i f a l l the e t h y l r a d i c a l s formed were simultaneously present i n the r e a c t i o n v e s s e l . This h y p o t h e t i c a l absorbance was c a l c u l a t e d by an e x t r a p o l a t i o n procedure which has been described i n Section B.2.C of Chapter 3« The measurement of the y i e l d s of the stable products was more elaborate than i n the methyl r a d i c a l system, because an estimate of k^/k2 was a l s o r e q u i r e d . The products were separated i n t o two f r a c t i o n s by f r a c t i o n a l d i s t i l l a t i o n under vacuum, and the number of moles of each f r a c t i o n was estimated by measuring pressure i n a known volume w i t h a c a l i b r a t e d McLeod gauge. The f i r s t f r a c t i o n was - 1 4 2 -n i t r o g e n , which w a s i s o l a t e d when the products were held at 73 K i n a bath of l i q u i d n i t r o g e n cooled by a stream of helium gas. The second f r a c t i o n comprised ethane and ethene, and was i s o l a t e d by r a i s i n g the temperature of the remaining products to 1 1 2 . 5 K i n an isopentane s l u s h bath. The t h i r d f r a c t i o n contains n-butane, which was d i f f i c u l t to separate from the moderating gas n-pentane, because the vapour pressures of these alkanes i a r e very c l o s e each other. Therefore the y i e l d of n-butane was c a l c u l a t e d as N 2 - ( C 2 H 4 + C2R"6 ), using the y i e l d s of the f i r s t and second f r a c t i o n s . The vapour pressures of these products at the r e l e v a n t temperatures are l i s t e d i n Table - 4 . 3 and these values were used to make minor c o r r e c t i o n s f o r the contamination of a given f r a c t i o n by small amounts of the c o n s t i t u e n t of another f r a c t i o n . The t o t a l y i e l d of e t h y l r a d i c a l s from a given experiment may be c a l c u l a t e d from the y i e l d of n i t r o g e n . In conjunction w i t h the e x t r a p o l a t e d value of the corresponding absorbance, t h i s y i e l d allowed the c a l c u l a t i o n of £(A). F i n a l l y a set of values of k was c a l c u l a t e d from the products of the corresponding values of 8(A) and k/£(x). Table-4.3 The vapour pressures of i n d i v i d u a l products at the r e l e v a n t temperatures Molecules Vapour Pressure ( m i l l i t o r r ) 73 K Helium Stream 77 K L i q u i d Nitrogen 112.5 K Isopentane Slush N 2 448 ( t o r r ) C2Hk 9-1 x 10" 1 3.14 C 2 H 6 1.2 x 10"1 4.6 x 10" 1 C 4 H 1 0 1.1 x 10"6 1.7 x 10" 1 C5 H12 ( n-pentane ) 4.8 x 10~ 3 - 144 -C, Re s u l t s . (1) Values of 6(A)A The r e s u l t s of the k i n e t i c measurements were assumed to conform to the second order r e l a t i o n s h i p : - L _ . 1 - g f J U t A W E W C o l l l E W r The corresponding numerical a n a l y s i s of the data from each experiment y i e l d e d a value f o r k/£(A) and a standard d e v i a t i o n was c a l c u l a t e d f o r each set of experiments. Two sets of experiments were performed, each with a band pass of 0.16 nm. The more comprehensive set allowed the separate e v a l u a t i o n of both E(A) and k from supplementary measurements of the y i e l d s of n i t r o g e n . These measurements spanned the more r e s t r i c t e d range of wavelength from 237-5 to 250 nm. The concentrations of azoethane and n-pentane were 5-46 x 10^ -3 -1 and 1.91 x 10-^  mole 1 r e s p e c t i v e l y . The r e s u l t s are presented i n Tables-4.4 and 4.7 and i n Figures-4.1 and 4.2. A more extensive s e r i e s of experiments y i e l d e d the r e s u l t s presented i n Table-4.5 and i n Figure-4.1 as a p l o t of 10 £(A)/k a g a i n i s t A, and therefore as a r e l a t i v e a b s o r p t i o n spectrum. The a n a l y s i s of the products was not attempted, so that absolute values of E(A) could be derived only i n d i r e c t l y . In these experiments the concentrations of azoethane and argon were 5.46 x 10^—4.59 x 10** and 6.01 x 1 0 3 ~ l . l 6 x 10 2 mole I 1 r e s p e c t i v e l y . - 1 4 5 -Table - 4 . 4 Values of the extinction coefficient and the rate constant for the mutual interaction of ethyl radicals, measured near maximum absorption Expt Mo. 1 H-122-A Photoflash Energy , Mixture « 1080 J ( « Et2N2« n-CjH]^ 12 xV, 7-5 )iF ) = 10 . 35 Wavelength nm 10"7 k / E(A) cm s e c - 1 A(A) 1 mole'^cm-1 10- 1 0 k 1 • o l e - 1 s e c ~ 1 237-5 2.92 ± 0.05 0.074 328 O.960 3.3* - 0.07 0.078 346 1.15 240.0 3-97 i 0.14 0.094 417 1.65 4.25 t 0.12 O.O99 439 •1.87 3.65 ± 0.10 0.100 444 1.62 242.5 3.47 + 0.14 O.O96 426 1.48 2.27 i 0.37 0.092 408 •0.925 2.70 i 0.07 0.098 435 1.17 2.35 i 0.07 0.090 399 0.937 245.0 3.^6 i 0.10 0.103 *57 1.63 3-24 • 0.14 0.103 457 1.63 2.74 t 0.08 O.O96 426 1.17 3-5* - 0.11 0.109 483 1.71 247.5 3-18 t 0.20 0.107 *75 1.51 3-35 i 0.16 0.109 483 1.62 3-*2 t 0.13 0.108 479 1.64 250.0 2.97 i 0.12 0.091 404 1.20 3.55 ± 0.12 0.102 452 1.61 mean value » x = ( 1.41 t 0.26 ) x 10 1 0 1 • o l e - 1 sec' 1 of 16 measurements above. Mote 1 These two values (*) were neglected. o - 146 -Table-4.5 Values of E(X) / k for the mutual interaction of the ethyl radicals Wavelength 10U £(A) / k sec cm"1 nm H-90-A H-97-A H-98-A H-99-A 220.0 - 6.37 - _ 222.5 - - - -225.0 5.66 7.23 4.83 227.5 - - 1.47 1.32 230.0 1.84 2.11 2.65 2.20 232.5 - 2.55 3.16 3-16 235.0 3-58 3.06 3.49 3.40 237.5 - 3.35 3.69 3.70 240.0 4.00 3-71 3-89, 4.03 4.36, 3.96 242.5 - 3.83 3.02 3.58 245.0 3.91 3.32 3.24 3.70 247.5 - 3.24 3.20 3.53 250.0 7-57 3.00 1.90 3-14 252.5 - 2.11 3.52 2.71 255.0 1.97 2.53 2.09 2.48 257.5 - 1.78 1.00 1.22 260.0 1.12 2.ia 0.32 1.18 Note 1 These are representative data, but this is not a complete l i s t of a l l the results. - 147 -Figure-4.1 The relative and normalized absorption spectrum of CH-,CR\X - 148 -Figure-4.1 i n d i c a t e s that the absorption spectrum of the e t h y l r a d i c a l i s broad and s t r u c t u r e l e s s , w i t h a maximum near 243 nm. D i r e c t measurements of presented i n Figure-4.2, show that the maximum probably l i e s c lose to 247 nm. However, the value of £(243)/k, estimated at 243 nm by i n t e r p o l a t i o n from -8 the curve f i t t e d to the po i n t s of Figure-4.1, i s 3-75 x 10 sec cm 1, i n reasonable agreement with the corresponding value of Q -I ( 4.13 t 0.17 ) x 10 sec cm obtained by Parkes and Quinn ( 39 ). An absolute absorption spectrum can be derived from these r e s u l t s by m u l t i p l y i n g each by the value of k = 1.41 x 1 0 1 0 1 mole 1 s e c 1 g i v e n i n Table-4.4; the r i g h t hand ordinate of Figure-4.1 provides the scale of the values of £(X). The mean of the values of k/£(A) measured at 245 and 247.5 nm, i s gi v e n by k/£ = ( 2,9 i 0.22 ) x 10'cm sec , which i s based 1 upon 7 measurements. This was c a l c u l a t e d from the corresponding r e s u l t s of Table-4.5, and i s r e q u i r e d f o r the summary of data i n Table-4.9 of Section D. (2) The d i s p r o p o r t l o n a t i o n : combination r a t i o The a n a l y t i c a l r e s u l t s on the y i e l d s of st a b l e products are l i s t e d i n Table-4.6. The i n i t i a l c oncentrations of azoethane l a y between 5.46 x 10^ and 4.91 x 10^ mole l 1, and the percentage of t o t a l decomposition of azoethane l a y between about 2.5$ and 0.80 %. According to the r e a c t i o n mechanism: k 3 / k 2 = [ c 2 H j / [ C 4 H 1 Q ] - 149 -Table-4.6 Values of the disproportionationi combination ratio Photoflash energyi 1080 J ( 12 kV, 7-5 >iF ) Exp No. Mixture ( No. of Flashes ) Pressure of Products m i l l i t o r r C2 H4 TH— ratio C4 H10 H-233-A Et 2 N 2 . n-C 5H 1 2 » 10 i ?0 ( 20 ) N 2 = 249 C2 H4 + C2 H6 = * 7 ' 6 3 C^H 1 0 = 201 0.118 H-235-A Et 2 N 2 i n-C^H12 - 10 t 240 ( 30 ) N 2 = 77.02 C2H^ • C 2H 6 * 16.43 C4 H10 = 6 0 ' 6 0.136 H-236-A E t 2 N 2 , n-C 5H 1 2 = 10 « 230 ( 40 ) N 2 = 114.1 CgH^ + C 2H 6 = 25.67 C „ H 1 0 - sa.4 0.144 H-237-A Et 2 N 2 i n—C^H^2 » 9 i 220 ( 30 ) N 2 = 71.63 C2H^ + C 2H 6 = 16.82 C 4H 1 Q = 54.8 0.153 H-240-A E t 2 N 2 i n-C^H12 = 9 i 60 ( 20 ) N 2 » 249.0 C 2H 4 • C 2H 6 = 54.97 V10 = 1 9 4 0.142 mean value of C-H.. / C kH i r, ratio 1 0.139 t 0.013 - 150 -and the values of k^ / kg in the fin a l column were calculated on the assumption that [CgH^J = [CgH^] Statistical analysis yielded the mean value: k^ / k 2 = 0.139 t 0.013 in f u l l agreement with the accepted value of 0.14 ( 67 )• (3) The rate constant for mutual combination, kg Values of the rate constant k were calculated from the product of corresponding values of k/£(A) and £(A) given in Table-4.4. The two extreme values of k were rejected on st a t i s t i c a l grounds, and numerical analysis of the remaining 16 values gave the result: k = ( 1.41 t 0.26 ) x 1 0 1 0 1 mole1 sec 1 The correlation coefficient between the value of k and the wavelength at which the measurement was made is 0.15, indicating that these quantities are independent and supporting the validity of the experimental procedure. Using the result k^ / kg = 0.14 we have kg / k = kg / ( kg + k^ ) =0.88, so that kg = ( 1.24 t 0.23 ) x 1 0 1 0 1 mole1 sec 1 (4) The absorption spectrum of the ethyl radical. The total yield of ethyl radicals was calculated from the yields of the products, and the corresponding absorbance from the extrapolation procedure described previously. These results allow the calculation of the set of values of £"(A) listed in - 151 -Table-4.7 The extinction coefficient of the ethyl radical at various wavelength Wavelength nm 1 E(X) •ole^cm - 1 Interpolated value 1 •ole'^cm-1 234.0 303 265 235.0 292. 271 295 236.0 315 320 237.0 354 345 237.5 329. 3*6 355 238.0 373 370 239.0 393 390 240.0 377. 417, 3*2, 440, 444 415 241.0 366 430 242.0 432 445 242.5 426, 408, 435. 399 *55 243.0 475 460 244.0 467 470 245.0 *63, 457. *57. *26. 483 475 246.0 478 480 247.0 478 *75 247.5 *75, 483, *79 *75 248.0 510 473 249.0 432 458 250.0 428, 404, 452 442 251.0 418 420 252.0 403 400 253.0 385 385 254.0 371 360 255.0 335. 330. 348 340 Note 1 Table-4.7 Includes a l l the results of Table-4.4 and some others. - 152 -Figure-4.2 The absorption spectrum of the ethyl radical X ( n m ) Table-4.7 and p l o t t e d i n Figure-4.2 as an absolute absorption spectrum. Each i n t e r p o l a t e d value i n Table-4.7 was obtained from the smoothed curve f i t t e d to the po i n t s i n Figure-4.2. The absorption spectrum of Parkes and Quinn was a l s o p l o t t e d f o r comparison i n Figure-4.2,<after n o r m a l i z a t i o n using t h e i r v a l u e s : Xmax = 248 nm and £max = 330 1 mole 1 cm 1, and the corresponding values of £(X) are l i s t e d i n Table-4.8. Each r a t i o of the values obtained i n t h i s work and by Parkes and Quinn f o r the e x t i n c t i o n c o e f f i c i e n t at each wavelength i s al s o l i s t e d there. The mean value of t h i s r a t i o i s 1.68 ± 0.26 i n the range 235 "to 255 nm, so that the standard d e v i a t i o n i s about 15 % of the mean value. I f the data at 235 and 255 nm are r e j e c t e d because a large e r r o r a r i s e s from the small absorption, then the mean value i s 1.57 - 0.15 i n the range 238 to 253 nm, so that the standard d e v i a t i o n i s about 10 <fc of the mean value. The two estimates of the ab s o r p t i o n spectrum of the e t h y l r a d i c a l presented i n Figure-4.2 are therefore i n good q u a l i t a t i v e agreement i n respect of the p o s i t i o n of the maximum and the breadth and general o u t l i n e , but d i f f e r c o n s i s t e n t l y i n the absolute magnitude of the e x t i n c t i o n c o e f f i c i e n t . A comparison of Figures-4.1 and 4.2 r e v e a l s minor d i f f e r e n c e s i n the p o s i t i o n of the absorption maximum and i n the estimate of the maximum value of £. The data of Figure-4.2 w i l l be taken as d e f i n i t i v e , as they were obtained by d i r e c t . measurement. In c o n t r a s t , values of £(X) can be derived from the data of Figure-4.1 only by m u l t i p l y i n g i n d i v i d u a l values of E(A)/k from one set of measurements by a mean value of k derived i n d i r e c t l y from another set of measurements, and t h i s i s c l e a r l y Table-4.8 A comparison of values of the absorption coefficient of the ethyl radical as measured in this work and as reported by Parkes and Quinn Wavelength £(A) 1 mole- 1cm _ 1 Ratio _ ( T h i s W 0 r k > nm This work Parkes & Quinn ( P 4 Q ) 235 295 143 2.06 238 370 204 1.81 241 428 274 1.56 243 460 306 1.50 246 480 328 1.46 248 473 330 1.43 250 442 305 1.45 253 385 220 1.75 255 340 162 2.10 mean v alue 1.68 + 0.26 Note • Parkes and Quinn's values ( A m a x • 2 * 8 £ B a x " 3 3 0 1 •o16""''0""1 > were used to normalise the absorption spectrum of Figure-2 i n their reference ( 39 )• - 155 -a less accurate procedure. Therefore, the direct measurement gives the value of E m a x of 480 1 mole1 cm1 by interpolation from the curve fit t e d to the points of Figure-4.2, and by simply multiplying individual values of E(A)A by the indirect measurement gives the value of E m a T of 520 530 1 mole cm1 by interpolation from the curve fit t e d to the points of Flgure-4.1. - 156 -D, D i s c u s s i o n The measure of agreement between the r e s u l t s of t h i s i n v e s t i g a t i o n and those obtained by Parkes and Quinn may be assessed from Table-4.9 and Figure-4.2. C l o s e s t agreement i s found i n the values of kg/£(Amax): the present work y i e l d s the mean value: kg/E(247) = 2.5 x 10' cm sec , whereas Parkes and 7 — 1 Quinn obtained the mean value: kg/EC248) = 2.4 x 10'cm sec . These r e s u l t s are i n good agreement i f we estimate that the standard d e v i a t i o n i s one f i f t h of the mean value of each estimate. This agreement i s s i g n i f i c a n t because k/£(A) i s estimated d i r e c t l y from the gradient of the p l o t of the r e c i p r o c a l of absorbance against time i n t h i s work, whereas the separate values of kg and £ are obtained only w i t h t h e _ a i d . o f " supplementary experiments. In r e l a t i o n to the c h a r a c t e r i z a t i o n of the absorption spectrum i n the gas phase, agreement i s e x c e l l e n t at the q u a l i t a t i v e l e v e l of l o c a t i n g the p o s i t i o n of the maximum and est i m a t i n g the approximate h a l f width of the absorption band. At the q u a n t i t a t i v e l e v e l we may expect the standard d e v i a t i o n of each value of Emax to be at l e a s t 0.2 Emax ( by analogy w i t h the corresponding values of kg ); then the two estimates of Emax do not d i f f e r s i g n i f i c a n t l y . The absorption spectrum of the e t h y l r a d i c a l i n aqueous s o l u t i o n was described by H i c k e l ( 28 ), who reported that the i n t e n s i t y increased monotonically as the wavelength was reduced from 270 to 200 nm, without passing through a maximum. However, h i s values of the e x t i n c t i o n c o e f f i c i e n t at 240, 245, 250 and Table-4.9 Spectral and kinetic characteristics of the ethyl radical Authors A max nm nm cEmax -1 -1 1 mole cm *2 -1 -1 1 mole sec k2 ^ Emax -1 cm sec Parkes and Quinn 24b" 20 3 - 3 ac 10 2 ( d i 2 ) x 10 9 2.4 x 10 7 This work 247 25 4.a x 10 2 ( 1.2 ± 0.2 ) x 10 1 0 2 . 5 x 10 7 - 158 -255 nm are r e s p e c t i v e l y 450, 400, 350 and 300 1 mole 1 cm 1, and l i e f a i r l y c l o s e to the corresponding value of 417, 457. 428 and 335 1 mole 1 cm 1 obtained i n t h i s work. The apparent continued increase i n the value of the e x t i n c t i o n c o e f f i c i e n t observed by H i c k e l as the wavelength i s reduced below 248 nm may be due to an unsuspected absorbing species i n h i s s o l u t i o n s . Values f o r the r a t e constant kg f o r the mutual combination of e t h y l r a d i c a l i n the gas phase of ( 1.2 - o.2 ) x 1 0 1 0 and ( 0.8 - 0.2 ) x l O 1 ^ 1 mole 1 s e c 1 were obtained i n t h i s work and by Parkes and Quinn r e s p e c t i v e l y . These r e s u l t s do not d i f f e r s i g n i f i c a n t l y , and may be s a i d to be i n agreement w i t h a value , , -.10.0 . , -1 -1 of kg = 10 1 mole sec . Indeed both values l i e c l e a r l y i n the set of " high " estimates f o r kg obtained i n the four d i r e c t methods l i s t e d i n Table-4.1. This agreement emphasises the disagreement between 10 0 the r e s u l t s of the methods, which are c l u s t e r e d about 10 ' 1 mole 1 s e c 1 , and the r e s u l t s of the i n d i r e c t methods, which are 8 4 - 1 - 1 c l u s t e r e d about 10 ' 1 mole sec . Reference has been made i n Section A.2 to the d i s c u s s i o n given by Golden, Choo, Perona and P i s z k i e w i c z on t h i s t o p i c i n 1976; since that date no new r e s u l t s have appeared that would serve to r e c o n c i l e t h i s disagreement. Accordingly i t seems to be reasonable to p r e f e r the r e s u l t s of the d i r e c t methods and to adopt a value of l O 1 ^ ' ^ 1 mole 1 sec as r e p r e s e n t a t i v e of our present knowledge of the r a t e constant of the mutual combination of e t h y l r a d i c a l s . - 159 -CHAPTER 5 THE MUTUAL INTERACTION OP METHYLPEROXY RADICALS A, Introduction (1) The absorption spectrum of the methylperoxy radical. The methylperoxy radical Is recognized as one of the principal chain carriers in the mechanism of the combustion of methane in air or oxygen. This oxidation is initiated by metathesis between oxygen and methane: C % + 0 2 - QEj + H00* The methyl radical is another principal chain carrier, and reacts rapidly with the oxygen molecule to form the methylperoxy radical: CH^ + 0 2 + M CH300*+ M The kinetic study of this oxidation would be simplified i f the absorption spectrum of the methylperoxy radical were characterized. Parkes, Paul, Quinn and Robson generated the methylperoxy - 160 -radical by the photolysis of azomethane in the presence of oxygen and a large excess of argon or nitrogen: CH3-N=»N-CH3 + hv 2 CH* + N 2 GH3 + 0 2 + M CH300*+ M and searched for the speotrum in the middle ultaviolet using the technique of molecular modulation spectrometry ( 73 ). They discovered a broad absorption band extending from 210 to 280 nm, they estimated that maximum absorption occurred at 240 nm - I 8 2 -1 with a molecular cross section er= 5*5 * 10 cm molecule , which i s equivalent to a molar decadic extinction coefficient £ = 1.44 x 10 D 1 mole cm ( 5 )• The decay of the absorbance of this band followed second order kinetics, suggesting removal by mutual interaction. Identical spectra were observed when methylperoxy radicals were generated by two other reactions; the photolysis of a mixture of di-tert-butyl peroxide and oxygen, and the photolysis of a mixture of acetone and oxygen ( 74 ). Parkes assigned this spectrum to the methylperoxy radical, and the decay of absorbance to the process: 2 CH^ OO* *• products Similar results were obtained by Hochanadel, Ghormley and Boyle from a study of the flash photolysis of azomethane in the presence of an excess of oxygen and of nitrogen at 295 - 2 K in 1977 ( 75 ). They observed a broad absorption band with a maximum at 235 nm which decayed according to second order kinetics. They estimated the extinction coefficient of the - 161 -methylperoxy radical by relating i t s absorption, extrapolated to the peak of the flash, to the consumption of azomethane, measured by a spectrophotometer. This method gave the value: £ ( 235 ) - 870 1 mole1 cm1, which i s only 60 % of Parkes's value, but otherwise the spectra are qualitatively similar. A broad, weak absorption band was observed by Calvert et a l i a in their study of the flash photolysis of azomethane In the presence of oxygen ( 76 ). Their results d i f f e r in placing the maximum at 254 nm with an extinction coefficient of 34-5 1 mole1 -1 cm . The absorption spectrum of the methylperoxy radical in aqueous solution was characterized by Hickel in 1975 ( 28 ) . The radicals were generated by the radiolysis of an aqueous solution of methane, oxygen and nitrous oxide. The solution was irradiated with a single 11-Mev electron pulse. Irradiation of water generates electrons, hydroxyl radicals and hydrogen atoms: H 20(1) — — H 2 0 + ( a q ) + e"(aq) H 2 0 + H +(aq) + OH*(aq) e-(aq) + H 20(1) - H*(aq) + OH~(aq) The hydrated electrons were scavenged by nitrous oxide ( NgO ) in solution: e"(aq) + N 20(aq) + H 20(1) *- N 2(aq) + 0H~(aq) + OH'(aq) This reaction suppressed the formation of hydrogen atoms in favour of the formation of hydroxy radicals. Methyl radicals were formed by the metathesis: OH'(aq) + CH^(aq) - H 20(1) + CH^(aq) - 162 -and subsequently react with dissolved oxygem CH^aq) + 0 2(aq) - CH^ OO'Caq) The formation of H00* radicals was minimized by the scavenging action of nitrous oxide, which suppressed the reactions: e"(aq) + 0 2(aq) ^ 0 2"(aq) H+(aq) + 02"(aq) - HOO*(aq) H'(aq) + 02(aq) ^HOO'(aq) The absorbance of the system was observed at 10 nm intervals between 210 and 310 nm, and was corrected for absorption by the hydroperoxyl radical. The resulting spectrum had a maximum at 3 -1 250 nm with an extinction coefficient of about 1.1 x 10^ 1 moleA cm1 which was independent of the pH of the solution between pH 4 and pH 10. It was thereby distinguished from the spectrum of HOO(aq), which varies with pH over this range because pK_ = 4.8 for the hydroperoxyl radical. The spectrum of CH-jOO*(aq) i s therefore similar in intensity distribution to the spectrum of CH-jOO*(g) described by Parkes, except for a 10 nm shift in the position of the maximum. Bennett and Parkes have observed a spectrum of the methylperoxy radical in cyclohexane solution with a maximum at the same wavelength as that observed in aqueous solution ( 77 ). (2) The mechanism of photooxldatlon of azomethane. A comprehensive mechanism for the photooxldatlon was proposed by Parkes in 1977 ( 5 ) and is given in a slightly modified form as Table -5 .1 . This mechanism w i l l be used as a - 163 -basis for the discussion of the kinetics of the generation and consumption of the methylperoxy radical. The value of certain of the rate constants i s in dispute, and a c r i t i c a l assessment of the published date is given in the next section. (3) Values of rate constants used in the computer programmes. (a) Assessment of existing data. Computer programmes were written to study the kinetic behaviour attending the generation and subsequent reactions of the methylperoxy radical, and to evaluate the rate constant k .^ Accordingly, values were required for the rate constants of reactions ( 2 ) to ( 12 ) in Table - 5 . 1 . Unfortunately, accurate values are available for only a few of these reactions. For some of the others, the estimates span a wide range of values. For the rest, the estimates either were obtained by a very indirect method, or were purely conjectural. The available estimates w i l l be reviewed for the rate constant of each reaction of interest, and a value selected for the programmes. (b) Mutual interactions. (i) 2 CH^ »• CgH^ ; k 2 = 3.2 x 1 0 1 0 1 mole1 sec 1 This is the value obtained in this work and discussed in Section C.l of Chapter 3. 9 -1 -1 ( i i ) 2 HOC *- HOOH + 0 2 ; k 1 2 = 2 x 10 7 1 mole1 sec This value was selected by Lloyd in 197^ ( 13 )» after a c r i t i c a l assessment of the published results in Table -5 .2 . ( i l l ) 2 OH^ OO* a l l products ; ^ s 3,5 1 10 1 mole sec The contributing reactions are: - 164 -Table-5.1 The mechanism of the photooxidation of azomethane CH^-N-N-CH^ + hv — *• 2 CH 3 • N 2 (1) 2 CH^ ~ C 2 H 6 (2) CH^ • 0 2 + M — - CH^OO* + M (3) 2 CH^OO* — 2 c H y r • o 2 (4a) »- CH3OH + CH 20 + 0 2 (4b) - CH3OOCH3 • 0 2 (4c) CH^ + CHyxr — 2 CH30* (5a) - CH3OOCH3 (5b) CH-jO* + CH-jOO* — * CH~3OOH • CH 20 (6) 2 CH^O • - CH3OH • CH 20 (7a) «- CH3OOCH3 (7b) CH^ + CH 3 0 # — CH^ • CH 20 (8a) - CH 3 0CH 3 (8b) c H y r • o 2 CH 20 • HOO* (9) CH^OO* • HOO* — - CH3OOH + 0 2 (10) CH^O* * HOO* — CH3OH + 0 2 (11) 2 HOO* - HO OH + 0 2 (12) CH^O* + H 2C0 — CH3OH • HCO (13) HCO • ° 2 ; CO • HOO* (1*) Table-5.2 Recent values of k-^ for the mutual interaction of hydroperoxyl radicals Authors Year Method Temp K k12 1 mole" 1sec~ 1 Ref. Burgess and Robb 1957 mercury photosensitized reaction of H 2 • 0 2 I temp.rise of system 293 to 319 6.5 x 10 1 0 78 Poner and Hudson 1962 e l e c t r i c a l discharge through H 20 2 » mass spectrometry. 300 1.8 x 109 79 Paukert and Johnston 1972 photolysis of H 20 2i molecular modulation spectrometry 298 ( 2.2 i 0.3 ) x 109 60 Hochanadel Ghormley and Ogren 1972 flash photolysis of H20 • H 2 • 0 2 i ultraviolet spectrometry 298 ( 5-7 i 0.5 ) x 109 81 - 166 -2 CH300* 2 CH30* + 0 2 ( 4a ) 2 CH300* CH3OH + CH20 + 0 2 ( 4b ) 2 CH300' CH3OOCH3 + 0 2 ( 4o ) The fraction of nonterminating interaction i s : f = *4a / < k4a + k4b + k4o ) The value of k^ given above represents the output rather than the input of the principal computer programme of this chapter. However, a value of k^ is used in another programme which estimates the fraction of methyl radicals that react with oxygen to yield methylperoxy radicals under various conditions. The published values of k^ are l i s t e d in Table-5«3» (iv) 2 CH30* a l l products ; k 7 = 1 x 10 1 0 1 mole1 sec 1 The contributing reactions are: 2 CH3C- • CH3OH + CH20 ( 7a ) 2 CH30' CH3OOCH3 ( 7b ) The value above was chosen to represent the wide range of experimental values. No direct measurement of the rate oonstants of these reactions has been published. The values l i s t e d below are derived Indirectly from pyrolytlc studies either of dimethyl peroxide or of methyl n i t r i t e with the aid of thermochemical calculations. In Chapter-4 the results of similar indirect estimates of the rate constant for the mutual combination of ethyl radicals in the system: Table-5-3 Recent values of k^ for the mutual interaction of methylperoxy radicals Authors Year Method Temp K f *4 1 mole^sec""1" Ref. Shortrldge and Heicklen We aver,Meagher Shortridge and Heicklen 1973 1975 photooxidation of azomethane i product analysis 298 0.45 82 83 Alcock and Mile 1975 photooxidation of azomethane i n presence of 2,3-dimethylbutane i product analysis 373 O.49 4 . 7 x 10° 84 Parkes Parkes 1975 1977 photooxidation of azomethane using molecular modulation spectrometry! product analysis 29a 29a 0.33 (0.33) 2.3 x 1 0 a 2.8 x 1 0 8 74 5 Hochanadel, Ghormley, Boyle and Ogren 1977 flash photolysis of azomethane + 0 2 1 kinetic spectroscopy 295 - ( 2.3 * 0.4 ) x 1 0 8 85 Anastasi Parkes and Smith 1977 flash photolysis of azomethane and 0 2 » kinetic spectroscopy 29a - ( 2.6 1 0.4 ) x 1 0 8 86 - 168 -2 G2E'5 - tt-C4H10 were found to be in conflict with the directly measured value. Furthermore the value of k^ a / was given as 10 by Heicklen and Johnston in 1962 ( 94 ), as 8 . 9 by Shortrldge and Heicklen in 1973 ( 82 ), and as 60 by Dever and Calvert in 1962 ( 95 ), whereas kr,b / k^ was given as zero by Weaver, Shortrldge, Meagher and Heicklen in 1975 ( 83 ); these values were c r i t i c i z e d by Batt and McCulloch in 1976 ( 90 ). The absence of a reliable value of for k«7a / k-j>D is especially unfortunate, as the principal studies have yielded a value for k ^ only, and the values of k-pa in the table below have been calculated using k 7 a / k7b = 1 0 l n t n e absence 0 a* an agreed estimate. The only exception is the work of Eremin et a l i a , which yielded k>pa directly. The selected value of 1 x 1 0 1 0 1 mole* sec 1 is identical with the value chosen both by Barker, Benson and Golden ( 9 2 ) , and by Selby and Waddington ( 93 ) for their computer studies. The values of k^ a and of kr,b are l i s t e d in Table-5.4. (c) Generation of the CH^ OO* radical . CH^ + 0 2 ( + M ) CH^OO* ( + M ) ; = ( 3 . 1 t 0.3 ) x 1 0 b 1 mole 1 s e c 1 . This value was obtained by Basco, James and James in 1972 ( 96 ). They applied the technique of flash photolysis and kinetic spectroscopy to a study of the photooxldatlon of azomethane in the presence of an excess of oxygen and of a moderating gas. Van der Bergh and Callear obtained the value: k 3 = 1.1 x 10 9 1 mole1 sec 1 in a similar study in 1971 ( 97 ) . Table-5.4 Recent estimates of k ? a and k ? b for the mutual interaction of methoxy radicals Authors Year Pyrolylic system Temp range K k7a 1 mole^sec1" lt7b 1 mole^sec 1 Ref. Kanst and Calverti Heicklen 1959 1968 dimethyl peroxide 109'« i o 8 ' a 87 88 Eremin et a l i a 1970 methyl n i t r i t e 1010.9 - 89 Batt and McCulloch 1976 dimethyl peroxide and isobutane 383 to 413 1011.3 1 0io.3 ± 0.5 90 Batt, Milne °and McCulloch 1977 methyl n i t r i t e and isobutanei methyl n i t r i t e and NO 440 to 473 443 to 473 91 Barker, Benson and Golden 1977 dimethyl peroxide 1 dimethyl peroxide and N02 391 to 432 10 1 0 • - 92 Selby and Waddington 1977 di-t-butyl peroxide and 0 2 410 10 1 0 • - 93 Notei * k„ = 10 i s an estimate used in the computer programme. - i ? o -Laufer and Bass used flash photolysis coupled with gas oo 9 - 1 chromatography and reported the value : k^ = 1.02 x 10 1 mole sec 1. However, this value was based upon the result : k 2 = 5«8 x 10 1 0 1 mole1 sec 1. A recalculation, based upon the result obtained in the present study, k 2 = 3.2 x 10 1 0 1 mole 1 -1 oo , a -1 -1 sec , gives the value: k^ = 5 » ° x 10 1 mole sec . Hochanadel et a l i a ( 75 ) used a flash photolysis technique and reported the value: k, = 1.3 i 10 7 1 mole sec . This rate constant, k-^ , is used only in the programme which estimates the fraction of methyl radicals which are converted to methylperoxy radicals by the reaction: CH^ + 0 2 - CH^OO' ( 3 ) The selection of the lowest estimate of k-j Imposes the severest conditions upon this test, (d) Generation of the H00* radical CH^O' + 0 2 - CH20 + HOO* ; ko. • 4 x 10^ 1 mole1 sec 1 This is based upon an extrapolation of the rate equation of Barker, Benson and Golden ( 92 ): log k 9 = ( 8.5 t 1.5 ) - ( 4.0 + 2.8 ) x 10 3 / 2.3 RT which is in reasonable agreement with most of the recent results in the Table -5 .5 . (e) Cross interactions of the CH^ OO* radical There are no direct experimental values for the rate constant of such interactions. Comparing the following reactions: Table-5-5 Recent values of k^ f o r the r e a c t i o n CH^O* • 0 o CHo0 + HOG' Authors If ear Method Temp. K k9 1 mole'^seo"1 Hef. Heicklen and Johnston Heicklen 1962 1968 photooxldatlon of CH-jI calculation from " i c / * ? ! = 2.0 x 10~2 1 mole*sec* 298 103'2 at 29a K 108-0 exp ( -6500 / RT ) 94 88 Johnston et alia 1970 1.2 x 106 98 Alcock and Nile 1975 photooxldatlon of asomethane in presence of 2,3-dimethyl butane 373 1.2 x 106 84 Heicklen et allai Batt, Milne and McCulloch 1974 1977 photolysis of methyl nitrite pyrolysis of methyl nitrite and NO 4^ 3 to 4?3 106 99 91 Barker, Benson and Golden 1977 pyrolysis of dimethyl peroxide 1 dimethyl peroxide • N0 2 391 to 432 10«-5 * I-* .xP - ^ • 0 t 2 - a > " 1 ° 3 RT 3.8 x 105 at 298 K 92 Selby and Haddington 1977 pyrolysis of dl-t-butyl peroxide • 02 410 4.3 x 10** 93 Walker 1977 reevaluation of Aloock and Mile'8 work 373 1.9 x 106 4 - 172 -2 CH?j - C2H5 ; k2 = 3.2 i 1 0 1 0 1 mole1 sec 1 2 CH^ O* - a l l products ; a 1 x 10 1 0 1 mole 1 sec 1 2 CH-jOO* 0 2 + a l l other products ; 8 1 — 1 = 3.5 x 10 1 mole1 sec , i t i s clear that the methylperoxy radical i s associated with a comparatively low rate constant for mutual interaction. We may expect comparatively low values for the cross interactions of the methylperoxy radical, especially where oxygen is eliminated. (1) CH300« + CH30« • CH300H + H2C0 ; k£ = 9.2 x 10 8 1 mole 1 sec 1 Selby and Waddington ( 93 ) obtained the value Q 1 — 1 k^  =s 9.2 x 10 1 mole sec from a study of the pyrolysis of t-butyl peroxide in the presence of oxygen at 410 K, in which a computer programme was written to slmilate the course of the reaction. Shortridge and Heicklen obtained the relationship: k 6 = 0.31 ( k ? k^ a )* from a study of the photooxidation of azomethane at 298 K ( 82 ). Using the values: k 9 = 1 x 10 1 0 1 mole1 sec 1 and k^ a = 1.75 x 10 8 1 mole1 sec 1, we obtain: k^ = 4.4 x 10^ 1 mole1 sec 1. However Heicklen and Johnston ( 94 ) obtained the relationship: k 6 = 0.15 ( k ? k^a )* 8 —1 —1 8 yielding: k^ = 2.1 x 10 1 mole sec . The value k^ = 9.2 x 10 1 mole1 sec 1 has been selected to represent these results. - 173 -( i i ) CH 300' + HOC-' - CH3OOH + 0 2 ; 8 1 1 k 1 0 3 8 3*3 x 10 1 mole1 sec This selection gives k 1 0 ^  k^ « 1/ 3 k^ * 1/ 6 k i 2 , which seems reasonable. ( i l l ) CB^ OO* + CH3 a l l products ; k^ = 1 x 1 0 1 0 1 mole1 sec 1 The contributing reactions are: CH 300 # + CH3 2 GH30* ( 5 a ) CH 300* + CH3 CH3OOCH3 ( 5b ) CH 300' + CH^ CH 30H + CH 20 ( 5c ) Estimating k^ on purely s t a t i s t i c a l grounds, we would have: k^ = 2 ( k 2 k^ ) ^  = 7 x 1 0 9 1 mole1 sec 1 However, molecular oxygen i s eliminated in reactions ( 4 a ) , ( 4b ) and ( 4 c ), so that reactions ( 5a ) ( 5b ) and ( 5c ) bear a much closer resemblance to reactions ( 7 a ) and ( 7b )• Accordingly, we have placed: kcj = k^ = 1 x 1 0 1 0 1 mole1 sec 1 (f) Cross interactions of the CH30* radical. There are no direct experimental values for the rate constants of such reactions. The values given below are chosen in relation to the following reactions: 2 CH 3 C 2H 6 ; k 2 = 3 . 2 x 1 0 1 0 1 mole1 sec 1 - 174 -2 CH-jO' a l l products ; k^ = 1 x 1 0 1 0 1 mole1 sec 1 2 HOO* HOOH + 02 ; *i2 - 2 x 1 0 9 1 mole1 sec 1 C H 3 O C + HOO* CH3OOH + 0 2 ; 8 - 1 - 1 k 1 Q = 3 . 3 i 10 1 mole sec (1) CH^ O* + CH3 • a l l products ; kg = 2 x 1 0 1 0 1 mole1 sec 1 The contributing reactions are: CH^ O* + CH3 «- CH3OCH3 ( 8 b ) CH30# + C H 3 - CH^ + CH20 ( 8 a ) The simple cross combination rule yields the value: k Q a + k 8 b = 2 ( k 2 k 7 a 3 . 6 x 1 0 1 0 1 mole1 sec 1 These reactions resemble reaction ( 7 ) more closely than reaction ( 2 ), and accordingly the estimate is reduced i s : k Q a + k g b = 2 x 1 0 1 0 1 mole1 seo 1 = 2 k-p = 2 k^ ( i i ) CR^ O* + HOO" *• CH3OH + 0 2 ; k j ^ = 1 x 10 1 mole sec The selected value of k ^ = k 9 = 3 0 k^Q, reflecting the greater reactivity of the C^O* radical, and in general agreement with the assignments made by Selby and Waddington, (g) A comparison with the values selected by Parkes in 1977 ( 5 ). The principal differences occur in the following reactions, and Parkes*s values are in brackets: - 175 -2 C H 3 0 # CH3OH + C H 2 0 ; k 7 = 1 x 1 0 1 0 ( 2.1 x 1 0 1 0 ) 1 mole1 sec 1 C H 3 0 ' + CH3OO* - CH3OOH + C H 2 0 ; k 6 = 5 x 1 0 8 ( 6 x 1 0 8 ) 1 mole1 sec 1 C H 3 + C ^ O O * • 2 G H 3 0 * ; k 5 = 1 x 1 0 1 0 ( 3 . 6 x 1 0 1 0 ) 1 mole 1 sec 1 (h) Excluded reactions. ( 1 ) R « + H 2C0 • R H + H C O ; R « = C B ^ O O * , C ^ O ' and H O O * . Formaldehyde i s formed in reactions ( 4b ),( 6 ), ( 7 a )» ( 8 a ) and ( 9 ) and the C - H bond in the molecule i s comparatively weak: H 2C0(g) - HCO(g) + H(g) ; A H ° = 87 kcal mole1 Metathesis between formaldehyde and of the radicals C ^ O O ' , H00* and CH30 # would lead to a reaction sequence of the type: R ' + H 2 C O - R H + H C O ( 1 3 ' ) 0 2 + H C O H O C + C O ( 14 ) which would influence the course of the reaction i f i t s rate were significant. Values of the rate constant for the class of reaction represented by equation ( 13* ) are not known with any accuracy at room temperature, but estimates can be made. Vardanyan et a l i a ( 100 ) studied the reaction: H00* + H 2 C O H O O H + H C O ( 13h ) - 176 -over the range from 770 to 970 K and obtained the expression: k 1 3 h * 1.1 x 1 0 1 0 exp ( - 1 0 . 4 x 1 0 3 / RT ) 1 mole1 sec 1 =* 2 . 6 x 1 0 2 1 mole1 sec 1 at 298 K. No reliable experimental rate constants are available for abstraction reactions of ROO* radicals in the gas phase. However, applying a suggestion made by R.W.Walker In 1975 ( 3 ) to the rate of the reaction : CH 3 00' + H 2 C0 - CH 3C00H + HCO ( 13P ) i t is probable that E^ 3p«; E i 3 n 8 X 1 ( 1 A 1 3 p ^ A 1 3 h * Accordingly 2 - 1 - 1 k l 3 p 4 2 « 6 x 10 1 mole sec at 298 K, and the consumption of methylperoxy radicals by reaction ( 13p ) would have been negligible in the system used here. The value of A factor for the reaction : CH30* + H 2 C0 -CH3OH + HCO ( 13 ) 8 -1 - 1 may be estimated as 1 x 10 1 mole sec from the value 7 -1 - 1 A = 5 - 3 x 10 1 mole sec per primary C - H bond for metathesis between the C^O* radical and a hydrocarbon ( a )• -1 ^ - 1 - 1 If Ej3 « 3 . 0 kcal mole , then k 1 3 = 6 . 3 x lO-' 1 mole sec at 298 K. Considering the competition for CH-jO* radicals only between reaction ( 13 ) and reaction ( 9 )• CH 30* + 0 2 - CH20 + HOO* ; k Q = 4 x 10^ 1 mole1 seo 1 at 298 K, i t follows that the ratio of rates: R 1 3 / R 9 ^ 0 . 0 0 1 only i f [CH 3 0 # ] / [ 0 2 ] ^ 0 . 0 0 1 6 , so that reaction ( 13 ) may be considered as negligible in the present system. - 17? -( i i ) CH^ + 0 2 -H2CO + #0H ( 15 ) Basco, James and James reported that i s not much greater than 2 x 10^ 1 mole1 sec 1 in 1972 ( 96 ). A low value was confirmed by very low pressure pyrolysis studies in 1973 ( 101 ). In a very recent review ( 4 ) H.W.Walker has attempted to correlate results obtained in eight studies of the shook-initiated oxidation of methane. The points from four of these studies l i e close to an Arrhenius plot of the equation: k 1 5 = 1 0 9 ' 1 exp ( -12.7 x 1 0 3 / HT ) 1 mole1 sec 1, which extrapolates to 0.8 1 mole sec 1 at 298 K. An extrapolation from a range of temperature from 1200 to 2500 K to a temperature of 298 K is unlikely to give an accurate value, but the result obtained upholds the view that reaction ( 15 ) is negligible in the present study. A very different Arrhenius expression was proposed for k j ^ by Washida and Bayes in 1976: =1 1.74 x 1 0 8 exp ( -1.86 x 1 0 3 / RT ) 1 mole1 sec 1 corresponding to: k ^ = 7.4 x 10^ 1 mole1 sec* at 298 K. Methyl radicals were generated in a fast flow system by the reaction: 0 + CH2=CH2 CH3 + *CH0 and were detected by photoionization mass spectrometry. The methyl radicals were allowed to reach a steady state concentration, then molecular oxygen was admitted and the resulting decrease in the methyl radical concentration was used to measure the rate constant for the reaction: - 1 7 8 -CEj + 0 2 »- products There i s a remarkable difference between the two estimates of E]^, 1 2 . 7 and 1 .9 kcal mole1, and between the three estimates of k 1 5 at 298 K, — 2 x 1 0 5 , 0 . 8 and 7 . 4 x 1 0 6 1 mole 1 seo 1. However none of the latter estimates i s greater than 2 % of the value a 3 . 8 x 10 1 mole sec for competing reaction between the methyl radical and the oxygen molecule. Accordingly reaotion ( 15 ) has been treated as negligible. (4) Method. (a) Generation of the methylperoxy radicals. Methyl radicals were formed by the flash photolysis of azomethane in.the presence of an excess of both oxygen and an inert moderating gas. The majority of these methyl radicals were converted to methylperoxy radicals by the reaction ( 96 ): CH^ + 0 2 ( + M ) »- CH^OO' (. + M ) ; k~ = 3 - 1 x 1 0 A 1 mole 1 s e c 1 A minority of these methyl radicals were inevitably " wasted n by two competing reactions: CH3 + CHj ~ C 2H 6 ; k 2 3 3 . 2 x 1 0 1 0 1 mole1 sec 1 ( Chapter-3 ) CH3 + CH^ OO* *- a l l products ; k^ = 1 x 1 0 1 0 1 mole1 sec 1 ( Seotlon I . e . i i i ) Experimental conditions were chosen so that the wastage of methyl radicals by reactions ;( 2 ) and ( 5 ) should be negligible. The conversion of methyl radicals to methylperoxy - 179 -radioals was then vi r t u a l l y quantitative. This has two important advantages. F i r s t , the evaluation of the rate constant for the reaction: 8 1 1 2 CH-jOO* a l l produots ; 1^ » 3 . 5 i 10 1 mole sec is simplified i f the consumption of methylperoxy radicals and the formation of methoxy radicals by the reaction: CH^ + CH300« • 2 CH^ O* ( 5a ) can be neglected. Secondly, the evaluation of the extinction coefficient of the methylperoxy radical required an estimate of the total number of methylperoxy radicals formed during the reaction period. This estimate was equated to the product of the total number of methyl radicals formed by the photolysis of azomethane and the efficiency with which they were converted to methylperoxy radicals. (b) A computer study of the generation. A computer programme was written to simulate the kinetic behaviour of the system over a sufficient range of reaction conditions to ensure that suitable conditions were chosen for the measurement of k^ and £. This programme computed at 50 equal intervals over the period of interest: (1) the instantaneous concentrations of CH^ and CH^OO'j ( 2 ) the instantaneous values of the fractions of methyl radicals generated up to that time which had been consumed by reactions ( 2 ) , ( 3 ) and ( 5 ) respectively; ( 3 ) the corresponding values of the fraction of methyl radicals wasted by reactions ( 2 ) and ( 5 ) up to that time; - 180 -(4) the corresponding values of the fraction of methyl radicals consumed by reactions ( 2 ) , ( 3 ) and ( 5 )» to test the preoision of the procedure by mass balance; ( 5 ) the instantaneous values of the ratio of number of methyl radicals generated up to that time to the total number formed, to measure the extent of the photolytlo generation. The programme was based upon a fourth order Hunge-Kutta integration of two rate equations: d [GH3 ] / dt = ( C m t / t / ) exp ( - t / t m ) - 2 k 2 [CH3]2 - k 3 [CH3 ] [ 0 2 ] - k 5 [CH3 ] [CH300«] d [CH3OO']/ dt = k 3 [ C H 3 J [ 0 2 ] - 2 ^ [CH 3 0 0 * ] 2 - k^ [CH3 ] [CB^OO'J The principal data required for these integrations comprised: (1) the values of k2, k3» k^ and k^ l i s t e d above; ( 2 ) the value of t m , the time required for the intensity of the flash to reach i t s maximum value ( measured as 4 jusec ); ( 3 ) the value of C M , the concentration of methyl radicals that would have been observed i f a l l the methyl radicals generated by the flash had been simultaneously present in the reaction c e l l ( estimated as 6 . 5 5 x 10 M under present conditions ); ( 4 ) the value of [o 2], which was varied widely in the search for the most suitable value; ( 5 ) the time period of interest, usually 50 jasec. The output of the programme is illustrated by Pigures-5.1.A and 5*1*B, and Tables-5»6.A and 5»6.B, which were computed for - 181 -the conditions: t m = 4 jisec, C m = 6 . 5 5 x 10 mole 1 , and [o2 ] = 0 . 0 3 2 3 mole 1* ( Series A ), or 0 . 0 0 1 0 mole l 1 ( Series B ). The concentrations are normalized in Figures-5«1»A and or 5.1.B, so that the symbol " 0 " represents 100 [CH3 ] / C m and 4 [CH3 ] / C m respectively, and the symbol " X " in the two figures represents [cH^CO* ] / C m. The methyl radical concentration follows the flash profile, and remains low, r i s i n g to a maximum of only 0 . 0 0 9 2 C m at t = 4 jjsec with the high oxygen pressure and 0 . 0 2 3 Cm at 7 jasec with the low oxygen pressure. In contrast, the methylperoxy radical concentration reaches i t s maxima of 0 . 9 9 Cm at t * 30 jjsec and 0 . 9 5 C m at = 34 jjsec respectively, and declines slowly thereafter by reaction ( 4 ) . Column 5 of Table-5.6.A shows that less than O.036 % of the methyl radicals are wasted at any stage in the reaction under the condition of high oxygen pressure, and column 2 shows that the overall conversion of methyl radicals to methylperoxy radicals i s 9 9 . 9 % efficient. Column 5 of Table-5.6.B. shows that about 3 . 1 % of methyl radicals are wasted in the reaction under the condition of low oxygen pressure, and column 2 shows that the overall conversion of methyl radicals to methylperoxy radicals i s 9 6 . 9 % efficient. Columns 3 and 4 give the percentages of methyl radicals wasted by reaction with methyl radicals and with methylperoxy radicals repectively; as expected, the latt e r predominates at the high oxygen concentration and the former predominates at the low oxygen concentration. The precision of the method is confirmed by satisfactory ratios for the mass balance. The generation of methyl radicals - 182 -i s 9 9 . 7 % and 9 9 . 9 % complete after 32 and 37 jjsec respectively, equal to 8 and 10 respectively. -.183 -;ure-5«l.A The normalized concentrations of CH^ and CH^ OO' in the presence of a high oxygen —2 — concentration! [02]= 3*23 x 10 mole 1 o o o ' o e i sassa e o eJo e oj 1° o e o o o q o o e o e o j o o a o o q o o o o o d It 6 rmbolsi 0 = 100*[CH;]/ C m and X = [cR\-,00*]/ C m o - 184 -Figure-5.1.B The normalized concentrations of CH^ and CH^ OO* in the presence of a low oxygen concentration! [o^]88 1«0 x 10"J mole l " fee?. l o , a 4 Hi u o d o o o j w u d • o 5|* Symbols: 0 = ^ [ C H } ] / C M and X - [cHoOO']/ C M - 185 -Table-5.6.A Material balance ratios for the methyl radical at a high oxygen concentration! [ o 2 ] = 3 . 2 3 x 1 0 " 2 mole l " 1 T USEC 100»PRI/PRF 1 0 0 * P R 2 / P M F 1 0 0 * P R 3 / P R F 1 0 0 * P H N / P f t F ! 0 0 * P * r / C f t - I WASTEO I COMPLETE 1 . 0 8 4 . 8 7 7 0 . 0 0 1 0 . 0 0 1 0 . 0 0 2 2 . 6 5 0 2 . 0 9 2 . 3 4 7 0 . 0 0 2 0 . 0 0 2 0 . 0 0 5 9 . 0 2 0 , 3 . 0 9 5 . 2 0 8 0 . 0 0 3 0 . 0 0 5 0 . 0 0 8 1 7 . 3 3 6 ( 4 . 0 9 6 . 6 9 3 0 . 0 0 3 0 . 0 0 8 0 . 0 1 1 2 6 . 4 2 4 5 . 0 9 7 . 5 9 0 0 . 0 0 3 O . O t l 0 . 0 1 4 3 5 . 5 3 6 6 . 0 9 8 . 1 8 4 0 . 0 0 3 0 . 0 1 4 0 . 0 1 7 4 4 . 2 1 7 r.o 9 8 . 6 0 1 0 . 0 0 3 0 . 0 1 7 0 . 0 2 0 5 2 . 2 1 2 • . 0 9 8 . 9 0 5 0 . 0 0 3 0 . 0 1 9 0 . 0 2 2 5 9 . 3 9 9 9 . 0 9 9 . 1 3 4 0 . 0 0 3 0 . 0 2 1 0 . 0 2 4 6 5 . 7 4 5 1 0 . 0 9 9 . 3 1 0 0 . 0 0 3 0 . 0 2 3 0 . 0 2 6 71 . 2 7 0 11 . 0 9 9 . 4 4 6 0 . 0 0 3 0 . 0 2 3 0 . 0 2 8 7 6 . 0 2 7 1 2 . 0 9 9 . 5 5 6 0 . 0 0 3 0 . 0 2 6 0 . 0 2 9 6 0 . 0 8 5 1 3 . 0 9 9 . 6 4 3 0 . 0 0 3 0 . 0 2 7 0 . 0 3 0 8 3 . 5 2 0 1 6 . 0 9 9 . 7 1 2 0 . 0 0 3 0 . 0 2 8 0 . 0 3 1 8 6 . 4 1 1 1 5 . 0 9 9 . 7 6 9 0 . 0 0 3 0 . 0 2 9 0 . 0 3 2 8 8 . 8 2 9 1 6 . 0 9 9 . 6 1 4 0 . 0 0 3 0 . 0 3 0 0 . 0 3 2 9 0 . 8 4 2 1 7 . 0 9 9 . 8 5 1 0 . 0 0 3 0 . 0 3 0 0 . 0 3 3 ; 9 2 . 5 1 1 1 8 . 0 9 9 . 8 8 0 0 . 0 0 3 0 . 0 3 1 0 . 0 3 3 •' 9 1 . 8 9 0 1 9 . 0 99 . 9 0 1 0 . 0 0 3 0 . 0 3 1 0 . 0 3 4 9 5 . 0 2 5 2 0 . 0 9 9 . 9 1 9 0 . 0 0 3 0 . 0 3 1 0 . 0 3 4 9 5 . 9 3 7 2 1 . 0 9 9 . 9 3 4 0 . 0 0 3 0 . 0 3 2 0 . 0 3 4 96 . 7 20 2 2 . 0 9 9 . 9 4 5 0 . 0 0 3 0 . 0 3 2 0 . 0 3 4 9 7 . 3 4 3 2 3 . 0 9 9 . 9 5 5 0 . 0 0 3 0 . 0 3 2 0 . 0 3 5 9 7 . 8 5 1 2 6 . 0 9 9 . 9 6 3 0 . 0 0 3 0 . 0 3 2 0 . 0 3 5 9 8 . 2 6 4 2 5 . 0 9 9 . 9 6 9 0 . 0 0 3 0 . 0 3 2 0 . 0 3 S 9 6 . 6 0 0 2 6 . 0 9 9 . 9 6 5 0 . 0 0 3 0 . 0 3 2 0 . 0 3 5 9 6 . 8 7 2 2 7 . 0 9 9 . 9 9 1 o.oai 0 . 0 3 7 0 . 0 1 5 9 9 . 0 9 7 2 8 . 0 9 9 . 996 0 . 0 0 3 0 . 0 3 2 0 . 0 3 5 9 9 . 2 7 0 2 9 . 0 '' 1 0 0 . 0 0 6 0 . 0 0 3 0 . 0 3 2 0 . 0 3 5 9 9 . 4 1 4 3 0 . 0 1 0 0 . 0 0 9 0 . 0 0 3 0 . 0 3 2 0 . 0 3 5 9 9 . 5 2 9 3 1 . 0 " 1 0 0 . 0 1 2 0 . 0 0 3 0 . 0 3 2 0 . 0 3 5 9 9 . 6 2 3 3 2 . 0 1 0 0 . 0 1 7 0 . 0 0 3 0 . 0 3 3 0 . 0 3 5 - 9 9 . 6 9 6 3 3 . 0 1 0 0 . 0 1 8 0 . 0 0 3 0 . 0 3 3 0 . 0 1 5 9 9 . 7 5 8 3 6 . 0 ' 1 0 0 . 0 2 0 0 . 0 0 3 0 . 0 3 3 0 . 0 3 3 9 9 . 6 0 6 -3 5 . 0 1 0 0 . 0 2 3 0 . 0 0 3 0 . 0 3 3 0 . 0 3 5 - 9 9 . 6 4 S 3 6 . 0 1 0 0 . 0 2 3 0 . 0 0 3 0 . 0 3 3 0 . 0 3 3 9 9 . 6 7 6 3 7 . 0 ' 1 0 0 . 0 1 3 0 . 0 0 3 0 . 0 3 3 0 . 0 3 3 9 9 . 9 0 1 3 8 . 0 1 0 0 . 0 1 4 0 . 0 0 3 0 . 0 3 3 0 . 0 3 S 9 9 . 9 2 1 3 9 . 0 1 0 0 . 0 1 5 0 . 0 0 3 0 . 0 3 3 0 . 0 1 5 9 9 . 9 3 7 4 0 . 0 1 0 0 . 0 1 6 0 . 0 0 3 0 . 0 3 3 0 . 0 3 5 9 9 . 9 4 9 4 1 . 0 1 0 0 . 0 1 6 0 . 0 0 3 0 . 0 3 3 0 . 0 3 5 9 9 . 9 6 0 • 4 2 . 0 1 0 0 . 0 1 4 0 . 0 0 3 0 . 0 3 3 0 . 0 3 5 9 9 . 9 6 8 4 3 . 0 1 0 0 . 0 1 4 0 . 0 0 3 0 . 0 3 3 0 . 0 3 5 9 9 . 9 7 4 4 4 . 0 1 0 0 . 0 0 5 0 . 0 0 3 0 . 0 3 3 0 . 0 3 5 9 9 . 9 7 9 4 5 . 0 1 0 0 . 0 0 5 0 . 0 0 3 0 . 0 3 3 0 . 0 3 5 9 9 . 9 8 3 4 6 . 0 1 0 0 . 0 0 9 0 . 0 0 3 0 . 0 3 3 0 . 0 3 5 9 9 . 9 8 7 4 7 . 0 1 0 0 . 0 0 9 0 . 0 0 3 0 . 0 3 3 0 . 0 3 5 9 9 . 9 8 9 4 8 . 0 1 0 0 . 0 0 6 0 . 0 0 3 0 . 0 3 3 9 . 0 3 5 99 . 9 9 1 4 9 . 0 1 0 0 . 0 0 6 0 . 0 0 3 0 . 0 3 3 0 . 0 3 5 9 9 . 9 9 3 5 0 . 0 1 0 0 . 0 0 5 0 . 0 0 3 0 . 0 3 3 0 . 0 3 5 9 9 . 9 9 4 - 186 -Table-5.6.B Material balance ratios for the methyl radical at a low oxygen concentration! [ o 2 ] = 1 .0 x 1 0 ~ 3 mole l " 1 r I USEC mo.pRi/pnf IOO»PR2/PRf 1 0 0 ' P K l / P P . r 100«?HW/PUt loo»p«r /Cr i • X MASIEU * C t l H P l F T t 1 .0 9 . 9 7 1 6 . 0 2 0 0.000 C . 0 2 0 2 . 6 5 0 ?.o 1 9 . 2 0 5 0.1 19 0 . 0 0 4 0 . 1 2 3 9 . 0 2 0 \ 1 . 0 2 7 . 7 1 5 0 . 1 0 5 0 . 0 1 4 0 . 119 1 1 . 1 1 k ( 4 . 0 1 5 . 5 1 4 0 . 5 4 9 0 . 0 3 5 0 . 5 8 4 2 b . 4 2 4 5 . 0 4 2 . 6 2 1 0 . 8 1 7 0 . 0 6 * 0 . 8 8 5 1 5 . 5 1 6 6 . 0 4 9 . 0 7 4 I . 0 8 0 0 . 1 1 2 . 1 . 1 9 3 4 4 . 2 1 7 T.O 5 4 . 9 0 0 1 . 1 2 0 0 . 166 1 . 4 8 6 5 2 . 2 1 2 8 . 0 6 0 . 1 4 1 1 . 5 2 6 0 . 2 2 6 1 . 7 5 1 5 9 . 3 9 9 9 . 0 6 4 . 8 3 8 1 . 6 9 5 0 . 2 9 1 1 . 9 8 6 6 5 . 7 4 5 10 .0 6 9 . 0 1 0 1 .828 0 . 3 5 7 2. 106 7 1 . 2 7 0 11 .0 7 2 . 7 5 9 1 . 9 2 9 0 . 4 2 3 2 . 3 5 2 7 6 . 0 2 7 12 .0 7 6 . 0 6 2 2 . 002 0 . 4 8 7 ? . 4 8 9 _ 6 0 . 0 8 5 1 1 . 0 7 6 . 9 7 7 2 . 0 5 1 0 . 547 2 . 6 0 0 8 3 . 5 2 0 1 4 . 0 8 1 . 5 1 9 2 . 0 8 6 0 . 6 0 4 2 . 6 9 0 8 6 . 4 1 | 1 5 . 0 8 1 . 780 2 . 1 0 7 0 . 6 5 5 2 . 761 B R . 8 7 9 1 6 . 0 8 5 . 7 1 4 2.1 18 0 . 70 1 2 . 8 1 9 9 0 . 8 4 2 I 7 . 0 8 7 . 4 1 1 2 . 1 2 2 0 . 7 4 2 2 . 8 6 4 9 2 . 5 1 1 1 1 . 0 8 8 . 8 9 7 2 . 122 0 . 7 7 8 2 . 9 0 0 9 1 . 8 9 0 1 9 . 0 9 0 . 1 5 9 2.1 19 0 . 8 1 0 2 . 9 2 9 9 5 . 0 2 5 2 0 . 0 9 1 . 24 1 2 . 1 14 0 . 8 3 8 2 . 952 9 5 . 9 5 7 21 . 0 9 2 . 165 2 . 1 0 9 0 . 861 2 . 9 7 1 9 6 . 7 2 0 22 .0 9 2 . 9 5 1 2 . 1 0 4 0 . 8 8 2 2 . 9 8 5 9 7 . 3 4 1 21.0 9 1 . 6 1 7 2 . 098 0 . 8 9 9 2 . 9 9 7 9 7 . 8 5 1 2 4 . 0 9 4 . 1 8 0 2 . 0 9 4 0 . 9 1 1 J . O O T . 9 6 . 2 6 4 2 1 . 0 9 4 . 6 5 4 2 . 0 8 9 0 . 9 2 6 1 . 0 1 5 9 8 . 6 0 0 2 6 . 0 9 5 . 0 5 1 2 . 0 8 5 0 . 9 1 6 1 . 0 2 1 96 . 8 7 2 2 7 . 0 9 5 . 1 8 1 2 . 0 82 0 . 9 4 5 V .07 6 99 . 0 9 7 2 6 . 0 9 5 . 6 6 0 2 . 0 79 0 . 9 5 2 1 . 0 1 1 9 9 . 2 7 0 2 9 . 0 9 5 . 8 9 0 2 . 0 7 7 0 . 9 5 8 1 . 0 1 4 9 9 . 4 1 4 1 0 . 0 9 6 . 0 8 1 2 . 0 7 5 0 . 9 6 2 J . 0 J 7 . , 9 9 . 5 2 9 . 1 1 . 0 9 6 . 2 1 9 2 . 0 7 1 0 . 9 6 6 1 . 0 1 9 9 9 . 6 2 1 1 2 . 0 9 6 . 1 6 * 2 . 0 7 2 0 . 97 0 1 . 0 4 1 9 9 . 6 9 8 i i . n OA.47* J.OTn 0 . 9 7 7 1 - 0 4 1 OO-758 1 4 . 0 9 6 . 564 2 . 0 7 0 0 . 9 7 5 1 . 0 4 4 9 9 . 8 0 6 1 1 . 0 9 6 . 6 1 T 2 . 0 6 9 0 . 9 7 7 1 . 0 4 5 9 9 . 6 4 5 1 6 . 0 9 6 . 6 9 6 2 . 0 6 8 0 . 9 7 8 1 . 0 4 6 9 9 . 8 76 1 7 . 0 9 6 . 7 4 4 2 . 0 6 8 0 . 9 7 9 1 . 0 4 7 9 9 . 9 0 1 1 8 . 0 9 6 . T 8 1 2 . 0 * 7 0 . 9 8 0 1 . 0 4 7 9 9 . 9 2 1 1 9 . 0 9 6 . 8 1 5 2 . 0 6 7 0 . 9 8 1 1 . 0 4 * 9 9 . 9 1 7 4 0 . 0 9 6 . 8 4 1 2 . 0 6 7 0 . 9 8 2 1 . 0 4 8 99 . 9 4 9 • 1 . 0 9 6 . 8 6 2 2 . 0 6 6 0 . 9 8 2 1 . 0 4 9 9 9 . 9 6 0 • 2 . 0 9 6 . 8 7 9 2 . 066 0 . 9 8 1 1 . 0 4 9 _ 9 9 . 9 6 8 4 1 . 0 9 6 . 8 9 1 2 . 0 6 6 0 . 9 8 1 1 . 0 4 9 9 9 . 9 74 4 4 . 0 9 6 . 9 0 5 2 . 0 6 6 0 . 9 8 1 1 . 0 4 9 9 9 . 9 7 9 4 1 . 0 9 6 . 9 1 4 2 . 0 6 6 0 . 9 8 1 1 . 0 4 9 9 9 . 9 8 1 4 6 . 0 9 6 . 9 2 1 2 . 0 6 6 0 . 9 8 4 1 . 0 4 9 9 9 . 9 8 7 4 7 . 0 9 6 . 9 2 7 2 . 0 6 6 0 . 9 8 4 1 . 0 5 0 9 9 . 9 8 9 4 8 . 0 9 6 . 9 1 1 2 . 0 6 6 9 . 9 8 4 3 . 0 5 0 9 9 . 9 9 1 . . ._ . 4 9 . 0 9 6 . 9 1 5 2 . 0 6 6 0 . 9 8 4 1 . 0 5 0 9 9 . 9 9 ] SO.O 9 6 . 9 1 8 2 . 0 6 6 0 . 9 8 4 1 . 0 5 0 9 9 . 9 9 4 - 187 -B, Experimental (1) Apparatus The photographlo detection system was employed in a preliminary search for the absorption spectrum of methylperoxy radical spanning a range from 180 to 320 nm. The photographic plate was processed according to the standard procedure described in Section C.18 of Chapter 2, and the plate was calibrated by reference to the absorption lines of s i l i c a . A broad absorption band with a maximum at or near 240 nm was observed, in general agreement with the results of Parkes, Paul, Quinn and Hobson ( 3b ). The work was transferred to the new apparatus with the photoelectric detection system as soon as i t had been completed. This change increased the accuracy of measurement substantially. The absorption spectrum was then determined in absolute units, and the quantitative kinetic study of the reacting system was undertaken. (2) Method. (a) Choice of reaction conditions. Reaction conditions were chosen so that v i r t u a l l y a l l of the methyl radicals formed i n i t i a l l y by the photolysis of azomethane were converted to methylperoxy radicals by the reaction: CKj + 0 2 + M CB^OO' + M ( 3 ) Any proposed set of reaction conditions was tested by the computer programme described in Section A.2.a to make sure that - 188 -Table-5.7 Typical reaction conditions for the quantitative study of the methylperoxy radical 1, Reactants: Material Range of concentrations(mole l - 1 ) Azomethane 4.4 x 10 _ Z f to 4.1 x 10 Oxygen 3.23 x 10" 2 to 1.0 x 10~3 Methylperoxy fi ^ . i n-7 radical, C0 6 , 6 5 x 1 0 (measured) 2, Photoflash: Photoflash energy 1080 J ( 12 kV, 7-5 uF )x 2 Time of maximum intensity ^ microsec. after f i r i n g Time of dissipation of ? 7 m i c r o s e c 99.9 % of flash energy 3 7 m i c r o s e c -Time of observation 4 millisec. - 189 -the wastage of methyl radicals would be neglglble. A typical set of reaction conditions for quantitative measurements is given in Table - 5 . 7 . (b) The measurement of kjj,' / £ ( A ) . F i r s t , a wavelength was chosen for the measurement of the absorbance A of the methylperoxy radical. Secondly, a reaction mixture was photolysed under appropriate conditions, and the decay of the absorbance was recorded over a period of several thousand microseconds. Thirdly, the reciprocal of absorbance A was plotted against the time t following the f i r i n g of the photoflash. If the methylperoxy radicals were the only significant absorbing species at the chosen wavelength, the absorbance may be written A =* £(A)C1 , where 1 i s the optical length of the reaction c e l l , and C i s the concentration of methylperoxy radicals at the time t. If the flash had instantaneously generated the methylperoxy radicals at a concentration Co, with an absorbance Ao at the time t = 0, and i f these radicals had been consumed solely by the overall second order reaction: 2 CH-jOO* •* inactive products ( V ) then 1/A would be linearly related to t by the equation: 1/A = 1/Ao + 2 ( k^V £(A) 1 ) t In fact, the s t a t i s t i c a l analysis of the plot of the experimental values of 1/A against t yields correlation coefficients in the range from 0.990 to 0.999. This is sufficiently close to unity to make the evaluation of k^'/ECA) - 1 9 0 -from the gradient a meaningful procedure. The value of k^» is independent of the wavelength chosen for the measurement of absorbance. Accordingly, a plot of £(A)/lty.' against A i s equivalent to a relative absorption spectrum of the methylperoxy radical. (c) The measurement of £ (A) . If a l l the methylperoxy radicals generated in this system had been simultaneously present in the reaction c e l l , they would have had a concentration Co and an absorbance A o at the chosen wavelength. The corresponding extinction coefficient i s then given by the equatlont 6(A) - A o / C o l and may be evaluated i f A o and Co can be measured. The measurement of Ao i s accomplished by extrapolating the observed values of A back to zero time. This extrapolation i s accurate because the formation of methylperoxy radicals is >99 % complete within 50 microseconds, whereas the half l i f e of these radicals is of the order of 2000 microseconds in a typical experiment. The measurement of Co is based upon the assumption that the yield of methyl radicals from the flash photolysis of azomethane is determined only by the intensity of illumination and the concentration of azomethane, and is not changed when oxygen i s present. The value of Co i s equated to the concentration of methyl radicals that would have been observed i f a l l the methyl radicals generated by the flash had been simultaneously present. Experiments were conducted in pairs. In each pair the intensity - 191 -of Illumination and the concentration of azomethane were identical} but one reaction mixture contained no oxygen and the other contained an excess of oxygen. The former system yielded the value of Co from the amounts of nitrogen and ethane formed, using the procedure described in Section B.2.C of Chapter 3; the latter yielded the value of A 0 from the linear extrapolation procedure described above. (d) The measurement of k^. (1) The nature of the problem. Methods for the measurement of k^'/£(A) and of £(A) have been described in the two previous sections, and clearly an estimate of k^» can be obtained at each wavelength observed from the product of k^'/^A) and £(A). These estimates are valid only for the hypothetical reaction: 2 CH-jOO* - inactive products ( 4» ) whereas the methoxy radicals formed in reaction ( 4a) : 2 CH300* *• 2 CH-jO* + 0 2 ( 4a ) are highly reactive, and may be expected to influence the course of the reaction significantly. In particular, the consumption of methylperoxy radicals by the reaotions: CH300' + CH30" CH3OOH + CH20 ( 6 ) CH300* + HOC CH3OOH + 0 2 ( 10 ) must be considered. On the other hand the reaction: Table - 5 . 8 Reactions used in the computer simulation of the decay of the methylperoxy radical reaction 2 CH^OO' a l l products (*0 rate constant at 298 K 1 mole'^sec - 1 3 . 5 x 10 8 * 2 CH-jOO* -»» 2 CH^O* + 0 2 t>a) 1.75 x 10 8 * CH^OO* + CH^O* CH^OOH + CH 2 0 (6) 9 . 2 x 10 8 2 CH^O* a l l products (7) 1 .0 x 10 10 C H y r + o 2 CH^OO* + HOO* CH^O* + HOO* 2 HOO* CH 2 0 + HOO* CH^OOH + 0 £ CH^OH f 0 2 HOOH + 0, (9) (10) (ID (12) 4 . 0 x 10^ ,8 3 - 3 x 10 v 1 .0 x 10 2 . 0 x 10-10 Note » * other values may be substituted as described in Section c .5»b - 193 -CH^ OO* + CH3 - 2 CR^ O* or CH^ OOCR^  ( 5 ) has already been shown to be negligible in Seotion 2 .a. Accordingly a computer programme was written to simulate the kinetic behavior of a system of methylperoxy radicals with the principal aim of deriving an accurate value of k^ from each estimate of k^'. The reactions included in this programme are l i s t e d with their rate constants in Table-5.8. ( i i ) The computer programme. The model assumes that the methylperoxy radicals were i n i t i a l l y present at the concentration Co, and that they decayed solely by the reactions in Table-5.8. Co i s the hypothetical concentration that would be observed i f a l l the methylperoxy radicals formed were simultaneously present in the reaction c e l l . The value of Co may be obtained from the experimental values of A 0(A)» £(A) and 1, using the equation Co » Ao(A) / £(A) 1« The model therefore assumes that a l l the methylperoxy radicals were formed instantaneously at zero time; this is a good approximation as the period of their formation i s a small fraction of the period over which their decay was observed. The programme was based upon a fourth order Runge-Kutta integration of three rate equations: d [CB^OO'] / dt - - 2 k ^ [ C H 3 0 0 * ] 2 - k 6 [cR^OO* ] [CH^O*] - k 1 Q [CH300*] [H00*] d [CH 30 -] / dt = + 2 f y a [ C H 3 0 0 « ] 2 - k 6 [cH^O'] [CR^O*] - 2 k 7 [ C H 3 C ] - k^ [CH 30'] [ 0 2 J - k n [CH 30' ] [ H 0 0 * ] - 194 -d [ H O O - ] / dt = + k 9 [ C H 30'] [ o 2 ] - k 1 Q [cH-jOO* ] [ H O O ' ] 2 - k l l [ C H 3 0 * ] [HOO*] - 2 k 1 2 [ H O O * ] Values of Co and [o2] were required for the integration: typical - 7 - 1 - 7 values lay in the ranges: 6 . 4 5 x 10 mole 1 4> Co 4 6 . 6 5 x 10 -1 - 2 -1 - 2 -1 mole 1 and 3 . 0 x 10 mole 1 4 [0 2] 4 3«28 x 10 mole 1 - 3 -1 ( Series A ), or 0 2 = 1*0 x 10 mole 1 ( Series B ). The i n i t i a l output of this programme comprised values of the concentrations of the radicals C H ^ O O ' , C B ^ O * and H O O * , computed at 50 equal intervals over the period of interest. A typical graph of the output is shown in Figure-5.2.A. The symbol X represents [ C H ^ O O * ] / Co • the symbol 0 represents 50 [ C H - ^ O * ] / C o f and the symbol # represents [ H O O ' ] / C O . In this graph [cH-jO*] ^ 0.0088 [ C H ^ O O * ] after 2000 microseconds whereas [H00*] maintains an almost stationary value of ~ 0 . 1 1 t 0 . 0 2 Co between 1000 and 5000 microseconds in the presence of high oxygen concentration. Moreover, the H00* radical is predominant over the CH^O* radical after the f i r s t 200 microsecond. The accuracy of the computation was confirmed by computing at 50 equal intervals over the period of Interest values of material balance ratios for each of the radicals C H ^ O O * , CR^O* and H00», and the results are given in Table-5.9.A. BAL(P) Is the instantaneous ratio of the sum of the concentration of the methylperoxy radicals and of the equivalent concentrations of these radicals consumed by reactions ( 4 ) , ( 6 ) and ( 10 ) to their original concentration C o . BAL(A) is the instantaneous ratio of the sum of the concentration of the methoxy radicals - 195 -Figure-5.2.A The normalized concentrations of CH^ OO*, CH-jO' and HOO* in the presence of a high oxygen concentration» [ 0 ~ ] - 3 - 2 3 x 1 0 " 2 mole l " 1 S o o 0-0 o o| 0 0 0 . 0 0 0 10 o o o o p 1 • • o o 7 O — O 0 I • o * o o « c I-*' Symbolst x = [CH^OO*]/ C0 , 0 = 5 0 * [ c H 2 0 * ] / C« and # = [HOO*]/ C, . - 196 -Figure-5.2.B The normalized concentrations of CH^OO'» CH^ O* and HOO* in the presence of a low oxygen concentration! [ 0 2 ] - 1.0 x 1 0 " 3 mole l " 1 Symbols! x » [CH^OO*]/ Co , 0 = lO^CH^O*]/ C0 and # = 10*[H00'] / Co . - 197 --C e • H H at O 0« CD 1 <o o I—1 o c c <s CD cd CO r H —< o cd u a CM r-t <o 1 cd si o • H +» r H • H or <n O '—' to X CVJ C o o T3 I . • H G +> s -cd c +» - H w +> CD OB O O U C c n + » o X C o O <B O T> - c CD ^ ofrj • H - ^ r H c cd O CD a O ttO ^ cn >» o z o o 3 O O 3* O 3 3 C UJ ' X l J J i*.. 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O O O O 3 3 3 3 J O O O O O O y n o P» a * +1 en .-n m 3 O O 3 O 3 | 0 3 O 3 J O O O 3 0 3 0 0 0 3 O o - * *M m y A y y y y - -...„ a J» o r y y r y A 1 CD CO E-t - 198 -•* u o e o o II CO -—s o cd o •H •—* +» a, cd o U CD r H <o O I o C r H C CD 3 co CD r H CD r H cd U O r Q Ot a r H CD en a a, 1 •H +> o r4 r H CD c -P •H cd o a • o r r H •— C • II 3 o o 1— I CO X CM C O o i i •H c 3 cd c o •< C +> CO • cd o o U c 0-\-H o c o O CD O c CD N o t4 04 o i H .—1 • c cd O CD a o ho cn >» o X X a: o o CP ON • i CD r H r O cd EH O O O c; o o c o o 0 ( 0 O O 3 CIO o o o o o o o o o o o o O O O O' u o o o O C J o «-» C -9 O O I 'J J u JJ O O O 9 O 0 3 9 O 0 0 9 O O 3 9 1 o l a o o o o o 1 * 1 1 1 1 - J U J J JJ -II J J 14 919 9 <> 9 9 ?> J».<J» > 0 » y 9 9 9 (9 J> <f *• <3> 9 9 9 9 9 9 C9 9 V 9 9 9 to 3 O O O O I I I I I I U j JJ y JJ 'J 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 0* ^ [ 9 9 9 9 9 9 > • • ' • • • ' 9 9 . 9 9 1* O O O O o o J O O 3 w w ^ - « J J O O a O O O ' O ' J O O 3 3 o o o o o o i o o o o o o lo o o n o o j o o o o o p o o o o o W U'iJ _ 19 9 9 9 9 ~ 9 9 9 J* 9 9 9 9 _ P 9 9 9 9 9 9 9*9 9 9 I _ -U UJ ui at UJ O O -3 O 0 O O O O «J O O o o o o o a o o T o o o I I JJ OJ UJ U_ p o o o o 3 |o o o o o o p Q O O O 0 H> o a o o o Q a O Q O 3 I -ii u 9 9 9 9 * 9 9 T 9 9 9 _ 9 9 9 9 9 9 9 9 9 9 ( 9 9 9 9 9 9 _ -JJ Ui -XI UI U., O 3 O 3 O O O O O O O <3 o o a o o o -3 O f O 3 " ^ a a a o 9 9 9 > T ? 9 9 9 9 9 J» 9 9 9 9 9 9 |0» 9 9'cj» 9 9| o o o o o o I I O 3 3 O 3 O O O O 13 t I U J _ J 'JJ u -a a a a ca 9 9 9 T 9 9 9 9 9 >J* 9 9 9 9 I U U 'JJ 9 i a a o a y : 9 T 9 9 919 9 9 9 ? | 9 9 9 9 9 9 9 9 9 9 9 9 9 0 3 3 0 0 1 0 3 0 0 3 3 , 3 0 0 3 O O O O O 3 | 0 O O O O C i O ' J O O o o o o o o i o O O O O OIO O O O 3 O O O O T | 0 3 O O 3 3 3 O O 3 — 3 "3 O C J 3 O 3 3 O J * o o o O O o I I I I I U J w ' J J ui j 9 9 * 9 [ 9 9 9 9 9 9 ;9 9 9 9 3» J 1 o o o o o o to o o o o o ^ 3 3 u i O O O 3 O 9>9 9 9 9 9 9 t9 J » 9 9 9 9 k 9 9 9 9 9 9 » 9 9 » 9 9 O 9 r» r*tr* — a .*! 9 0 -n O ^ p» A O j>r«^ 3 M J" . ^ J H T ** CM ">4 •** >J 3 -J* J^ — 'O, J 3 O a O — r» 9 <-» C 3 O 3 — — — 3 a 3 o l a 3 3 3 3 C B N ^ O 3 3 3f*. sir-»\if*» .^irt O ^ J»njjlJ-t(<N Or" a ^ r ^ ^ O O * * »> ^  O -o 9 >• > ia O ^ 3 r * 3 J - 3 O - 0 k a o T - ^ ^ - > f 3 ) nr» — 4 * . - - ' O M J , 4 a j * l < j M f l / n . l f l f l . l l f l A J a 9 o - • ^ r"* J - ^ ^ a ^ r » * a 9 9 ? -a o 0 0 0 3f—• — — — — — i — — - . — - « _ - - - . — lUi *4J _ _ _ |9 9 9 9 19 It9 9 9 - 9 9 9 19 9 * 9 9 9 |9 9 9 9 9 9 O O O O O O O O 3 O O Oi O O 3 o o 3 0 a O 3 J JJ w 9 J» a a a ( 9 9 9 9 9 ? 0 9 9 7* 9 9 K9 9 9 9 9 J» a a a |9 9 9 9 9 9 ~ " 9 9 3* ( 9 9 9 9 9 9 I ii UJ -1*9 » 9 9 9 9 jo a -*» m a a a -a s 9 9- 9 9 91 9 9 9 9 9' 9 9 9 9 9 9 7» 9 J» T » : 9 9 9 9 9 9 9 9 9 - . 9 9 9 9 9 9 9 9 9 9 9 9 O O O O O O O O O O 0 3 0 0 0 0 0 0 0 0 0 0 p o o o o o N O O O O O O JO O O O O O ' O O O O O O j o o o o o 9 9 a^ 'OS7r*rs i . "a^ -p>« 0 0 r * 0 3 M ^ J | * / s i O N | ^ *»asrmO(M9 -f * i 9 9 j * o — i o •*>>•— .*»4*r^»-*9i>.-u O — 4**5O0! ,J^.-n-«OB0k/^j-*9^.O o . s i i 9i«n o « J 0 -O\*Q -o a a J \ j>kn J> A J f / ^ ' • J 0 3 3 0 0 0 0 0 0 0 0 0 0 iJ O ' J 3 I N 9 9 j h i N ? r » r i > ^ - » i - a . N J * 7 - ^ J 3 ' ^ I 9 9 9 0 J 9 B 9 0 0 0 ) H f 9 a 9 — N O A 4 * ^ . ^ 9 I j i iA O i\jCO > K\ -O — 3 - ^ 9 9«<9a -0 HT — O ^ J ^ ^ - o > ar* irt ^  . ^ r > , \ - o 3»a a *na o x > 9 9 -r 9 9 9 * i*> mlrO c» flwm^ if** N J < N ^ . " S * ^ * (OO 3 O U W > O O O 0 O 0 p O O O 0 O | 0 O O O O w jo o rM a -* 'O -^ J J N O ; — 9 a 9 f*4 - * A a J I ->J -vj — ,CV* (Ni fM ->« O O 3 O O 3 3 O OIO O 3 O 3 0 J 0 0 0 O 0 0 O 0 O O 0 0 »o a s t 0 0 p 0 0 0 3 0 f 0 0 0 0 0 0 p 3 0 0 0 0 c 3 ^ 3 ( ^ " > . a 9 o — !»n 9 a a a -* -it *i ^ r» a a J> M r- o c j - .**t9 — HT\ J> .*I c a .-n — a •n a ->.T a -r r- ^ r— D |o o J a *i a o *^  *J* a -r.-j i c *) . N N j* o "Zi• r> — r-,.-i c r- r — J* a J * - ' J o a o < J 9 9 - IO Er*«"-r*- J l O O O O ^ * -1 • O O OI 0 0 0 0 0 0 ( 0 3 0 0 0 0 i "si fll-f A 4r» a 9fO — O 9 9 1 .fi N a j) g r* ^ •r s - M g A O 9 o a 3 J1 ^ . N Q / • 3 A A < l i A T / p o o o o o M a 9 *o 9 — ^ 9 r- -> .-v* ^ |rn 9 9 9 «-» •4 t -* *• J» - -a a a „ ft J « I M -f !• 9 9 -r 0 9 ^ 1 * . .-i*. r- J « 9 9 9 0 f « j | 9 J rfl » 1 J 1 *n N J1 v J7 j*A ' r »99- -*r»;9^ — ••*#f^ H*|— 9 a 3» -A 3 « 3 O O O k M A IN « f n A 8 4 r> O A,C ^ A <f j J) ' , l910 -A - - '<8 iAA«iOflN-NJ ; : r»N>dn p - 9 — «a> 8 - / r > - A ^ ! ? a ^ a ! . - r i 9 9 3 a 0 9 9 a p - O - a t A * 4* I ^ J W - N — 3 3 9 : 9 a a ar» o o o o o o o o o o o o p o u o o w l o o o o o M m / J1 p 0 3 0 3 0 0 3 0 0 3 0 p 3 1 0 0 110 3 0 3 3 0 0 3 0 3 1 O i O 3 3 3 0 O O O O O O 0 0 3 0 0 l O O O O O O ' O 3 0 0 0 0 0 0 0 3 0 3 0 0 3 0 3 O 9 O rvi f j\ j N ^ l j i O ^ ^ A ^ A Of» 8 T ' O J A | J N a 9 0 - 199 -and of the equivalent concentrations of these radicals consumed by reactions ( 6 ), ( 7 ), ( 9 ) and ( 11 ) to the equivalent concentration of these radicals generated by reaction ( 4a )• BAL(Q) i s the instantaneous ratio of the sum of the concentration of the hydroperoxy radicals and of the equivalent concentrations of these radicals consumed by reactions ( 10 ), ( 11 ) and ( 12 ) to the equivalent concentration of these radicals generated by reaction ( 9 )• The accuracy of the computation is confirmed by the fact that none of these values of the material balance ratios deviates from unity by more than 0.00005. Pigure-5.2.B and Table-5«9.B represent analogous -3 computations with a low oxygen concentration of 1.0 x 10 mole 1*, but otherwise under conditions identical with those of Pigure-5.2.A and Table-5.9«A. The lower oxygen concentration decreases the conversion of CH^ O* radicals into H00* radicals by reaction ( 9 ): CEjO' + 0 2 CH20 + HOC and accordingly the CH^ O* radical i s predominant over the H00* radical for 3.4 msec. Accuracy of computation i s again confirmed by the material balance ratios. The principal output of the programme was the value of ki|,»A^. T r i a l values of k^ , and of kij,a were entered with the other data. Values of Co/C, the normalized reciprocal of the methylperoxy radical concentration, were computed at 50 equal intervals over the period of interest, and plotted against time, t, as shown in Figure-5.3»A. This graph simulates the normal - 200 -input to the s t a t i s t i c a l programme for computing the value of kjj,», and visual inspection reveals almost no perceptible deviation from linearity. A regression line was fi t t e d to the corresponding values of Co/C and t. Table-5.10 .A shows the output of such a procedure. The input i s represented by X = t and Y = Co/C. The regression line was used to calculate the output Y(CALC), consisting of the corresponding computed values of Y at each value of X. Deviations of the actual values of Y from the regression line are represented by DY = Y(CALC) - Y and by TY = DY/cY where o-Y i s the standard deviation of the values of Y. The degree of curvature of the actual plot of Co/C against t is judged to be negligible on the basis of the values of TY, so that the procedure of f i t t i n g a regression line is valid. The values of kit' and i t s standard deviation were accordingly calculated, and are given as K2(CALC) and ST.DEV respectively in Table-5.10.A, while K2(CALC)/K2 3 8 k^'/k^. The values of k^Vk^ obtained are determined mainly by the value of k^a/k ,^ and are relatively insensitive to the values of the other rate constants given in Table-5.8; this topic i s more f u l l y discussed in Section C.5. Pigure-5.3»B and Table-5.10.B present analogous computations -3 -1 with a low oxygen concentration of 1.0 x 10 mole 1 , but otherwise under conditions identical with those of Pigure-5.3.A and Table-5.10.A. The procedure of f i t t i n g a second order regression line i s again validated by the small degree of curvature. - 201 -Figure-5.3«A A simulated second order plot for the decay of the CH^OO' concentration! computed values of Co/C plotted against time for a system with a high oxygen concentration: [ o 2 ] = 3^ 23 x 10~2 mole l " 1 time - 202 -Figure-5.3«B A simulated second order plot for the decay of the CH^OO' concentration! computed values of Co/C plotted against time for a system with a low oxygen concentration, [ o 2 ] = 1.0 x 10"^ mole l - 1 o o o o o d o o e ) K « « OS O - ' < o ) o o o o d o • -0 « »- • o> o time - 203 -Table-5.10.A Pitting a second order regression line to values of Co/C = Y computed for the decay of the CH^OO* concentration in a system with a high concentration! [0 2] - 3.23 X 10"2 mole l " 1 *c4w - l J 3lAi.l<Akll 1)1.V UTIuU uf K2ICAtCI AND INTCHCtfT I IM.U » Y or IT U.J oO.O u.o 60. J 1 .000 1.UI7 0.9/0 1.017 0.02-.02 u.01.9d ..449 /.037 1 uO.O /40.0 3/0.0 4ao.o boO.i 160.0 / - .u .J 320.0 400.0 4o0,0 SoO.O 1.075 1.112 1.151 Lid-) 1.224 1. 26 / 1.0513 1.099 1.140 l . l d l 1.222 1.264 0. 011.44 0.01^23 O.U-35 0.00/&9 0.001*2(3 u.00.,10 l.a76 ,.351 4.055 J . 3 39 J . 316 640. 0 720.0 ULO .0 UbO.il 96C.0 1040.0 640.0 72O.0 dUO.U ~ d c O . O 9uO.U 1040.0 1.306 1. 345 1.305 1.424 " ~ 1.464 1. 504 1.305 1.346 1,307 1 " 1 . 4 2 b " 1.4o9 1.510 0.00.11 -u.LJ.J64 -0 .00.21 -0.U0J61 -0.CO-.dl -U.OOjO* a.115 -0.06} •J.226 -J.16H -J.492 -J .600 l l/o . O 1/CO.O U /0.0 1200.0 12liO .0 1.J44 "• 1.5(5 1.625 1.551 1.592 1.633 -0.00/5S -U.00.J1S -0.692 -J.770 -J.834 1360.0 1440.C 1!>20.0 l icO.O 1441.0 13/0.0 1.66a 1. 706 1.74 7 l.o7* I. 715 1. 757 -0.00u68 - 0 , 00-406 - 0 . 00*31 - j . S d i -j.924 -j.951 11.00.0 I60O.O 1760.0 u o o . a 1 1.0O.O 1760.0 1.784 1.829 1.870 1.79a 1 .039 1 .ddu -0.00*49 -u.0J*5o -0.01*53 -0.964 -u.97* -J.971 Id 40.0 192U.0 /JOO.U 1640.0 1420.0 2L00.0 1.411 1.951 1.994 1.921 1.9o2 2 .003 -0.00*41 - 0 .00 * 2 2 -0.O0..94 "-ji960 -J.939 -J .911 20d0.0 21CO.0 22^.0.11 20u0.0 216U.0 2/40.0 2,036 2.077 2. 119 2.044 2.003 2. 126 -0.00^ 59 -0.00*17 -0 . 0 0 / 6 9 -0.1)76 -w.Bjl - j . 7d4 2120.0 24CC.0 2s oO.O 2J20.O 24C0.0 2<.uO.U " 2. 160 2 .202 2. 244 2.167 2.20a 2 . /50 -0.0071S -0.00i.55 -O.OOJSIO -J.729 -j.668 -J.60I 2560.0 2t46.0 2//0.0 2560.0 2640,0 2720.0 2.2d5 2.327 2. 369 2.291 2.332 2.173 •0.00319 -0.00-.44 -0,00364 -0.529 -J.451 . "- i t"! 2000.0 2oo0.0 2960.0 2000 .Q 2oo0.0 29 (.0,0 2.41 t 2.451 2.445 2.414 2. 455 2.496 -OiOOidO -0.00192 -O.OOtOO - w . 2 o « - J . 19o -J.102 3040.0 Jl20.C 120O.0 j/dO.O tiuli.ii 3440.U 3040.0 112C.0 3200.J 12»0.0 33uO,tl 3*iU.0 2.537 2. 579 2.621 2.66J 2. 706 2. ?4d 2.5 2.57a 2 .o l9 2.660 2.701 2.743 -0.00u04 0.00j95 0.00 ,97 o.oa>oi 0.00*11 0.00321 -0.0O4 J.09I J.201 j .109 J.419 J . 531 - •-3320.0 3600.0 36d0.0 3/60.0 3D-.U.0 J420.0 3520.0 3600.U 3 L bC . 0 ilU.O 3d40.0 39/0.0 2.790 ' 2.832 2.874 2.917 2.959 3. 001 2.7d4 2.1)25 2 .066 2.907 2.94t3 2 .9o9 0.C0-36 0.00/53 u. 00x72 0.00*93 0.01,16 u.01/42 0.644 j , 7o7 j . 089 i.012 1.131 1 . 266 4i«0.6 4000.0 3. 04^ 3.030 0.01-.64 1.196 uHAultil ST.l.lY I M U t t k M sx.uey iI0.b6v.Uf .» K2U<UC| ST.uiy *2<C»lCI/»2 d.OJOil* O.JOuOOl 0.97O0 0.0027 0,0094 3.9k0£-04 d , 9 0 4 £ - 0 7 1.1200C 00 - 204 -Table-5*10.B Fitting a second order regression line to values of Co/C - Y computed for the decay of the CH^ OO' concentration in a system with a low concentration* [ 0 2] = 1.0 x 10"3 mole l " 1 MEAN ANU STANDARD DEVIATION OF K2ICALC) A NO INTERCEPT TIME X r . YCCALCI DY . . IV 0.0 0.0 1.000 0.981 0.01920 2 .908 HO .a AO .n 1 . 017 1 .071 0.01479. 7.165 160.0 160.0 1.075 1.065 0.01020 1 .544 240.0 240.0 1.114 1. 10 7 0.00682 1 .033 320.0 320.0 1.153 ... 1.149 0.00407 0.616 400.0 400.0 1.191 1.191 0.00186 0.281 480.0 480.0 1.211 1.233 0.00009 0.014 560.0 560.0 1.774 1 .775 - o . n o n o -0 . 197 640.0 640.0 1.115 1.31 7 -0.00238 -0.361 720.0 720.0 1.156 1.359 -0.00121 -0.486 800.0 800.0 . 1.397... 1.401. -0.00384 -0.581 _ .... . 880.0 880.0 1.419 1 .443 -0.00429 -0.650 960.0 960 .0 1.480 1 .485 -0.00461 -0.698 1040.0 1040.0 1.577 1 . 577 -0.00481 -0. 779 1120.0 1 120.0 1.564 1.569 -0.00493 -0. 746 1200.0 1200.0 1.606 1.611 ,-0.00496 -0.751 1280.0 128U.0 1.648 1.653 ... -0.00494. _ -Q.748. 1360.0 1360.0 1.690 1.695 -0.00486 -0.736 1440.0 1440.0 1.712 1.737 -0.00474 -0.718 1520.0 1520.0 1.775 1 .779 -0.00459 -0.604. 1600.0 1600.0 1.817 1.821 -0.00440 -0.667 1680.0 1680.0 1.859 1.863 -0.00420 -0.633 ._ 1760.0 1760.0 .1.901 1.905 -0.00397 -0 .601 1840.0 1840.0 1.944 1.947 -0.00171 -0.564 1920.0 1920.0 1.986 1.989 -0.00347 -0.525 2000.0 2000.0 7.078 7.011 -0.00170 -0 .484 2080.0 2080.0 2.070 2.073 -0.00292 -0.442 2160.0 2160.0 2.111 2.115 -0.00261 -0.399 2240.0 2Z4O.0 2.155 2.15 7 ..-0.00234 -0.354 2320.0 2320.0 2.197 2. 199 -0.00204 -0.309 2400.0 2400.0 2.240 2.241 -0.00174 -0.263 2480.0 2480.0 2.282 7.^83 -0 .00141 -0.716 2560.0 2560.0 2.324 2.125 -0.00112 -0.170 2640.0 2640.0 2.367 2.167 -0.00081 -0.122 ...... 2 720.0 2720.0 . 2.409 .. 2.409 -0.00049 _ -0.0 74 .. ... 2800.0 2800.0 2.451 2.451 -0.00017 -0.026 2880.0 2880.0 2.494 2 .494 0.00014 0.022 7960.0 2960.0 2.516 2.516 0.00046 0 .070 3040.0 3040.0 2.578 2.578 0.00078 0.119 3120.0 3120.0 2.621 2.620 0.00111 0.167 3200,0 3200.0 .. 2.663 . . 2.062 0.00143 0.216 _ 3280.0 3280.0 2.705 2.704 0.00175 0.265 3360.0 3360.0 2.748 2. 746 0.00207 0.313 3440.0 1440.0 2.790 2.788 0.00719 0.162 3520.0 3520.0 2.832 2.830 0.00271 0.410 3600.0 3600.0 2.875 2.872 0.00103 0 .459 3680.0 3680.0 2.917 2.914 . ... 0.00335 0.508 3760.0 1760.0 2.959 2.956 0.00167 0.556 3840.0 1840 .0 3.002 2.998 0.00199 0.605 3920.0 1420.0 3 .044 1 .040 0.00411 0 .651 4000.0 4000.0 3.086 3.082 0.00463 0.702 . CftAQIENt .. ST.OEY INTERCEPT ST.OEV . STO.OEV.QF.I K2ICALCI ST.OEV K2ICALC1/K2 0.000521 0.000001 0.9808 0.0018 0.0066 4.010E-04 3.994E-07 1.14561 00 - 205 -C, Results. (1) The value of ]%»/£(A). The consumption of the methylperoxy radicals in these experiments can he treated as though i t occurred exclusively by the hypothetical bimolecular reaction: 2 CH3OO* *• unreactive products ( 4' ) and the variation of the concentration C of the methylperoxy radicals with time can be represented by the equation: 1/C = 1/Co + 2 lci+* t The corresponding equation for the absorbance A of the methylperoxy radicals i s : 1/A « 1/Ao + ( 2 y / £ U ) 1 ) t The va l i d i t y of this equation was tested by f i t t i n g a straight line to simulated data and by comparing the deviation of individual points from this line with the corresponding standard deviation, as explained in Section B.2.d.ii. The high degree of correlation observed is evidence that this procedure is valid. The s t a t i s t i c a l analysis also computed the ratio k '^/k^, where k^  is the rate constant for the actual reaction. 2 CH300* »> a l l products ( k ) The ratio k^ Vkjj, was computed for various fractions k^a/k^ of nonterminating interactions of the methylperoxy radical in conjunction with six other reactions of the daughter radicals - 206 -CH-^ O* and HOO* l i s t e d in Table-5.8. The values of the ratio kj^Vlty, did not deviate much from unity and depend mainly upon the estimate of kj^/k^, which is somewhat in dispute. The value of k^'/EtA) at each chosen wavelength A was derived from the gradients of the corresponding plots of 1/A against t. The set of values of k^'/EfA) represent the most directly determined and therefore least ambiguous results of this part of the work, and may be compared directly with the value of k/4'/E(248) obtained by Hochanadel et a l i a in 1977 ( 75 ) • The corresponding set of values of k^/EfA) depend upon the estimate of k^/k^, and to a lesser extent on other rate constants, and are correspondingly less certain. Accordingly this section w i l l be concerned with k^'/^A) alone. Values of k^'/^A) were measured at various wavelengths from 210 nm to 285 nm In the presence of a large excess of oxygen at room temperature. The results are l i s t e d in Table-5«H«A. A minimum value was observed at 240 nm, where k/4,'/£(240) = ( 2.48 +0.18 ) x 10^ cm sec*; this result was based on five measurements, as shown in the Table. Hochanadel et a l i a observed a similar variation of k^'/EtA) with wavelength, and reported a minimum at 235 nm ( 7 5 )• Their 5 - 1 value: kJ+*/£(248) = 3.0 x 10 cm sec was measured at 248 nm and accordingly may be compared with the results: k/+'/£(245) = 2.6 x 10^ cm sec 1 and k> + , /£(250) = 2 .9 x 10^ cm sec 1 obtained in the present work. Substantial agreement exists between the results of the two studies. No other direct measurement of k4'/£(A) has been reported to date. The value of kjj,V£(?0 was also measured at 240 nm in the - 20? -Table-5.11.A Values of k '^/EXA) f o r the mutual i n t e r a c t i o n of methylperoxy r a d i c a l s at various wavelengths i n the presence of a high oxygen concentration Photoflash energy « 1080 J ( 12 kV, 7.5 ) * 2 Wavelength ma 10"^ k^ * / £ cm sec - 1 H - 86 - A H - 88 - A 210.0 11.90 7.93 212.5 4.32 215.0 4.36 3.59 220.0 3.42 3.62 225.0 2.85 2.88 230.0 2.88 2.50 235.0 2.53 ' 2.81 240.0 2.5*i 2.39 2.26,2.46,2.75 245.0 2.56 2.56 250.0 2.85 3.04 255.0 3.20 3.05 260.0 3.62 3.94 265.0 3.9* 4.66 270.0 5.29 4.57 275.0 8.46 280.0 14.07 10.31, 9.71 282.5 11.68 285.0 33.00 15.37 Notet Mixture Exp No. Concentration mole l " 1 H-86-A Me2N2-4.42xl0"1\ 02»3.32xl0~2 H-88-A Me2N2-4.15x10"1*, O 2«3.Uxl0" 2 - 208 -T a b l e - 5 . 1 1 . B V a l u e s o f k / ^ / e C A ) f o r the m u t u a l i n t e r a c t i o n o f m e t h y l p e r o x y r a d i c a l s a t 2 4 0 nm i n the p r e s e n c e o f a low oxygen c o n c e n t r a t i o n J [ o 2 ] - 1 .1 x 1 0 " 3 mole l " 1 1 0 5 k,' / £ ( X ) ( cm s e c A ) 3 . 2 6 0 . 0 4 4 3 . 2 9 0 . 0 8 6 2 . 8 7 + 0 . 1 6 8 3 . 4 6 + 0 . 1 0 8 2 . 7 3 0 . 1 0 9 2 . 8 7 + 0 . 1 9 4 2 . 5 0 + 0 . 2 2 4 3 . 1 5 + 0 . 0 7 1 3 . 6 9 + 0 . 0 8 0 3 . 0 9 + 0 . 0 9 9 2 . 7 4 0 . 1 0 4 2 . 7 4 0 . 0 7 9 2 . 7 7 + 0 . 7 4 2 . 9 5 + 0 . 0 3 5 2 . 4 1 + 0 . 1 2 2 3 . 0 6 + 0 . 1 6 5 3 . 4 2 + 0 . 0 5 2 mean ( 3 . 0 1 i 0 . 4 2 ) - 209 -presence of a low oxygen pressure at room temperature under otherwise similar experimental conditions. The pressure of -3 -1 oxygen used was 20 to 22 torr( 1.1 ~ 1.2 x 10 mole 1 ). The results are listed in Table-5.11.B; the mean and standard deviation are given by k / +»/e(240) • ( 3.01 + 0.42 ) x 105 cm sec*, in general agreement with the value of ( 2.48 ±0.18 ) x 10^ cm sec 1 measured at the higher oxygen concentration. The latter value is preferred as that system is better defined. (2) The values of The principle of the method of measurement has been discussed in Section B.2.C. The fundamental assumption is that the quantum yield of methyl radicals from the photolysis of azomethane is the same in the absence and In the presence of molecular oxygen. Experiments were conducted in pairs under conditions that differed solely in the absence or presence of oxygen. The oxygen-free system yielded a value of Co from product analysis, and the oxygen-containing system yielded the corresponding value of Ao by linear extrapolation of A to zero time; by definition, = Ao / Col. Values of E(A) are listed in Table-5.12. Maximum absorption occurs at 240 nm, with £(240) = 1.55 x 103 1 mole1 cm1. The corresponding results of other workers are listed In Table-5.13. There is close agreement on the wavelength of maximum absorption in the gas phase, with a single exception; moreover the shift of the maximum in aqueous solution is only sbout 10 nm. There is also no significant difference between the values of E m a x - 210 -Table-5.12 Values of the extinction coefficient of the methylperoxy radical at various wavelengths Photoflash energy i 1080 J ( 12 kV, 7.5 /*P ) x 2 Exp No. & Mixture Wavelength ( nm ) Ao 1 0 " 3 1 mole3" cm1 10" 3 £ (A)* 1 mole 1 cm1 210.0 0.063 0.63 212.5 0.057 0.95 0.74 215.0 0.057 0.95 O.89 H-119-A 220.0 0.060 1.00 I . 0 9 225.0 0.076 1.27 1.28 Azomethane 230.0 0.076 1.27 1.42 . o 2 235.0 0.090 1.50 1.50 = 3'660 240.0 0.093 1.55 1.55 245.0 0.090 1.50 1.4b 250.0 0.077 1.29 1.36 255.0 0.069 1.15 1.20 260.0 0.059 0.99 0.87 265-0 0.052 0.87 0.70 270.0 0.048 0.80 0.52 275.0 0.034 0.57 0.38 280.0 0.023 0.3a 0.29 282.5 0.027 Note 1 * These values of E{>0 were obtained by the interpolation from the curve f i t t e d to the points of Pigure -5.7 [CH^0 2 ] = 7-56 x 1 0 ' ? mole l " 1 for one photoflash sCo [Azomethane3 = 1.638 x 10"^mole l " 1 [o 2] = 3.60 x 1 0 " 2 mole l " 1 Table-5.13 The maximum in the absorption spectrum of the methylperoxy radical Authors Year Method Amax (nm) 10"3 £ ( Amax ) ( 1 mole"1 cm"1 J Parke3, Paul, Quinn and Robson 1973 Molecular modulation spectrometry 240 1.15 Parkas 1975 Molecular modulation spectrometry 240 1.15 Parkes 1977 Molecular modulation spectrometry 23a 1.44 1 0.26 Anastasi, Parke s and Smith 1977 Flash photolysis 23« 1.44 • 0.26 ( Value of Parkes (1977) adopted ) Calvert 1975 Plash photolysis 256 0.345 Hickel 1975 Radiolysis of solution of CH^ , N20 and 0 2 in water 250 1.15 Hachanadel, Ghormley, Boyle and Ogren 1977 Plash photolysis 235 0.64 This work 197a Plash photolysis 240 1.55 - 212 -reported in this work and by Parkes in 1977. The only anomalous result i s £ ( 2 3 5 ) 5 8 840 1 mole1 cm1 reported by Hochanadel et a l i a in a study of the flash photolysis of a mixture of azomethane and oxygen (7 5 ). Their value was deduced from the consumption of azomethane by the flash, which was determined by measuring the change in optical density at 193 nm with a Cary spectrophotometer. This wavelength was chosen to minimize the absorption due to oxygen in the Schumann Hunge bands. The authors claimed that the change in optical density could be measured to an accuracy of t 2 %» The analogous procedure yielded the value of 9000 t 800 1 mole1 cm1 for the extinction coefficient of the methyl radical at 216 nm in close agreement with the result of this work reported in Chapter 3. -1 -1 Their " low * value of 840 1 mole cm i s therefore puzzling; in conjunction with the agreement between their values of k/£(A) and those of the present work i t leads to a oorrespondly low estimate for k^', which w i l l be discussed below. (3) The value of k^'. Pairs of values of k^'/^A) and £(A) are l i s t e d in Tables-5.11.A and 5 . 1 2 for 14 wavelengths in the range from 212.5 nm to 280 nm. The corresponding estimates of k^' are l i s t e d in Table-5«l4 and plotted in Pigure-5.4. The set of five values of k^* measured at 240 nm may be represented by the mean and standard deviation: 10 k/^ * = 3.84 t 0.28 1 mole1 sec 1 Table-5.14 The apparent rate constant k^' for the mutual interact! of methylperoxy radicals at various wavelengths Wavelength 1 0 " 3 £ R 1C ~° lc^' ( 1 mole" 1 sec" 1 ) ( nm ) ( 1 mole 1 cm1) H - 86 - A H - 8 8 - A Estmate from Quadratic Regression Curve 212.5 0 . 9 5 4 . 1 0 5 3-742 2 1 5 - 0 0 . 9 5 4.146 3-412 3-741 2 2 0 . 0 1 . 0 0 3 . ^ 1 9 3.642 3.740 2 2 5 . 0 1 . 2 7 3 . 6 1 6 3 - 6 5 3 3-741 2 3 0 . 0 1 . 2 ? 3 - 6 5 4 3 . 1 7 0 3 . 7 4 3 2 3 5 . 0 1 . 5 0 3 . 7 9 8 4.208 3 . 7 4 9 240 .0 1.55 3 . 9 3 2 . 3 . 7 0 9 3 . 8 1 9 , 3 . 5 0 0 , 4 . 2 5 5 3 . 7 5 1 245 .0 1 . 5 0 3.842 3 - 8 3 3 3 - 7 5 7 2 5 0 . 0 1 . 2 9 3 . 6 7 0 3 - 9 1 8 3 - 7 6 5 2 5 5 . 0 1 . 1 5 0 3.681 3 . 5 H 3 . 7 7 4 2 6 0 . 0 0 . 9 9 3 - 5 8 1 3 . 9 0 5 3 - 7 8 5 2 6 5 . 0 0.87 3.424 4 . 0 5 4 3 - 7 9 7 2 7 0 . 0 0.80 4 . 2 3 5 3 - 6 5 6 3-811 2 7 5 . 0 0.57 3-826 280 .0 0 . 3 8 3 . 9 1 8 . 3 . 6 9 1 3.840 Mean 1 3 . 7 5 i 0 . 2 5 - 2 1 4 -Figure-5'4 Experimental values of 10 k^' with mean, standard deviation and linear and quadratic regression lines 4.4 4.2 4.0 3.8 3.6 3.2 o o o o o STANDARD O DEVIATION o o o o QUADRATIC REGRESSION =A°R"'^ MEAN LINEAR REGRESSION Q Q O o o o o o o o o o o o o . o 1 • 1 1 1 200 220 240 260 280 A ( n m ) - 215 -The set of thirty values of k^ ' measured at wavelengths from 212.5 nm to 280 nm may be similarly represented: 10 8 k// = 3 . 7 6 t 0.27 1 mole 1 see 1 There is no significant difference between the means of these two sets. It is obviously desirable to establish that the value estimated for ki^' i s independent of the wavelength used in the experiments of Table-5«l4. Accordingly, a linear regression line and a quadratic regression curve were f i t t e d to these results by standard s t a t i s t i c a l methods. The results are expressed by the equations below, where k^ ' i s given in 1 mole1 sec 1 and A in nm. The linear regression line i s : 10 8 ty* = ( 3.40 t 0 . 6 3 ) + ( 1 .51 t 2 . 5 8 ) x 10 3 A = ( 3.76 + O.63 ) + ( 1.51 t 2.58 ) x 10 3 ( A - 240 ) The gradient does not d i f f e r significantly from zero and the intercept at A = 0 does not di f f e r significantly from the mean value of 3 . 7 6 . The correlation coefficient has the low value of 0.11. A quadratic regression procedure i s more appropriate to this problem because the associated variable £(A) has a single maximum and i t s variation with A has a roughly parabolic shape. The quadratic regression curve i s : 1 0 8 k^ ' = 5 . 1 6 - ( 1 . 2 9 x 1 0 2 )A + ( 2 . 9 2 x 1 0 5 ) A2 -3 = 3 . 7 5 + ( 1.12 x 10 ) ( A - 240 ) + ( 2.92 x 10 5) ( A - 240 ) 2 - 216 --8 The corresponding estimates of 10 k^ at each wavelength of interest are given in the f i n a l column of Table-5.14. The parabola has a minimum of 3.7^0 at 220 nm, with values of 3.7^2 and 3.840 at 212.5 and 280 nm repectively. A minimum towards the lower end of the wavelength range is consistent with the positive gradient of the linear regression l i n e . Figure-5.4 -8 displays the experimental values of 10 k|j/ in relation to the mean value and i t s standard deviation; the linear regression line and the quadratic regression curve are also drawn. This Figure provides s t a t i s t i c a l evidence that the value of an estimate of k^* i s not significantly influenced by the wavelength chosen for the measurement. (4) The absorption spectrum of methylperoxy radical. (a) The absorption spectrum of CH-jO-? by photographic detection. The absorption spectrum of the methylperoxy radical was detected by the photographic technique as a broad peak without fine structure centred on 240 nm. The spectrum and the microphotodensitometer traces of the methylperoxy radical are shown in Figure - 5 . 5 . The calibration of the photographic plate was carried out using the absorption lines of s i l i c a . The l i f e time of methylperoxy radical was expected to be comparatively long from the time sequence of the spectrum. (b) The absorption spectrum of CH-^ O^  by photoelectric detection. The photoelectric technique confirmed and extended the results of the photographic technique. The values of ^(AJ/kii/ at various wavelengths are shown in Table - 5 . 1 5 ; each value i s - 21? -Figure-5.5 Absorption spectrum of CH^OO* by photographic d e t e c t i o n and the corresponding microphotodensitometer t r a c e s Blank Before After 20 lis 40 80 120 150 200 Before After Blank 220 230 240 A ( nm) 250 260 Before 220 240 260 A(nm) - 218 -Table -5 .15 Values of e(A)A^ for the mutual interaction of methylperoxy radicals Wavelength 10 6 6 (A )A; sec cm nm H-86-A H-ya-A 2 1 0 . 0 0 . t t 4 l 1 .26 2 1 2 . 5 2 . 3 1 2 1 5 . 0 2 . 2 9 2 . 7 8 2 2 0 . 0 2 . 9 3 2 . 7 6 2 2 5 . 0 3 . 5 1 3.48 2 3 0 . 0 3.48 4 . 0 1 2 3 5 . 0 3 . 9 5 3 . 5 7 240.0 3 . 9 4 , 4.18 4.06, 4 . 4 3 , 3-64 245.0 3 . 9 1 3 - 9 1 2 5 0 . 0 3 . 5 2 3 . 2 9 2 5 5 . 0 3 . 1 2 3.28 2 6 0 . 0 2 . 7 7 2 . 5 4 2 6 5 . 0 • 2 . 5 4 2 . 1 5 2 7 0 . 0 I . 8 9 2 . 1 9 2 7 5 . 0 1.18 280.0 0 . 7 1 1 0 . 9 7 0 , 1 . 0 3 2 8 2 . 5 0 . 8 5 6 2 8 5 . 0 0 . 3 0 3 0 . 6 5 1 - 219 -Figure-5.6 The relative and normalized absorption spectrum of CH^ OO* by photoelectric detection 220 240 260 280 X ( nm) Note i the right hand ordinate was calibrated using Q the normalizing factor » k = 3«75 x 10 1 mole~1sec~'1". - 220 -Figure-5.7 The absolute absorption spectrum of the methylperoxy radical ~° ThJS WOrk(kinetic method) 'E u o E UJ C\J ' O 15 • • ThiS WOrk (analytical method) A A parkes et al o © Hochanadel et al • Hickel 10 0 220 240 260 A ( nm ) 280 Note i 1) Parkes et al's curve was scaled up to give £(238)= 1.44 xlO 3 1 moli1cm1 to conform with Parkes (1977). 2) Hickel's curve was measured for an aqueous solution. - 221 -the reciprocal of the corresponding value of Table-5«11«A. A plot of. the value of E(A)/k^* against wavelength represents the absorption spectrum of transient species in arbitary units and is shown in Figure-5.6. The absolute absorption spectrum of the methylperoxy radical was obtained by measuring the absorbance A m p y and the data of product analysis. Other absolute determinations of this spectrum have been described by Anastasi, Parkes and Smith in 1977 ( 86 ) ( based upon the spectrum of Parkes, Paul, Quinn and Robson of 1973» but with revised normalization scaled on a change from £(240) = 1150 1 mole1 cm1 to £(240) = 1^38 1 mole1 cm1 ), by Hochanadel, Gormley and Boyle in 1977 ( 75 )» and ( in aqueous solution ) by Hickel in 1975 ( 28 ). The two gas phase and one li q u i d phase spectra are included for comparison in Figure - 5 . 7 . There is excellent qualitative agreement about the general form and the position of the maximum, but the absolute values of €E(A) reported by Hochanadel et a l i a are uniformly lower than the values of the other authors. (5) The value of k k. (a) The output of the computer programme. Reaction conditions were chosen so that v i r t u a l l y a l l the methyl radicals generated by the photoflash were oxidised to methylperoxy radicals. A computer programme was written to study the kinetics of the decay of the methylperoxy radical concentration, and for this programme i t was assumed that a l l the methylperoxy radicals formed were simultaneously present at the concentration Co at zero time. The mechanism used in the - 222 -Figure-5-8 The effect upon the computed value of ki^ /k^ of varying the value of each of the rate constants k^, k 6, k ?, kQ, k 1 0 , k n and k 1 2 used in the programme - 0 . 5 0.5 log k/k° Note : ( 1 ) s 3<5 x 10 1 mole" sec" for each t r i a l . (2) each curve shows the effect of varying a single rate constant, with the remainder held constant at the k° values. ( 3 ) the effect of varying either k^  or k^  is negligible, so the corresponding points lie on a common horizontal line. - 223 -programme comprised the eight reactions given in Table-5.8 in Section B.2.d.ii. The main purpose of the programme was to calculate an appropriate value of the ratio k^'/k^ for each experiment so that a value of the fundamental rate constant could be deduced from the experimental value of k^'. A preliminary study of the computer programme was undertaken to find out how sensitive the value of the ratio k/^ '/k/j. would be to the choice of values of the rate constants of the mechanism used in the programme. The principal values k° of these rate constants are those of Table-5.8, and are given below in units of 1 mole1 sec 1: k£ = 3.5 x 10 8 k° = 4.0 x 10 5 = l-?5 x 10 8 k J Q = 3.3 x 10 8 k£ = 9.2 x 10 8 k j x » 1.0 x 10 1 0 k° = 1.0 x 10 1 0 k j 2 = 2.0 x 10 9 One of these was varied in each t r i a l , while a l l the others were held constant, and the output gave the corresponding value of k/j.'/k/j,. The results of this study are illustrated by Figure-5.8, where the percentage deviation of k^' from k^ is plotted against k/k° and each line shows the effect of the variation of the value of a single rate constant. The horizontal axis gives the value of k/k° for each line on a logarithmic scale. The effect of the variation of each rate constant of Figure -5.8 upon k^'/kjij, may be correlated with its effect upon the balance between the eight reactions of Table-5.8. An increase in the value of can cause the value of - 224 -k^'/kzj, to increase only between two well defined limits. The lower limit occurs for k ^ a — 0 when reactions ( 4 ) and ( 4* ) are identical, so that kl^ »/ki+—*• 1» The upper li m i t i s reached when each CH^ O* radical formed in reaction ( 4 a ) consumes one CH-jOO* radical: either directly in reaction ( 4 ), or indirectly in reactions ( 6 ) and ( 10 ). The upper limit i s k^/k^ 1 + ( ^ a / k 4 )• The influence of each of the rate constants k ^ to k^ 2 upon the value of k^'/k^ may be explained qualitatively by reference to Table-5.16. This describes the instantaneous condition of a representative reacting system at a representative time. The characteristics of the system are given in Figure-5«2.A and Tables-5.9»A and 5«17. The half l i f e of the CH^ OO* radical was adopted as the representative time; this i s 2000 microsec in that system. The corresponding concentrations of QKjQQ*, CH^ O* and HOC were found in Table-5»9.A; the percentage of each radical consumed in each reaction was calculated from the instantaneous rates of reaction in Table-5.16. An increase in k^ a has the positive effect of increasing ^4'/ki|, because i t causes an Increased consumption of CH-jOO* radicals by the CH-jO* and HOO* daughter radicals. However, only a minority of the daughter radicals react with the CH-^ OO* radicals, so that the value of ki^/kjj, i s closer to i t s lower limit than to i t s upper l i m i t . The effect of k^ g. upon the value of k^Vk^ is therefore significant and positive, but not large. The general lnsensitlvlty of k^'/k^ to the values of the other rate constants, k^ to k l 2 is due to the fact that the vast majority of CH^ OO* radicals are consumed by mutual interaction: Table -5 .16 Relative rates of reaction and patterns of consumption of radicals at the half l i f e of the reacting system of Table - 5 . 9 .A and Pigure -5 .2 .A. Reactions and rate constants as listed in Table 5 - « Conditions i time * 2000 pec , [ 0 2 ] " 3-23 x 10~2 mole l " 1 , [ C H 300-] =3.3 x 10"7 mole l " 1 , [cH-jO-] = 2.9 x 10"^ mole 1"1, [ H O O * ] - 8.4 x 10 " 8 mole l " 1 Reactions ( n ) Rate of reaction value i n mole l - 1 1 and s e c - 1 Percentage of each radical consumed by reaction ( n ) CH 300* cHyr H O O " 4 2 k^ [ C H 3 0 0 ' ] 2 7.6 x 10~5 88. 4a kjy [ c ^ O O ' ] 2 3.8 x 10'5 6 k 6 [ C H ^ O O * ] [cHyr] 8.7 x 10 - 7 1. 2. 7 2 k ? [cH-jO*]2 1.6 x 10"7 0.4 9 k 9 [cH 30-][0 2] 3.7 x 10"5 92. 10 k 1 Q [cH-jOO*] [ H O O * ] 9.7 x 10"6 11. 24. 11 k l l [ C H3 0' ] [ H O O # ] 2.4 x 10"6 6. 6. 12 2 k 1 2 [ H O O * ] 2 2.8 x 10"5 70. - 226 -88 % as Table-5.16 shows. Reaction ( 10 ) comes next, with 11 % consumption and so the value of k^Q has a significant positive effect upon the value of k^'/k^. Reaction ( 6 ) comes last, and the influence of k£ is perceptible but minor and positive. The relative influence upon the value of k^Vk^ of k^, kr>, k^ and k^ 0 is consistent with the relative rates of the corresponding reactions, which a l l consume the CH^ O* radical. Reaction ( 9 ) plays the dominant role, converting 92 % of the CH^ O* radicals to HOO* radicals and causing [ HOO*] »[CH-jO'] after a brief i n i t i a l period, as Figure-5«2.A shows. Indeed, 98 % of the CH-jO* radicals are consumed by the participation of reaction ( 9 )i either directly, or indirectly by reaction with the HOO' radical formed in reaction ( 9 )• Although reaction ( 9 ) occupies such a predominant position in the pattern of consumption of the CH-jO* radical, i t merely converts the GH-jO* radical into the HOO* radical, so that an alteration in the value of ko, does not have a significant effect upon k/^'/k^. The latter is influenced by the CH^ Q* radical through reaction ( 6 ), which removes 1 % of the CH^ OO* radicals; accordingly k^ has a perceptible but small positive effect. Reaction ( 7 ) removes no CH^ OO* radicals and only 0.4 % of the CH-^ O' radicals, and consequently kr, has a negligible effect. The HOO* radical is the dominant daughter radical in this system, and the pattern of its reactions has a significant effect upon k^'Ajj,, because 11 % of the CH^ OO* radicals react with 24 % of the HOO* radicals and k 1 Q has a significant positive effect upon k^'/k^. Both k ^ and k 1 2 have a significant effect upon the value of k^'/k^; the effect is - 22? -negative, because an increase In the rate of reaction ( 11 ) or ( 12 ) leaves fewer HOO* radicals to react with the CHQ00* reaction ( 12 ) removes the larger percentage of HOO* radicals. An alternative approach to the interpretation of Pigure - 5 . 8 could be based on the data of Table-5.17. Each entry gives the extent of the specified reaction ( n ) up to the specified time t. The extent of reaction ( n ) i s expressed as the integral R n dt of the rate R n over the elapsed time t. For reactions at a time t may be assessed by comparing the corresponding entries in Table-5.17. These entries may then be used to discuss the detailed pattern of Figure - 5 . 8 . If the relative values of the entries at 2000 microsec are compared with the relative values of the rates of reaction in Table-5.16, i t w i l l be seen that a similar pattern emerges in each case, even though the former are integrated data while the latter are instantaneous data. Similar conclusions would therefore be drawn from either method, suggesting that each method i s quantitatively valid. The secondary purpose of the computer programme was to plot the variation of the concentrations of the radicals CH^ OO*, CH-jQ* and HOO* throughout the period of observation. Flgures-5«2.A and B represent two contrasting typical plots obtained by using - 2 - 3 -1 oxygen concentrations of 3 . 2 3 x 10 and 1 .0 x 10 mole 1 respectively with otherwise Identical conditions. At the higher oxygen concentration H00* is the dominant daughter radical, with 3 radicals. The negative effect of k l 2 i s the greater, because Table-5.1? Extents of reaction for reactions k to 12 expressed as the integral si J** R n dt of the rates R n usee 4a 4 6 7 9 10 11 12 f O.OOOul -01 o.oooot -0 1 O . O O O u i . -01 o.oooot -01 U.OOOjc -01 O.OOOOc -01 O.OOOOE -01 0.0000k-01 i U l l . 1 . 4 J 3 J L - uz 2 . 0/05( -02 2. It 3 36h -04 5.6b37c -Ob 6.2514.. -03 4.8140. -0 5 1. 5006. -05 3.551lk-06 ZOO. 2 . 74 7 /f -Cz b.4954k - 0 2 7 . 6 6 * . uc -Oi 2.0b2 7 £ -04 l . / J o l . -02 2,7897c -04 1.140-.E -04 6,0009E-05 300. 3.9bl/t -uz 7.9024k - 0 2 1. 24H-.C -03 3.63o7t -04 2.6868c -02 7. 1046c -04 3.1148k -04 2.6343E-04 4 . 0 0 . 5.0b79C -0/ I.01IU - 0 1 1.683/c -0 3 5.0482C -04 3.9732. -02 1. 3125c -03 b . b i b / t -04 6.86426-04 boO, t, 07obi. -0/ 1.2 I57i -01 2,0tn-.L -03 6.250UE -0-. 4.V748C -02 2.0-.9bi. -03 9.0596E -04 1.3758E-03 600. 7.0/19£ -0 2 1.4044E -01 2.4095/ -03 7.2711E -04 5.69 73c -02 2. 813-.4c -03 1.2556k -03 2.139 7E-01 (00. 7.D963E -02 1.5793E -01 2.7125E -03 a.1395t -04 6.7484c -02 3.d056c - J3 1.6216k -03 3.576IE-03 600. 6.70tf6t -02 1.74176 -01 2.9826E -03 8.8624E -04 7.5357c -02 4. 7762c -03 1 .9936k -03 5.06896-03 900. 9.46471: -Oz 1.6V29L -01 3.2243E -03 9.5/16E -04 8.2659c -02 5.7d34c -03 2.3647k -03 4.7952E-03 1000. 1.01 7oL -01 2.0 340E -01 3.441 be -03 1.0074c -03 8.9450c -02 6.8110c -03 2.729>3k -03 •.72796-03 l l o u . 1 . ( Jb iot -01 2 . 1 6 5S1 -111 3.6 37zt -03 I.05bbt -u3 9.5782. -02 7.8534/ -03 3.0659E -03 1.0839E-02 120b. 1.1447F -01 2.2845E -01 3.dl43E -03 1.0975E -0 3 1.0170c -01 8.8954c -0 3 3.4302E -03 1.310OE-02 1300. 1.2027C -01 2.40541 -01 3.9749E -03 1.1343E -03 1.0724c -01 9.9320c -03 3.7613E -03 1.5484E-02 1430. 1.2b71c -01 2.5143r -01 4.12ICt -03 1. 1667ii -0 3 1.1244. -01 1.095dc -02 4.0765C -03 1.7967E-02 1560. 1.3C84E -OT" 2.6 16UE -01 " "' 4.2544E -03 I.1954E -0 3 1. 17 34c -01 1.1968c -02 4.3613E -03 2.0526E-02 1600. 1.3bcuE -01 2 . 7 1356 -01 4.3763c -03 1.2209E -03 1.2194c -01 I.2959c -02 4 . 6 6 96k -03 2.3140E-02 1700. 1.43/41: -01 2.6d4oE - 0 1 4.4DU/C -03 1.2435E -0 3 1.2629. -01 1.3929c -02 4.44171 -03 2.5792E-02 1800. 1.4s56E -01 2.8912F -01 4.59106 -03 1.263bE -03 1.3040c -01 1.4877c -02 5.2038E -03 2.8465E-02 1900. 1 .48631: -01 2.9729E -01 4.6657k -03 1.28196 -0 3 1.3430c -01 1.5801c -02 5.4505k -03 3.1148E-02 2000. 1.5/5/6 -01 3.0505E -01 4.7731c -0 3 1.29b3c -03 1.3799c -01 1.6699c -02 5.6642E -03 3.362 7E-02 2100. 1.5620E -01 3. 1 24 Ik -01 ' '4.8540c -03 1.3130E -03 1.4149c -01 1.7573c -02 5.90566 -03 3.6494E-02 2200. 1.59 7 0 E -01 3.194IE -01 4.929UE -03 1.3262E -03 1.4462. -01 1.8422c -02 6.1152E -03 3.9140E-02 2->00. 1 .6 lO 31 -01 3. 260 71 -01 4 . S S b t c -01 1.3383E -C3 1.4799. -01 1.9245c -02 6 .3116i -03 4.I759E-02 2400. 1.66/Of -01 3.324 IE -01 S.0633E -03 1.3492E -03 1.510U -01 2.0044c -02 6.S0U6 -03 4.4344E-02 2500. 1.6923E -01 3.3846E -01 5.123et -03 1.35926 -03 1.5389c -01 2.0818c -02 6.6 7 95k -03 4.6692E-02 2600. 1.72I2E -01 3.4424E -01 5. I79*»c -03 1.36d2E -03 1.5664c -01 2.1569c -02 6.8481C -03 4.93996-02. 2700. 1.7488E -01 3.4976t -01 5.2325c -03 1.3765E -03 1.5927c -01 2.2296c -02 7.0076k -03 5.16616-02 2800. 1.7752E -01 3. 5 504E -01 5.2817c -03 1.384U -0 3 1.6179c -01 2.3000c -02 T.1593E -03 5.42 78E-02 2900. 1.bOObE -01 i . t o c v i -01 5.1279t -03 1.391 IE -01 1.6420c -01 2.3663c -02 7.30291 -03 5.6647E-02 3000. 1.0 / - .7E -01 3.6494E -01 5.37122 -03 1.3975E -03 1.6651c -01 2.4344c -02 7.4391E -01 •..•9676-02 310U. 1.U479E -01 3.695SE -01 5.4118E -03 1.4034E-03 1.6873c -01 2.4985c -02 7.56846 -03 6.12376-02 3200. 1.8702E -01 3.74056 -01 5.4501L -03 1.40866 -03 1.7066. -01 2.5605c -02 7.6913c -03 6,345.6-02. 3 J O O . 1.8916E -01 """ 3.7633L -01 S.486/C -03 1.41386 -03 1.7290c -01 2.6207c -02 7.8080k -03 6.5&29E-02 3400. 1.9I22E -01 3.62451 -01 5.5202c -03 1.4185c -03 1.7487c -01 2.6790c -02 7.9I89C -03 6.77516-02 3S0u. l . - » 3 / 0 f -01 3.b641t -01 5 . 5 5 2 -03 1.4//6C -0 3 1. 7 6 77. -01 2.7355c -02 6.0245E -03 6.9824E-02 3e00. 1.951 IE -CI 3.9023E -01 5.5u2oE -03 1.4268E -03 1.7859c -01 2.7903c -02 6.1250k -03 7. 1847E-02 3700. 1.96956 -01 3.9 1906 -01 5.611 J t -03 1.4305E -0 3 1.6035c -01 2.8435c -02 i.22071 -03 7.1823E-02 J600. 1.98 721: -01 3.9745E - u l 5.6385c -03 1.4339k -03 1.6205c -01 2.8950. -02 8.3I19E -03 7,57526-02 '3900i 2.C04JC -CI 4.0066E -01 5.6642C -03 1.4371E -03 1.8368c -01 2.9451c -02 8.39H9E -03 7.76356-02 4000. 2.0/OdE - t l 4.04161 -01 5.68H7E -03 1.4401E -03 1.6b/6c -01 2.9936c -02 8.4618E -03 7.94736-02 4100. 2.0367E -01 4.0I35E - 0 1 5.7119E -03 1.4429E -0 3 1 .6679c -01 3.0406. -02 6. 56 lOll -03 8.12666-02 4 200. 2.OS/IE -01 4.1043E -01 5.733*6 -03 1.4455E -OS 1.8827c -01 3.0865c -02 8.63661 -03 •.30166-02 4300. 2.067JE -01 4.1341t -01 5.I54VL -03 1.4480E -03 1.8910c -01 3.1310c -02 6.70891 -03 •.47246-02 4400. 2.L814E -01 4. 162'* -01 5.774>»t -0 3 1.4503E -0 3 1.9108c -01 3.1742c -02 6, 7 7a01 -03 •,63916-02 4500. 2.0-.S3E -01 " 4. 190 7E -01 5.793*k -03 1.4524E -03 1.9242c -01 3.2162c -02 8.84411 -03 •.8018E-02 460o. Z.loduf -01 4 . 2177E -01 5.8120c -03 1.4544k -0 3 1 .9372c -01 3.2510c -02 6. 90 HE -03 (.96066-02 4700. 2 . 1/ l i t -01 4. 2 4 3S1 -CI 5. 82"<4t -C3 I,4b63c -0 3 1.9498. -01 3.2968c -02 8. 96dOt -03 9.1I56E-02 4800. 2.1346E -01 4.26921 - 0 1 5.8459c -03 1.45816 -03 1.9620c -01 3.33S4c -02 9.0261E -03 9.26696-02 4930. 2.1469E -01 4.29361 -01 5.8617c -03 1.45986 -0 3 1.9738c -01 3.3730c -02 «.081ek -03 9.41466-02 5000. 2.15666 -01 4.3177E -01 5.0766E -03 1.4614k -03 1.9853c -01 3.4096c -o? 9.1352k -03) - 2 2 9 -[HOO'l/fcH^O*] reaching 15 at 1000 microsec and 64 at 5000 microsec. In contrast, at the lower oxygen concentration CH^ O* i s the dominant radical from the start to 3500 microsec, and [CH^O*]/[HOO*] = 3 . 9 at 1000 microsec. This difference i s due to the c r i t i c a l effect of [o2] upon the rate of reaction ( 9 )s R9 = [o 2 ] [cH-jO* ], which converts the CH^ O* radical into the H00* radical. At the lower oxygen concentration R9 i s minor; at the higher concentration R9 is dominant. As a valuable consequence of this difference we may measure the value of k/j,* in two systems in which the balance of the reactions ( 6 ) to ( 12 ) i s significantly different. The value of kj^'/k^ may then be computed for each system, and the resulting values of k^ , compared. If these are in agreement, the va l i d i t y of this method of computing the value of k^ receives significant support. The accuracy of the computing procedure w i l l be Insensitive to the choice of values for k^, kr, and k^, as Pigure - 5 . 8 shows, but moderately sensitive to the choice of values for k^a* k l o » k^i and k^2« The value of k^ 2 1 3 reasonably well known from experiment, but there is less agreement about k^^, and the value t of k^ Q i s frankly speculative. However the chosen values do f i t a general pattern of reactivity for radical species. Literature values of k/j^/k^ were reviewed by Parkes in 1977 ( 5 ); the principal results are O .43, 0.48 and 0 . 3 4 , and are included in Table-5.18. The two values 0 . 5 0 and O.33 have been adopted for the calculation of k^ '/k/^  by the computer programme in conjunction with the values of k^ to k 1 2 given in Table -5 .8 and an appropriate value of k^. The latter is found by iteration - 230 -from the experimental value k^t = ( 3 . 7 6 + 0.27 ) x 10° 1 mole sec 1. Thus for k^aAi* = 0 .50 and the higher oxygen pressure the 8 —1 l values k^ » 3.4 x 10 1 mole sec 1, k^'/k^ =» 1.11 are a self consistent set. Since two oxygen pressures were used, and two values of k^a/k^ were adopted, there w i l l be four sets of this kind. (b) The evaluation of k^. The experimental value of k^* measured with -2 — 1 Q [ 0 2 ] = 3 . 2 3 x 10 mole 1 i s : k^» = ( 3 . 7 6 t 0 .27 ) x 10 1 mole1 sec 1. This result is based upon 30 values of k^»/£(X) measured over a range of wavelength from 212.5 to 280 nm. With k^g/k^ =s 0 . 5 0 the programme gives k^'/k^ = 1.11, so that 8 —1 1 fy, = ( 3.4 i 0.24 ) x 10 1 mole sec . The experimental value of k^' measured with [0 2] - 1.0 x 10 mole l 1 i s : k^* = ( 4.6+0.65 ) x 10 8 1 mole1 seo 1. This result i s based upon 17 values of k^'/EXTO measured at 240 nm. With k^a/k^ = 0 . 5 0 , the programme gives k^'/k^ = 1.18 and = ( 3*9 t O .55 ) x 10° 1 mole sec . These two estimates of kjj, are in reasonable agreement, as the difference of their means divided by the sum of their standard deviations i s only O .65 . Each estimate was weighted in proportion to the inverse square of i t s standard deviation. The weighted mean value i s : 1% = ( 3.5 t 0 .3 ) x 10 8 1 mole1 sec 1 The calculations were repeated with k^/k^ = O . 3 3 . This yielded the results: (i) When [ o 2 ] = 3«23 x 10 mole 1 and ty' = ( 3.76 t 0.27 ) x 10 1 mole sec : fy'/fy - 1.07 and - 231 -\ = ( 3.5 t 0.25 ) i 108 1 mole1 sec 1. ( i i ) When [o2] - 1.0 x 10^  mole 1 and * V = ( ^ . 6 t O.65 ) x 108 1 mole1 sec 1: fy'/fy 3 3 1-10 and k^ = ( 4.2 + 0.60 ) x 10 1 mole sec . ( i i i ) the weighted mean i s : ^ 3 ( 3.6 - 0.3 ) x 10 1 mole sec A. (iv) the difference of the means divided by the sum of the standard deviations i s 0.80, so that agreement between these two estimates of is slightly less satisfactory than when calculated with k^a/kij, as 0 .50. The f i n a l estimate of k^ i s not affected significantly when the value of k^/k^ is varied from 0.33 to 0 .50, which spans the range of the published values. The preferred value of this work 8 —1 —1 i s k^ = ( 3 . 5 t 0 . 3 ) x 10 1 mole sec , based upon the two estimates of k^' at the high and low oxygen concentrations, and fya/fy = 0.50. Table-5.18 l i s t s the published values of both ]%' and k^. The estimates given by Parkes in 1977 are in reasonable agreement with the results of this work. The value: k^ = io8*5~0** 1 mole1 sec 1 is probably a f a i r statement of our knowledge of this quantity. Table-5.18 Values of k^', k^ and related quantities X Authors Year Method 10 U V ( 1 mole" ] 15 6 k 4  L sec" 1 ) V k^a 15 8 V ( 1 moj l58^4b-Hc) Le" 1 aeo" 1 ) 10 8 kk Weaver, Shortrldge, Meagher and Helchklen 1975 photolysis and gaa chromatography analysis — — — 0.43 — — Alcock and Mile 1975 photolysis — — 0.48 2.3 2.4 2.4 Parkes,Paul Quinn and Robson 1973 molecular modulation spectrometry 2 .65 — — — — — — Par Ices 1975 molecular modulation spectrometry 2 .65 2.3 1.13 0.37 1.47 0.8? 2.3 Parkes 1977 molecular modulation spectrometry 3.3-0 . 06 2.80 1.18 0.34 1.8410.48 0.9610.24 2.810.7 Anastasl, Parkes and Smith 1977 f l a s h photolysis 2.6510.42 — — — — — • — Hochanadel, Ghormley, Boyle and Ogren 1977 f l a s h photolysis 2 .310.3 — — — — — — This work 1978 f l a s h photolysis 3.7610.27 — — — — . — 3.510.4 - 233 -D, Conclusions* Reviewing the spectra shown in Pigure-5«7 and the kinetic results in Table-5«18 and in Section C5«h» three main conclusions may be drawn: (i) there is good agreement between the results of this investigation and corresponding reports in the literature; ( i i ) the absorption spectrum of the methyperoxy radical has been characterized, both qualitatively and quantitatively; ( i i i ) the rate constant for the mutual interation of methylperoxy radicals at 298 K has been determined, and the most recent estimates are consistent with a value of 10 * 1 mole -1 sec • - 234 -CHAPTER 6 THE MUTUAL INTERACTION OF ETHYLPEROXY RADICALS  A, Introduction (1) The absorption spectrum of the ethylperoxy radical The ethylperoxy radical i s the second member of the homologous series of n-alkylperoxy radicals. The characteristic behaviour of this radical i s analogous to that of methylperoxy radical. For example, the ethylperoxy radical i s one of the principal chain carriers in the mechanism of the combustion of ethane in air or oxygen. The ethyl radical i s formed in the in i t i a t i o n step: CH^CH^ + 0 2 - CH^CH^ + HOO* The ethyl radical i s another principal chain carrier, and reacts rapidly with the oxygen molecule to form the ethylperoxy radical* CH^CH; + Q0 + M -CH-aCHoOO* + H - 235 -The absorption spectrum of the ethylperoxy radical was f i r s t determined by Parkes, Paul, Quinn and Robson ( 38 ) using the technique of molecular modulation spectroscopy. The ethylperoxy radical was generated by the photolysis of azoethane i n the presence of oxygen and a large excess of argon or nitrogen as diluents* C2H^-N=N-C2H5 + hv - 2 + N£ C2H*j + 0 2 + M » C 2H 5 00* + M They discovered a broad absorption band extending from 220 to 290 nm: maximum absorption occurred at 235 nm. However they could not characterize the spectrum unambiguously. The absorption spectrum of the ethylperoxy radical i n aqueous solution was characterized by Hickel in 1975 ( 2 8 ). The radicals were generated by the radiolysis of an aqueous solution of ethane, oxygen and nitrous oxide. The ethylperoxy radicals were generated by a mechanism analogous to that given for methylperoxy radicals in an aqueous solution in Section A.l. of Chapter 6 . Radiolysis yielded ethyl radicals by metathesis between the hydroxyl radicals and the ethane molecules dissolved in water: C 2H 6(aq) + OH'(aq) * C2H^(aq) + H 2 0 ( 1 ) and yielded ethylperoxy radicals by addition of oxygen: C2H^(aq) + 0 2(aq) C^OO* (aq) The absorbance of the system was observed at 10 nm intervals - 236 -between 210 and 310 nm, and was corrected for absorption by the hydroperoxy radical. The spectrum had a maximum at 250 nm with a extinction coefficient of about 1 .25 x 10-^ 1 mole cm which was independent of the pH of the solution between pH 4 . 1 and pH 9 . 9 , and was thereby distinguished from the spectrum of the hydroperoxy radical. (2) The mechanism of the photooxidation of azoethane. A comprehensive mechanism for the photooxidation of azoethane has not been postulated, but i t should be analogous to the mechanism proposed for azomethane by Parkes in 1977 ( 5 ) , supplemented by the disproportionation reactions ( 3c ) , ( 5c ) and ( 8c ) that yield ethene. Such a mechanism for azoethane i s given in Table - 6 . 1 . This mechanism w i l l be used as a basis for the discussion of the kinetics of the generation and consumption of the ethylperoxy radical. The value of certain of the rate constants i s in dispute, and a c r i t i c a l assessment of the published data i s given in the next section. ( 3 ) Values of rate constants used in the computer programme,  (a) Assessment of existing data. Computer programmes which were written to study the kinetic behaviour of the methylperoxy radical were adapted to study the kinetic behaviour attending the generation and subsequent reactions of the ethylperoxy radical, and to evaluate the rate constant k^ = k^ a + k ^ + k^c- Therefore values for the rate constants of reactions ( 2 ) to ( 12 ) in Table - 6 . 1 were required. Unfortunately, accurate values are available for only a few of - 2 3 ? -Table-6.1 The mechanism of the photooxidation of azoethane C2H5-N=N-C2H5 • hV 2 CgH^ • N 2 (1) 2 C2H5 n- C i fH 1 0 (2a) - C 2H 4 • C 2H 6 (2b) C2H'5 * 0 2 C2H500' ( 3 a ) - CH^ CHO + OH (3b) - c2\ • HOO* ( 3 c ) 2 C2H500* 2 C2H50* • 0 2 (4a) - C2H50H • CH^ CHO • 0 2 (4b) *• C2H^00C2H5 + 0 2 (4c) C2H^ C2H500* 2 C2H50* ( 5 a ) CgHyJOCgH^ (5b) - C2H^00H • CgH^ ( 5 c ) C2H50* • C2H500' C2H500H • Ch^ CHO (6) 2 C2H50* C2H50H • CH3CHO (7a) +* C2H^00C2H5 (7b) C2H^ • C2H50* C 2H 6 • CH3CHO (8a) - CgH^OCgH^ (8b) - C^ H^ OH • CpH^ (8c) continued.... - 23a -C2H50' • 0 2 - CH3CHO •HOO' ( 9 ) C2H500* • HOO* C2H5OOH • 0 2 (10) C2H50* • HOO* - C2H5OH • 0 2 (11) 2 HOO* - HOOH • 0 2 (12) CgH^ O* • GH-jCHO - C2H^0H + CH^ CO ( 13) CH^ CO • 0 2 - CO • CH^ OO (14a) » HOO* + CH2=C=0 (14b) » CH^ COOO* (14c) CH^ CO* CH^ *• CO (15) CH^ • 0 2 CH300* (16) The characteristic disproportionation reactions are ( 3 c ) , ( 5 c ) and ( 8 c ) and yield ethene. - 239 -these reactions. For some of the others, the estimates span a wide range of values. For the rest, the estimates either were obtained by an indirect method, or were purely conjectural. The available estimates w i l l be reviewed for the rate constant of each reaction of interest, and a value selected for the programmes. (b) Mutual interaction. (i) The mutual interaction of ethyl radicals. 2 C2H^ k £ a . n-C 4H 1 Q j k 2 a = 1.24 x 1 0 1 0 1 mole 1 sec 1 ^ 2 b - CgH^ + C 2H 6; k 2 b = 0 . 1 7 x 1 0 1 0 1 mole 1 sec 1 ; k 2 = 1.41 x 1 0 1 0 1 mole 1 sec 1 This i s the value obtained in this work and discussed in Section C .4 of Chapter 4 . ( i i ) The mutual interaction of hydroperoxy radicals. 2 HOO' HOOH + 0 2 ; k 1 2 = 2 x 1 0 9 1 mole1 sec 1 This value was selected by Lloyd in 1974 ( 1 3 ) and the c r i t i c a l assessment of the published results list e d in Table-5-2 was given in Section A.3«h of Chapter 5« ( i i i ) The mutual interaction of ethylperoxy radicals. 2 C2H^00* - a l l products ; k^ = 5-8? x 1 0 7 1 mole1 sec 1 The contributing reactions are: 2 C 2H 5 00* 2 C 2Hyr «> 0 2 ( 4 a ) C2H^0H + CH^ CHO + 0 2 ( 4b ) - 240 -2 C2H^00* *• C2H^00C2H^ + 0 2 ( 4c ) The fraction of non-terminating interactions i s : f = k4a / < k4a + k4b + k4c > The value of k^ given above represents the output rather than the input of the principal computer programme. (iv) The mutual interaction of ethoxy radicals. 2 C2H^0' - a l l products j kr, = 2 x 10 1 0 1 mole1 sec 1 The contributing reactions are: 2 C2H^0* »-.C2Hy)H + CH^ CHO ( ?a ) - C 2H 500C 2H 5 ( ?b ) No value has been published for the rate constants of those reactions. In general the reactivity of the ethoxy radical towards mutual combination should be similar to that of the methoxy radical. However, mutual disproportionation may be more favourable for the ethoxy radical than for the methoxy radical. The selected value of 2 x 10 1 0 1 mole 1 sec 1 i s twice as large as the rate constant for the mutual interaction of methoxy radicals. (c) Generation of the CgH^ OO* radical C 2 H 5 + °2 ( 4 M ) * C 2 H 5 ° ° ' ( + M ) ! k 3 a " 1 A x l o b 1 m o l i l sec"1 Hickel obtained the value: k^ a = ( 2.9 + 0.8 ) x 10 9 1 mole1 sec 1 from a study of the radiolysis of ethane in the presence of oxygen i n aqueous solution. The comparison of values for two different phases i s not s t r i c t l y valid. However, the value - 2 4 1 -obtained in the aqueous phase i s more than twice the value found by Hochanadel et al i a ( 75 ) for the corresponding reaction of the methyl radical in the gas phase, and i s about ten times the value adopted in Section A.3.C of Chapter 5 for that reaction: CH^ + 0 2 «• CH^ OO* ; ( 3-1 - 0.3 ) x 1 0 b 1 mole1 sec 1 In that chapter the lowest estimate was adopted in order to impose the severest conditions upon the test of the efficiency of the conversion of the alkyl radical to the alkylperoxy radical. The same considerations apply in this chapter, and therefore the value adopted here for k^ w i l l be chosen in relation to the value adopted in Chapter 5« The ethyl radical may be expected to possess a greater measure of stabilization than the methyl radical, due to the effect of the hyperconjugation of the extra methyl group in the ethyl radical. Therefore the reactivity of the ethyl radical towards the oxygen molecule should be less than that of the methyl radical. This rate constant k^ a i s used only in the programme which estimates the efficiency of the conversion of ethyl radicals to ethylperoxy radicals by reaction ( 3a )• The selection of a value for k 0„ which i s about one half of the value chosen for 3a the methyl radical imposes severe conditions upon this test. (d) Generation of the HOP* radical. C2H^0* + 0 2 •CH3CH0 * HOO* > ( 9 ) L = 1 x 10 6 1 mole 1sec 1 - 242 -C 2 H 5 + ° 2 C 2 H 4 + H 0 ° * { ( 3c ) k~ = 6 . 8 x 1 mole1 sec 1 at 298 K. 3c The rate constant of the reaction ( 9 ) has not yet been reported, but the abstraction of a hydrogen atom by the oxygen molecule from the ethoxy radical should be significantly faster than from the methoxy radical: CH^ O* + 0 2 CHy> + HOO* s k = 4 x 10^ 1 mole1 sec 1 where k i s the value adopted in Chapter 5« Accordingly, the value: k^ = 1 x 10^ 1 mole1 sec 1 was selected. The value of the rate constant for the reaction ( 3c ) i s based upon an extrapolation of the rate equation given by Knox in 1968 ( 1 0 2 ) : k~ = 1 0 9 * 5 exp ( - 5 0 0 0 / RT ) 1 mole1 sec 1 There i s no other result for comparison. This reaction i s unlikely to compete significantly with reaction ( 3 a ) i f the estimated ratio ^a/^Jo ~ 2 x 1 0 * s °* t h e r*Sht order of magnitude. (e) Cross interactions of the C^ H^ OO* radical. There are no experimental values for the rate constants of such interactions. Comparing the following reactions: 2 C?H*. • n-C kH 1 A , 2 5 * 1 0 ; k 2 = 1 .4 x 1 0 1 0 1 moli 1 seS 1 - CgH^ • C £H 6 2 C2H^0* a l l products ; k ? = 2 x 1 0 1 0 1 mole 1 sec 1 - 243 -2 C2Hj.OO* 0 2 + a l l other products ; k^ = 5 . 6 7 x 1 0 7 1 mole 1sec 1 Although the ethylperoxy radical i s associated with a comparatively low rate constant for mutual interaction, we may expect high values for those cross interactions of the ethylperoxy radical with the C2H^0*, C 2H£ and HOO* radicals which proceed by the abstraction of a weakly bonded hydrogen atom. (i) C^ H^ OO* + C^O* CgH^ OOH + CH^ CHO ; k^ = 2 x 1 0 9 1 mole 1 sec 1. There i s no available result for the rate constant of this reaction. The selected value, k^, i s about twice as large as the corresponding result for the methylperpxy radical: CH^ OO* + CH^ O* - CH^ OOH + CHgO J k » 9.2 x 1 0 8 1 mole1 sec 1 ( 9 3 ) ( i i ) C 2H 5 00* + HOO* - CgH^ OOH + 0 2 ; 8 —1 -1 k 1 Q » 1 x 10 1 mole sec This selection gives k 1 Q = l / 2 0 k 1 2 » l / 5 0 k-^ , which seems reasonable. ( i i i ) C2H^00* + C2H^ - a l l products? k^ = 2 x 1 0 9 1 mole 1 sec 1 The contributing reactions are: C2H^00* + C£H^ • 2 C2H^0* ( 5a ) C 2H 5 0 0 C 2H 5 ( 5b ) - 24-4- -C2H500H + C2Ek ( 5c ) Estimating on purely s t a t i s t i c a l grounds gives the value» k^ = 2 ( k 2 k^ )* = 2 x 10 9 1 mole 1 sec 1. (f) Cross interactions of the C-^ H^ P* radical. There are no direct experimental values for the rate constants of such reactions. The values given below are chosen in relation to the following reactions: 2 C2H* • n- C / +H 1 0 j k 2 = 1.4 x 10 1 0 1 mole 1 sec 1 C2 H4 * C2 H6 2 C2HjO' a l l products ; k ? = 2 x 10 1 0 1 mole 1 sec 1 2 HOO* HOOH + 0 2 I k 1 2 = 2 x 10 9 1 mole 1 sec 1 CgH^ OO' • HOO* CgH^ OOH + 0 2 ; 8 1 1 k 1 Q = 1 x 10 1 mole sec (i) C2H^0* + C2H^' a l l products ; k g = 3.5 x 10 The contributing reactions are» 10 1 mole 1sec 1 C^O* + C2H^ C 2H 6 * CH^ CHO ( 8a ) CgH^OCgH^ ( 8b ) C2H^0H + CgH^ ( 8c ) The simple cross interaction rule yields the value ky a + A. 1Q -1 -1 k y b + ky c - 2 ( k 2 kr, ) 2 - 3«3 x 10 1 mole sec . These reactions resemble reactions ( 7 ) more closely than reaction - 245 -( 2 ), and accordingly the estimate i s placedi 3 . 3 x 10 1 0 «kg $ 4 x 10 1 0 1 mole 1 sec 1. ( i i ) CgH^ O* + HOO* C2H^0H + Qz 1 k n 8 5 x 10 9 1 mole 1 sec 1* The selected value of - l / 4 k^ , = 2 . 5 k 1 2 = 50 k 1 Q. (g) Excluded reactions. (i) R* + CH^ CHO RH + CH^ CO ; R = CgH^OO*, C^O* or HOO*, Acetaldehyde i s formed i n reactions ( 3b )» ( 4b ), ( 6 ), ( 7a ), ( 8a ) and ( 9 ), and the C-H bond in the aldehyde group in the molecule i s comparatively weak* CH-^ CHOtg) CH3C0(g) + H*(g) « AH° = 86 Kcal mole1. and has a reactivity similar to that of formaldehyde. Metathesis between acetaldehyde and any of the radicals C2H^00', C2H,-0' and HOO' would lead to a reaction sequence of the type: R* + CH^ CHO »» RH + CH^ CO ( 1 3 ' ) CH^ CO + 0 2 CH^ OO' + CO ( 14a ) - HOO* + CH2C0 ( 14b ) CH3C000' ( 14c ) If any of these reactions proceeded at a significant rate, i t could influence the course of the reaction. Values of the rate constants are not known with any accuracy at room temperature. However, i n Section A .3.h.i of Chapter 5 the following estimates were made for the corresponding reactions from the mechanism of - 2 4 6 -the oxidation of the methyl radical* CH^ O* * H2C0 CH^ OH + HCO* I k 1 3 = 6 . 3 x 10^ 1 mole 1 sec 1 CH^ OO* + H2C0 CH^ OOH + HCO* ; k i 3 p ^ 2 , 6 x 1 q Z 1 m o 1 ® 1 s e c" 1 HOO* + H2C0 - HOOH • HCO* i 2 -1 -1 k 1 Q. = 2 .6 x 10 1 mole sec 13h and i t was argued that each of those reactions would be negligible under the reaction conditions of that oxidation. The rate constants of the corresponding reactions from the mechanism of the oxidation of the ethyl radical: C 2H 50* + CH^ CHO C^OH + CH^ CO ( 13 ) C^OO* * CH^ CHO C2H^00H + CH^ CO* ( 13p ) HOO* + CH^ CHO HOOH • CH^ CO* ( 13h ) are unlikely to differ from the estimates given above by more than an order of magnitude. Accordingly we may conclude from an analogous argument that reactions ( 13 )» ( 13P ) and ( 13h ) are negligible in the present system. ( i i ) C2H^ + 0 2 - CH^ CHO • HO* ( 3b ) • C2H^ • HOO* ; ( 3c ) k~ = 6 . 8 x 10^ 1 mole 1 sec 1. 3c The value of kjQ was derived in Section 3.d. No experimental value i s available for k^^. However, the rate constant for the reaction of the methyl radical corresponding to reaction ( 3b ) : - 24? -CH^ + 0 2 H2C0 + OH was estimated to be not much greater than 2 x 10^ 1 mole 1 sec 1 by Basco, James and James i n 1972 ( 96 ). and a more recent evaluation placed i t much lower, as described in Section A . 3.h.ii of Chapter 5. Reactions ( 3b ) and ( 3c ) can not therefore complete effectively for the ethyl radical with reaction ( 3a )1 C 2 H 5 * °2 ( * M ^ C 2 H 5 0 0 ' ( • M ) 1 0 0 = 1.4 x 10 8 1 mole1 sec 1 " 3 a and are unlikely to act as significant sources of the hydroxyl or hydroperoxy radicals. (4) Method. (a) Generation of the ethylperoxy radical. Ethyl radicals were formed by the flash photolysis of azoethane in the presence of an excess of both oxygen and an inert moderating gas. The majority of these ethyl radicals were converted to ethylperoxy radicals by the reaction: C2H^ + 0 2 ( + M ) C^OO* ( + M ) } c 3 a k? = 1.4 x 10 8 1 mole 1 sec 1 A minority these ethyl radicals were inevitably " wasted " by several competing reactions: C 2 H 5 + C 2 H 5 " n" C4 H10 k 2 = 1.41 x 10 1 0 r l _ . r l r u . r u 1 moli sec ( Chapter 4 ) G2 H4 + C2 H6 - 248 -C 2 H 5 + °2 C H 3 C H 0 + 0 H ; k ^ < 2 x 10^ 1 mole1 sec 1 ( Section 3 . g . i i ) C2H^ + HOO* ; kjQ = 6.8 x 10^ 1 mole 1 sec 1 ( Section 3.d ) C2H^ + C2H^00* a l l products i = 2 x 1 0 9 1 mole 1 sec 1 ( Section 3 . e . i i i ) Experimental conditions were chosen so that the wastage of ethyl radicals by reactions ( 2 ) and ( 5 ) was negligible. The conversion of ethyl radicals to ethylperoxy radicals was then virtually quantitative. This has two important advantages. First, the evaluation of the rate constant for the reaction* 2 C2Hj,00* a l l products ; k^ = 6 . 0 x 1 0 7 1 mole 1 sec 1 i s simplified i f the consumption of ethylperoxy radicals and the formation of ethoxy radicals by the reaction: C 2 H 5 + C 2 H 5 0 0 ' 2 C 2 H 5 ° * ( 5 a ) can be neglected. Secondly, the evaluation of the extinction coefficient of the ethylperoxy radical required an estimate of the total number of ethylperoxy radicals formed during the reaction period. This estimate was equated to the product of the total number of ethyl radicals formed by the photolysis of azoethane, which can be found by analysis, and the efficiency with which they were converted to ethylperoxy radicals, which can be taken as unity. A computer programme was used to simulate the kinetic - 2-+9 -behaviour of the system over a sufficient range of reactions to ensure that suitable conditions were chosen for the measurement of k^ and This programme was similar to the corresponding programme for the methyl radical described in Section A.4.b of Chapter 5. The programme was based upon a fourth order Runge-Kutta integration of two rate equations* C2H^] / dt = [cfflt / t m 2 ] exp ( -t / t m ) - 2 k 2 [c 2H^] 2 " * 3 L C2 H5. [° 2] " *5 - C2 H5] l C 2 H 5 0 0 ' ] d [c^OO*] / dt = k^  [c 2H^] [ 0 2] - 2 k^  [c^OO*] - k 5 f C 2 H 5 ] [ C 2 H 5 0 0 ' ] The principal data required for these integrations comprised: (1) the values of k 2 , k ,^ k^  and k^  l i s t e d above; (2) the value of t f f l t the time required for the intensity of the flash reach i t s maximum value , measured as 4 jasec; (3) the value of C m, the concentration of ethyl radicals that would have been observed i f a l l the ethyl radicals generated by the flash had been simultaneously present in the reaction vessel, estimated as 2.-4-7 x 10 mole l 1 under present conditions; ~2 ~1 (4) the value of the concentration of oxygen, 3->b x 10 mole 1 ; (5) the time period of interest, usually 50 |Asec. The output of the programme is illustrated by Figure-6.1, and Table-6.2, which were computed for the conditions given above. The concentrations are normalized in Figure-6.1 and Table-6.2, so that the symbol " 0 " in the Figure represents 40 [c2H^] / C m and symbol " X " represents [c2H^00*] / Cffl. The ethyl radical concentration follows the flash profile closely, rising to a - 250 -Figure-6.1 The normalized concentrations of C2H^ and C2H^00* i n the presence of a high oxygen concentrationi [ o 2 ] = 3-8 x 10 " 2 mole l " 1 | s e o o e e e e e e o o | O — M W JO 6 V O D D B e o e o e » e e © © ote o o o o o 9 a o o ob o a o o op o o o a op —  ODBCo o o o O B • o • e Note: symbols; 0 = 40* [c2H^] / C m, X = [c^OO*] / Cra. Table-6.2 M a t e r i a l balance r a t i o s f o r the e t h y l r a d i c a l at a high oxygen concentration! [o2] 3.8 x 10"2 mole l " 1 f uJtc 1 .0 2 . 0 _ 3 . 0 4 . 0 5 . 0 6 . 0 7 . 0 8 . 0 9 . 0 T o .Ti-l l . 0 1 2 . 0 1 3 . 0 1 4 . 0 1 5 . 0 1 T . 0 1 S . 0 1 9 . 0 2 0 . 0 2 1 . 0 2 1 . 0 2 4 . 0 2 9 . 0 2 6 . 0 2 8 . 0 2 9 . 0 3 0 . 0 3 1 . 0 3 2 . 0 3 3 . 0 ino«PBl/Pi»r ? 2 . 1 8 8 8 9 . 4 3 6 9 0 . 7 7 0 _ 93^ 58 2 9 5 . 2 9 5 9 6 . 4 3 4 9 7 . 2 3 6 9 7 . 8 2 4 9 8 . 2 6 7 9 8 . 6 0 8 9 8 . 8 7 5 9 9 . 0 8 6 9 9 . 2 5 5 9 9 . 3 9 0 9 9 . 4 9 9 I00«PM2/PRF 0 . 0 0 9 0 . 0 1 1 0 . 0 1 5 99 .> f l8 9 9 . 6 6 0 9 9 . 719 9 9 . 766 9 9 . 8 0 9 _ 9 9 . 8 3 7 99.46T" 9 9 . 8 8 4 9 9 . 9 0 1 9 9 . 9 1 5 9 9 . 9 2 6 9 9 . 9 3 5 9 9 . 9 4 3 9 9 . 9 4 9 9 9 . 9 5 3 9 9 . 9 5 7 9 9 . 9 6 0 9 9 . 9 6 3 9 9 . 9 6 5 " 9 9 . 9 6 7 9 9 . 9 6 8 9 9 . 9 6 9 9 9 . 9 7 0 9 9 . 9 7 0 9 9 . 9 7 1 9 9 . 9 7 1 9 9 . 9 7 2 9 9 . 9 7 2 9 9 . 9 7 2 9 9 . 9 7 2 ~ 9 9 \ 9 ? 3 9 9 . 9 7 3 9 9 . 9 7 3 9 9 . 9 7 3 9 9 . 9 7 3 0 . 0 1 7 0 . 0 1 9 0 . 0 1 9 0 . 0 1 9 0 . 0 1 9 _ 0 . 0 1 9 _ 0 . 0 1 9 o.oia 0 . 0 1 8 0 . 0 1 7 o.oir 0 . 0 1 7 b.o IT 0 . 0 1 6 0 . 0 1 6 0 . 0 1 6 0 . 0 1 6 0 . 0 1 6 0 . 0 1 6 0 . 0 1 6 0 . 0 1 6 0 . 0 1 6 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 o.ols 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 " 0 . 0 1 5 0 . 0 1 5 0 . 0 1 9 0 . 0 1 9 1 0 0 ' P R l / P R f 0 . 0 0 1 0 . 0 0 3 2..00 7 o.bii 0 . 0 1 5 0 . 0 1 9 0 . 0 2 3 0 . 0 2 6 0 . 0 2 9 0 . 0 3 2 " 0 . 0 3 4 0 . 0 3 6 0 . 0 3 8 0 . 0 4 0 0 . 0 4 1 0 . 0 4 2 0 . 0 4 3 0 . 0 4 3 0 . 0 4 4 0 . 0 4 4 0 . 0 4 5 0 . 0 4 5 0 . 0 4 5 0 . 0 4 5 0 . 046 0 . 0 4 6 0 . 046 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 0 . 046 0 . 0 4 6 _ 0 . 0 4 6 _ 0^046 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 0 . 0 4 6 l O O . P f l k / P d r • I M4SIR0 0 . 0 0 3 0 . 0 1 4 _ 0 . 0 2 l 0 . 0 2 8 0 . 0 1 3 0 . 0 ) 8 0 . 0 4 2 0 . 0 4 6 _ 0 . O 4 8 6 .051" 0 . 0 5 3 0 . 0 5 4 0 . 0 5 6 0 . 0 5 7 ^ ) . 0 5 B _ . 0 5 8 . 0 5 9 . 0 5 9 . 0 6 0 . 0 6 0 0 . 0 . 0 . (. c. C . 0 6 0 _ .061 ,061 ,061 061 ,061 061 0 0 0 0 0 0 0 . 0 6 1 0 . 0 6 1 0 . 0 6 1 0 . 0 6 1 0 . 0 6 1 0 . 0 6 1 0 . 0 6 1 0 . 0 6 1 0 . 0 6 1 0 . 0 6 1 0 . 0 6 2 0 . 0 6 2 0 . 0 6 2 0 . 0 6 2 0 . 0 6 2 0 . 0 6 2 0 . 0 6 2 0 . 0 6 2 0 . 0 6 2 ' 0 . 0 6 2 0 . 0 6 2 0 . 0 6 2 0 . 1)62 inn*ppi/CM < L U M P l E t t 2 . 6 5 0 9 . 0 2 0 1 7 . 3 3 6 _ 2 6 . 4 2 4 3 5 . 5 3 6 4 4 . 2 1 7 5 2 . 2 1 2 5 9 . 3 9 9 6 5 . »45_ M . 2 70 7 6 . 0 2 6 8 0 . 0 8 5 8 3 . 5 2 0 8 6 . 4 1 1 as.a;a_ 9 0 . 8 4 1 9 2 . 5 1 1 9 3 . 8 8 9 9 5 . 0 2 5 9 5 . 9 5 6 »6 ±7 2 0 ^ 9 7 . 3 4 3 9 7 . 8 5 1 9 8 . 2 6 4 9 8 . 6 0 0 9 8 . 8 7 2 99 . 092 9 9 . 2 70 9 9 . 4 1 3 9 9 . 5 2 9 9 9 . 6 2 2 9 9 . 6 9 7 9 9 . 757 9 9 . 8 0 6 9 9 . 8 4 4 9 9 . 8 7 5 9 9 . 9 0 0 9 9 . 9 2 0 _ 9 ? . _ 9 3 6 _ 9 9 . 9 4 9 9 9 . 9 5 9 9 9 . 9 6 7 99 . 9 74 9 9 . 9 7 9 9 9 . 9 8 3 _ 9 9 . 9 8 6 9 9 . 9 8 9 9 9 . 9 9 1 9 9 . 9 9 2 9 9 . 9 9 4 - 252 -maximum of only 0.0173 Cm at t = 4 usee. In contrast, the ethylperoxy radical concentration reaches i t s maximum of 0.99 Cm at t = 28 microsec, and declines slowly thereafter by reaction ( 4 ). Column 5 of Table-6.2 shows that less than 0.063 # of the ethyl radicals are wasted at any stage in the reaction, and column 2 shows that overall conversion of ethyl radicals to ethylperoxy radicals i s 99.9 % efficient. This analysis confirms that suitable conditions have been selected for the investigation. - 253 -B. Experimental (1) Apparatus The photoelectric detection system was employed for the search for the absorption spectrum of the ethylperoxy radical, which spanned the wavelength range from 200 to 450 nm. A broad absorption band with a maximum at or near 240 nm was observed, in general agreement with the results of Parkes, Paul, Quinn and Robson ( 38 ). The absorption spectrum was determined in absolute units, and the quantitative kinetic study of the reacting system was undertaken. (2) Method. (a) Choice of reaction conditions. Reaction conditions were chosen so that virt u a l l y a l l of the ethyl radicals formed i n i t i a l l y by the photolysis of azoethane were converted to ethylperoxy radicals by the reaction* C2H^ • 0 2 ( + M ) - C 2H 500* ( • M ) ( 3 ) A typical set of reaction conditions for quantitative measurements i s given in Table-6.3• (b) The measurement of k^' / E(X). The procedure used for the measurement of k^' / £(» for the ethylperoxy radical i s analogous to the procedure used for the methylperoxy radical, which has been described in Section B. l.b of Chapter 5- If the ethylperoxy radicals had been consumed solely by the hypothetical second order reaction ( 4 * )s - 254 -Table-6.,3 Typical reaction conditions for the quantitative study of the ethylperoxy radical (1) Reactants Material Range of concentration(mole l " Azoethane 4.3 x 10 to 4.8 x 10 ^  Oxygen 3-3 x 10' 2 to 3.6 x 10" 2 Argon(moderating gas) 2.7 x 10 J Ethylperoxy radical(Co) 2.47 x 10" 6 (2) Photoflash Flash energy 1080 J ( 12 kv, 7-5 uF )x 2 Time of max intensity ,. a 4- microsec after f i r i n g Time of dissipation of 99.9 % flash energy 37 microsec Time of observation 4 millisec - 255 -2 C2H^00* unreactive products ( *V ) then l/A would be linearly related to time by the equation* 1/A = 1/A, + ( 2 fy* / £(X) 1 ) t and k^'/gKA) could be evaluated from the gradient of a plot of l/A against time at a chosen wavelength A. In practice a plot of l/A against time i s almost linear so that k^'/2(A) can be found in this way. The value of k^,'is independent of the wavelength chosen for the measurement of absorbance. Accordingly, a plot of the value of E(A)/k^' against A i s equivalent to a relative absorption spectrum of the ethylperoxy radical. (c) The measurement of £(A). The procedure used for the measurement of E(A) for the ethylperoxy radical i s analogous to the procedure used for the methylperoxy radical, which has been described in Section B.l.C of Chapter 5- If a l l the ethylperoxy radicals generated in this system had been simultaneously present i n the reaction vessel, they would have had a concentration Co and an absorbance Ao at the chosen wavelength. The corresponding extinction coefficient i s given by the equation* £(A) = Ao / Co 1 and may be evaluated i f Ao and Co can be measured. The measurement of Ao i s accomplished by extrapolating the observed values of A back to zero time. This extrapolation i s accurate because the formation of ethylperoxy radicals i s 99.9 % - 256 -complete within 50 microseconds, whereas the half l i f e of these radicals i s of the order of 2000 microseconds in a typical experiment. The measurement of Co i s based upon the assumption that the yield of ethyl radicals from the flash photolysis of azoethane i s not changed when oxygen i s present. Experiments were conducted in pairs i i n each pair the reaction conditions were identical, except that one system contained an excess of oxygen, whereas the other contained none. The latter system yielded the value of Co from the amounts of nitrogen, n-butane, ethane and ethene formed using the procedure described in Section B.3 of Chapter 4; the former system yielded the corresponding value of A o . (d) The measurement of k;). (i) The nature of the problem. An estimate of k^' can be obtained at each wavelength observed from the product of k^'/jrCA) and These estimates are valid only for the hypothetical reaction* 2 C 2 H^00' unreactive products ( 4» ) Whereas the ethoxy radicals formed in reactions ( 4a ) and ( 5a ): 2 CpH^OO* 2 C 2 H 5 0 ' + 0 2 ( 4a ) C 2 H 5 + C 2 H 5 0 0 ' 2 C 2 H 5 ° * ( 5 a ) are highly reactive, and may be expected to influence the course of the reaction significantly. In particular, the consumption of ethylperoxy radicals by the reactionsJ - 257 -C2H^00* + C2H^0' C^OOH + CH^ CHO ( 6 ) C2H^00' + HOO* • C2H^00H + 0 2 ( 10 ) must be considered. On the other hand the reaction* C^OO* + C2H^ " 2 C 2Hyr or C^OOCgH^ ( 5 ) has already shown to be negligible i n Section A.4.a. Accordingly, a computer programme was used to simulate the kinetic behaviour of the system and to derive an accurate value of k^ from each estimate k^'. The reactions included i n this programme are li s t e d with their rate constants i n Table-6.3* ( i i ) The computer programme. The programme i s analogous to the programme used for the methylperoxy radical, which has been described i n Section B.2. d . i i of Chapter 5. It was based upon a fourth order Runge-Kutta integration of three rate equations* d [ c 2H 500*] / dt = -2 k^ [ c ^ O O * ] 2 - k 6 [ C^OO*] [ c^O*] - k 1 Q [C 2H 500'] [HOC] d [C 2H 50*] / dt » 42 k ^ a [ c 2 H 5 0 0 ' ] 2 - k 6 [C 2H 500*] [ c^O*] - 2 k ? [ C 2 H 5 0 ' ] 2 - k 9 [C 2H 50 - J [ 0 2 ] - k u [ c 2 H 5 0 - ] [ H 0 0 •] d [HOO* ] / dt = +k9 [ c 2H 50*] [ 0 £ ] - k 1 Q [ c^OO'j [HOO* ] - k u [ c 2H 50*] [HOO*] - 2 k 1 2 [HOO*]2 Values of Co and [ o 2 ] were required for the integration* typical values are 2.47 x 10 mole 1 amd 3.8 x 10 mole 1 respectively. The i n i t i a l output of this programme comprised values of the Table-6.4 Reactions used in the computer simulation of the decay of the ethylperoxy radical reaction rate constant at 29b K ( 1 mole"1 sec" 1 ) 2 C^OO' a l l products (4) ( 5.07 x 1 0 7 ) * 2 CpH^ OO* 2 C 2 H^0* + 0 2 (4a) ( 2.935 x 1 0 7 )' C^OO' • CgH^O' 2 CgHyr C 2H 5 0' • 0 2 C 2 H 5 0 0 * • HOO' C 2H^00H • CH^CHO a l l products CH^CHO * HOO' C 2H^00H + 0 2 (6) (7) (9) (10) 2 x 10' 2 x 10 1 x 10 6 10 1 x 10 8 c 2 H y + HOO* C2H^0H • 0 2 (11) 5 x 10-2 HOO' HOOH + 0, (12) 2 x 10-Notei * other values may be substituted as described in Section C.5.a. - 259 -concentrations of the radicals C 2 H ^ 0 0 * , C ^ H ^ O ' and H O O ', computed at 50 equal intervals over the period of interest. A typical graph of the output for a high oxygen concentration i s shown i n Figure-6.2. The symbol " X " represents [ c 2 H^00*]/ Co , the symbol " 0 " represents 200 [ c 2 H^0*] / C o , and the symbol " # " represents 3 [HOO* ] / C o. In this graph [ c 2 H5°'] =0.0021 [CgHt-OO' ] after 2000 microseconds whereas [HOO* ] maintains an almost stationary value of O . O 6 7 ± 0.003 ) Co between 900 and 3100 microseconds. Moreover, the HOO' radical i s predominant over the C 2 H^0* radical after the f i r s t 100 microseconds. The accuracy of the computation was confirmed by the material balance ratios. Values of the material balance ratio for each of the radicals C 2 H ^ 0 0 * , C 2 H^0* and HOO' are shown Table-6.4. BAL(P) i s the instantaneous ratio of the sum of the concentration of the ethylperoxy radicals and of the equivalent concentrations of these radicals consumed by reactions ( 4 ), ( 6 ) and ( 10 ) to their original concentration C o. BAL(A) i s the instantaneous ratio of the sum of the concentration of the ethoxy radicals and of the equivalent concentrations of these radicals consumed by reactions ( 6 ), ( 7 )• ( 9 ) and ( 11 ) to the equivalent concentration of these radicals generated by reaction ( 4a ). BAL(Q) is the instantaneous ratio of the sum . of the concentration of the hydroperoxyl radicals and of the equivalent concentrations of these radicals consumed by reactions ( 10 ), ( 11 ) and ( 12 ) to the equivalent concentration of these generated by reaction ( 9 ). The accuracy of the computation i s confirmed by the fact that none of the values of the material balance ratios deviates from unity by more than - 260 -Figure-6.2 The normalized concentrations of C 2 H^00* , C 2 H^0" and HOO* in the presence of a high oxygen concentration?. [ o 2 ] = 3.8 x 10"2 mole l " 1 . J . . . ' ' ' . . o o o o o o o o o o o o o o o o o o o •C5 • m • a .... S S • • • • • • • • • • • ! • « • • • • ] • • • ! • S0222 2 22220000 0 0 s p o e o o o b o s s o o b o o o o o o o o o p o o e o 5 o o o O o o E o o o o o o «« ft. *• ft* ft. M M«M «K *» <•» " H - l * • # , « * « fX — o O ( c 3 r; O I l-> 9 I * O •*» o -e •M O O i * o -* o J* o -— O o * • * o - 3 • I •a. J t o •— o «k i m m o O »-> K O i • o F -Symbols: X = [c^OO*] / Co , 0 = 200*[c 2H 50*]/ Co and # = 3*[HOO*] / Co . Table-6.5 Normalized concentrations and material balance ratios for: of a high oxygen •Co . CJ^OO* (P), CphVO'tA) and H00*(Q) in the presence •2 r l -2 - l concentration! [ 0 2 J = 3 . 8 x 1 0 mole 1 » P(0)< J . ua. 2u0. 4 00. 500. 600. 70u. BOO. 4 j 0 j 1363. 1 loo. 1 i Ou . 1)00. 140J. i spc^ . 1 600. w o o . m o o . 1*00. 2000. 2IOU. — 2 2 0 0 : — 2303. 2400. 2500. 2600. 2 700. 2800. 29O0. iuOO. 313J ; 3203. J JOO. 3400. J 500. J 6 J i i . 3700. Jbuu. ) 4 0 u . 4000. 4lu0. 4203. 4 iOu. 4 4 0 0 . 4 b 0 0 . 4600. 4 / 0 3 . V U J J . 4403. Soot. P l I I / P l O l 1.OUOJOOO i>. 470b 706 0.4-.22714 _ 0 . _ 4 1 b J 6 6 2 _ 0.ba97 7b9 0.B654251 0. B S 2 2 4 19 0.«20l60d 0.7441204 0.7 79054o_ 6.75442)5 0.7416540 0.7242144 U.707542} 0.641b4b4 0. o 76 1 IMS 0.6M7244 0.6477174 0.6J42a32 Ci.621Jo97 0. 60 4005b 0.3471023 0.5746360 0.5640242 0.55)7471 0. 54)43bl 0.5J441B5 0.5252302 0.51635)6 0.5077732 0.499*748 0.441-.443 it. 4b3otBb 0.4761376 0.46dB)b) 0.4617614 0.4540453 0.44b2)24 0.4<.176)2 0.436V7U8 0.4293 124 0.42)4357 0.-.1760 IB 0.4120444 _0. 4u6b7/a_ 0^4012563 6. J460 7 34 0. 3410237 0. )B6|0*0 0.idl30)5 A| I1/HI01 O.OOJOOOJ 0.00)1604 0.00)0204 _0.OJ28bl4_ 0.0026461 O.U02b525 0.0024144 0.0022473 0.002111)8 _O.O0^O7B5 O'. 0019807 0.O01bd97 0.001B048 0.0017256 0.0016515 _p.0015B21/ o ; b o i 5 i 7 i 0.001«560 0.00139a} 0.0013444 0.0012934 0.0012-.5) ~T)700ll998~ O.OOllbttt 0.0011161 O.OU10775 0.0010409 _O iOOI006l 0.0009 731 0.0004417 0.0009117 0. 0 0 0 B O J 2 0.0008560 0. OOOBiOl 0.000OO53 0.0007816 O.OC07540 0.0007)73 0.0007166 _0^00C64i>7 0. 6006 7 77 0.0006594 0.000641b O.OC06250 0. OCObObB 0.0005432 O70O0S7B2 0.00056)8 O.OOubbOO 0. OuJS3tc 0.00052)7 uiri/f I U I O.OCOJOUO 0.009s110 0.0206065 0 . 0 i 0 4 2 4 4 _ " 0.03BBJ22 0.0454437 0.051aoC4 0.0566526 0.0604407 0 . 0 6 3 J 7 & 6 _ " 0 . 0 6 5 5 4 ) 4 0.0672015 0.0683061 0.0684970 0.064)307 0 . 0 6 4 s 1 1 7_ 0^06~92437 0 . 0 o b 4 b l ) 0.0665 ) 1 2 0.06747)4 0.067)324 0 . 0 6 6 6 2 b 1 0.0658767 0.0650414 0.0642826 0.063»bB9 0.0626271 _O .06|7427_ 0.0604600 0.0601)24 0.0593127 0.0585030 0.0577048 0.0564144 '016561477" 0.055-.405 0.0546474 0.0534204 0.0532060 _O.Ob25ICe_ Ol651b2b7 0.0511616 0 . 0 5 0 5 U 4 2 0 . 0 4 9 B 7 1 4 0.0492478 0.0< . B 6 ) B ) " 6r04bC4 25 " 0 . 0 4 7 4 3 9 9 0 . 0 4 6 B <05 0.0-.6 J J J 7 0.04bJ»4) 1 J U . 200. iOo. 4J0. bOOT 60 J . 700. BOO. 900. 1003. 1|66. 1200. 1300. 14U0. 1500. _|600._ 1700. IbOO. 1400. 2000. 2100. _2200^_ 2~)00. 2400. 2500. 2600. 2700. 2 b O O . "7966. iOOO. )100. 3200. 3) 00. 3-.00. 3500. 3600. 3700. 3BO0. )400. 4000, 4100. 4200. 4) 00. 4400. 4500. scOO. 4>66. 4B00. 4400. 5000. b A L I P I l.OOOOL 0 0 l.OOOOt 00 4.4494t-01 ^. 9444Cj01_ "9;9999£-6l 9.99991-01 9.494o£-01 ».444B£-01 9.444d£-01 _9.494Bt-0l_ 9.9998E-01 9.944bt-0l 9.449b£-01 9.9997E-01 9.9447E-01 _9.4447E-0l_ 979997f-6l 9.9997E-01 4.4446£-01 9.444o£-01 9.9946E-01 4.999u( -0I_ "Tr*«96£-6i 9.4996E-01 9.9996E-0I 9.444bt-01 9.444>t-01 4.949b£-01 9.9495E-01 9.9994t-01 4.49441-01 9.9994E-01 4.94S4E-01 9.9943£-0l 9.9493E-01 9.4993C-01 4.994^1-01 9.944<;£-0l 9.4442E-01 4.44921-01 9.9991E-01 9.494IE-01 V.994U-01 9.499OC-01 V.9940E-01 _ 9 i 4 4 4 0 L - 0 1 _ 9.444uE-0l 9.9990E-0I 9.4440t-Ol ».4940£-0l O U I t l 4. 4 4 B 6 t -01 9.4992E-01 9.9945E-01 4^9446t-0l_ "4.4947E-01 9.99971 -01 9.944»fc-01 9.994BE-01 9.999bE-01 _9 i9S4B£ r0l_ 9.999b£-6i ».444dt-0l 9.994BE-01 9.999BE-01 9.444OE-01 9.9494E-01 9.9994E-61 4.4944E-01 9.9949E-01 «.4949£-01 9.4994E-0I _9. 49941 -Ol_ 4749<4£-6l «.9449t-01 9.9944E-01 9.4444L-01 9.4444E-01 9.9944E-01 9.9449E-01 9.9999E-01 9.9499£-01 9.9994E-01 9.9944E-01 9.999',E-01 9.9999E-01 9.4444t-0l 9.4944E-01 9.4494E-01 V.9499E-01 9.4999t-01 9.9494E-01 9.94446-01 9.4944E-01 9.9999E-0I 9.4449E-01 _9^9994£ -Ol_ 9.9494E-01 ».9494£-0l 9.9499E-01 «.«9S4t-0l JO 00 00 00 B4L10I l.UOO^k 00 1.0001E 00 l.OOOU 00 l.OOOCfc 00 " i . o o o o t ' o o " l.OOOOE I.OOOOL l.OOOOE 00 l.OOOOt 00 _1.0000£_00_ u o o o o t 66 1.00004 00 l.OOOOE 00 l.OOOOE 00 l.OOOOt 00 __1.0000£_00_ KOOOOE 00 l.OOOOE l.OOOOE l.OOOOE 00 l.OOOOt 00 l.OOOOt _oo__ "UOCOOE 00 i . o o o o t 00 l.OOOuE 00 l.OOOOt 00 l.OOOOt 00 _l.O0OOE 00_ 4;9944£-0l 9. 44441:-01 9.9444t-01 9.4494t-0l 9.4999E-01 9.44441-01 979999L-01 9.4944t-01 9.4494E-01 9.9999E-01 9.4994E-01 9.4449t-01 9.9444t-01 9,9994t-01 9.944Bt-0l 9.944at-0l 9.449at-0l _9.944Bt-01_ 9i994a£-0l 9.994BE-01 4.444it-0l 9.4»«»t-0l N3 ON - 262 -0 . 0 0 0 1 . The principal output of the programme i s a value for k^'/lfy. This was computed i n two stages. F i r s t , t r i a l values -of k^ and k^ a were entered with the other data, and a set of f i f t y values of C o / C , the normalized reciprocal of the ethylperoxy radical concentration, were calculated. Such a set of values i s listed under the symbol Y in Table-6.5, and plotted in Figure 6.3. This set constitutes the input of the second part of the programme, which f i t s a regression line to this second order plot. A s t a t i s t i c a l analysis of the f i t yields a standard deviation, and the ratio of the deviation of each value of C o / C to this standard deviation i s listed under the symbol TY. Each of the values of | TY | i s less than unity, with the exception of the f i r s t two, so that the procedure of f i t t i n g a regression line to such data i s valid. The output comprises the computed values of k^'t i t s standard deviation, and the ratio k^'/k^, which are given in the table as K2 ( C A L C ) , ST.DEV and K2(CALC)/K2 respectively. - 263 -Figure-6.3 A simulated second order plot for the decay of the CgH^ OO' concentration* computed values of Co/C plotted against time for a system with a high oxygen concentration* [ o 2 ] = 3.8 x 10~2 mole l - 1 . C I 1 t o e c > o o e o o-o o o e o o o o r O - r • -o o o o c o <3 o o e > ole o © o o o » O i O o o o o o - _ O o O o O O O O O O « 0« O — I o -O O 3 ? — o •V I -* e time - 264 -cd +•> A +•> Qi • H e o o a - H +•> 1 CO r H n >> CO CO o r - l \ cd O o S O C • H CNJ <tn 1 O c o O r H CO • H a> +•» X cd u CO cd • > c o O II -p c o <0 o C o • H a r H O o c o o • H CM i H CO O +•> CO cd CO 0) U ft A +•> +-> c CD o O c cd o >> o cd c o c • H CO CO +-> +-» >> • H CO fa A o -p bO • o • H J3 CO r H r 3 cd E H r et ,3 tr © O * M * ff1 — * O * O "* -« B, _ r» 4 « — "-'fst « » O <•<* r*ifM I N -SiD'O o oo o O ' O e so <~> ^ o o f» CP- • -flU • oL o <Q •» » *L • » o o> crL .A m » *s -L o *j * * «U o o l o o o d o o ' j o o o o o o o o < * ? ? ? ! ? ? o o o o o o o ? ? o . o o o o o ojo O = O O OIO o o o o o o *!•» o •">» *"i O ^ <^i«n •»> " -B <N » oio o — — •* » — • — -<r » — — o »r^ ;»-"4.#r»0'N»-«"'"©^ "",*'o'** * » "^l-C » — •« . O "» -5<n»» © " I •* O -OO'** « » N * ) » i N * 9** > £ i OS « 0* 9 O O . O O — — — •^ l"><'N»rg*» r* "*V if c r>i »/\ a — tr. » — * • — •# o--r o * i*. O"* - - - ^«sm.f,^ 8 . 9 © « C r>i «n a» — tr: : O O'O O — — — o#'fM « o oio o © © © ©lo 3 O O O 0(0 O O O O op OOOOO I I I . lo o o o o ©jo o o o o o i o o o o o ojo o o o o o o « -» « o o o o O'O o o o o o.o o o o o o o o o o o O Ol3 © o o o o i o o o o o o l o o o o o o _ o o o o < OIO O O O ' — * )T» « |o 3 o o o o i o O O O O OIO o o o o o O O O O O O > O O O-O O O O O oio o o o o oio 5 o ) O O OjO O O O O O'O O O O © OiO o o - — — — - — »"•(»•>©— I* VS« »*0'««0 - , >«0 '*'«* i ' '* ,*> l^«<-> , ,^<C^***'' ,C>' s* • •)0»»t>OOO — — — — \r* ** o* m m m;+ + •* W\ <f* +ir+ *-o o O o o o o o 3 o o 3 - 265 -C. Results (1) The value of k^VgQJ. The consumption of the ethylperoxy radicals in these experiments can be treated as though i t occurred exclusively by the hypothetical bimolecular reaction:' 2 C2H^00* *- unreactive products ( V ) and the variation of the concentration C of the ethylperoxy radicals with time can be represented by the equation: l/C = l/Co + 2 k^'t The corresponding equation for the absorbance A of the ethylperoxy radicals i s : l/A = 1/Ao + ( 2 k^'/eU) 1 ) t The validity of this equation was confirmed by f i t t i n g a straight line to simulated data and by showing that the ratios of deviations of individual points from this line to the corresponding standard deviation are negligible, as explained B.2.d.ii of Chapter 5. Accordingly, the value of k^'/£(X) at each chosen wavelength A was derived from the gradients of the corresponding plots of l/A against time. Values of k^'/£(A) were measured at various wavelengths from 212.5 nm to 290.0 nm in the presence of a large excess of oxygen at room temperature. The results are listed in Table-6.6. A minimum value was observed at 235 nm, where - 266 -Table-6.7 Values of k^'/i-iOO and of the extinction coefficient «=(>.) of the ethylperoxy radical at various wavelenghs. Photoflash energy: 126?.5 J (13 kV, 7-5 uF)x2 wavelength ( nm ) 1 mole - 1cm _ 1 1 0 " 4 ' / £(*) cm sec"'*' H-•91-A H-93-A 212.5 239 • 28 215.0 14.6 1.0 217.5 4 9 . 0 l 2.9 26.5 1 6.6 220.0 5-63 16.2 i 1.5 9-93 t O .69 222.5 225.0 7.71 9-12 • 0.29 11.0 i 0.2 227.5 a. 11 10.1 i 0.2 230.0 9.O8 8.14 4 0.33 7.30 * 0.21 7.74 • 0.44 232.5 9.72 235-0 10.18 5.58 + 0.22 6.15 + 0.14 237-5 10.12 6.71 t 0.22 240.0 9.60 6.65 * 0.23 6.88 ± 0.24 8.95 • 0.29 242.5 9.02 7.98 i 0.30 245.0 8.69 6.61 0.39 6.16 i 0.22 247-5 8.79 7-37 i 0.33 250.0 8.27 7-01 • 0.33 7.10 t 0.14 252.5 7.65 255.0 7-^7 11.2 t 0.2 260.0 6.48 8.34 • 0.37 10.2 t 0.3 265-0 5.30 16.7 + 0.8 8.94 ± 0.21 270.0 ^.37 10.8 + o.5 15.0 t 0.4 275.0 3-39 24.4 i 0.6 280.0 2.72 22.8 4 1.8 50.5 t 2.5 290.0 83.0 4 3.6 280 t 31 Note: Mixture Exp No. concentration mole l - 1 Et-N- - 4.75 x 1 0 " 4 H-91-A 0 2 » 3.62 x 10 c H-93-A E t 2 N 2 = 4 , 2 6 o 2 * 3.30 -4 x 1 0 ^ x 10~ 2 - 267 -k^'/E(235) = ( 5-87 t 0.52 ) x 10** cm sec 1; this result i s an average of the two measurements at 235 nm in Table-6.6. Unfortunately, no direct measurement of k ^ ' / ^ A ) has been reported to date. A plot of the reciprocal values of k^'/gtA) against wavelength represents the relative absorption spectrum of ethylperoxy radical. The values of £(A)/k^' are lis t e d i n Table-6.7» and are shown in Figure-6.4. (2) The values of g ( A ) . The principle of the method of measurement has been discussed in Section B.2.C of Chapter 5- The fundamental assumption i s that the quantum yield of ethyl radicals from the photolysis of azoethane i s the same in the absence and in the presence of molecular oxygen. Experiments were conducted in pairs, under conditions that differed solely i n the absence or presence of oxygen, and yielded values of Co and Ao respectively. Each pair yielded a value of £i(A) by the equation £ ( A ) = A o / C o l . The procedure i s analogous to that described in Section C.2 of Chapter 5. Values of £ ( A ) are lis t e d in Table-6.6 and plotted in Figure-6.5. Maximum absorption occurs at 235 nm with £(235) = 1.02 x 1(P 1 mole 1 cm1. Maximum absorption at 250 nm 3 -1 -1 with £ = 1.25 x 1CK 1 mole cm was reported for the ethylperoxy radical in aqueous solution by Hickel in 1975 ( 28 ), who generated the radicals by the radiolysis of aqueous solutions containing ethane, oxygen and nitrous oxide. The shift of 15 nm in the position of the maximum i s small for such a change in phase. This spectrum i s also shown in Figure-6.5. - 268 -Figure-6.4 Relative and normalized absorption spectrum of ethylperoxy r a d i c a l Notes* (1) the r i g h t hand ordinate was calib r a t e d using 7 -1 -1 the normalizing f a c t o r i 6.6x10' 1 mole sec (2) the superimposed curve i s the curve f i t t e d to the values of £(A) i n Figure-6.5, which were measured independently by the d i r e c t a n a l y t i c a l method. - 269 -Table-6.8 Values of £(>\) / k^' for the ethylperoxy radical at various wavelengths 10 6 s o ) / v ( sec cm"1 ) wavelength ( nm ) H-91-A H-93-A 212.5 0.42 215.0 0.69 217.5 2.04 0.38 220.0 6.17 10.1 225.0 11.0 9.13 227.5 9.88 230.0 12.3 , 13.0 13.7 232.5 14.0 235.0 17.9 16.3 237.5 14.9 240.0 15.0 14.5 , 11.2 242.5 12.5 245.0 15.1 16.2 247.5 13.6 250.0 14.3 14.1 255.0 8.94 260.0 12.0 9.83 265.0 6.10 11.2 270.0 9.23 6.67 275.0 4.11 280.0 4.38 I.98 290.0 1.20 0.36 - 270 -(3) The value of k^'. Pairs of values of k^'/irCA) and are listed i n Table-6.6 for 19 wavelengths in the range from 220 to 280 nm. The corresponding estimates of k^' are derived from the product of the values of k^'/EKA) and £(A) and are lis t e d i n Table-6.8. The set of six values of k^' measured at wavelengths from 232.5 to 240 nm may be represented by the mean and standard deviationi 10 7 k^' = 6.59 - 0.28 1 mole 1 sec 1 excluding one value which deviates by 3'8o~ from the mean. The set of twenty two values of k^' measured at wavelengths from 220 to 280 nm may be similarly represented: l5 7 k^' = 6.62 i 0.86 1 mole1 sec 1 There is no significant difference between the means of these two sets, indicating that the value estimated for k^' i s independent of the wavelength used in the experiments. An 7 7 7 -1 -1 estimate of k^' = 10'*f = 5 x 10' 1 mole sec was given by Parkes et a l i a in 1977, without any limits of error ( 77 )• This estimate i s 75 # of the present mean value, and thereby affords i t a limited measure of support. (4) The absolute absorption spectrum of the ethylperoxy radical. (a) The direct determination. The analytical method described in Section B.2.C allows the - 271 -Table-6.9 Values of k^' at various wavelengths wavelength ( nm ) 1 6 7 V ( 1 mole"1 sec" 1 ) H-91-A H-93-A 220. 0 * 9.13 5.59 225.0 7.03 8.44 227.5 8.21 230.0 7.03 6.63 232.5 6.93 235.0 5.67 6.26 237.5 6.80 240.0 6.38 6.60 242.5 7.20 245.0 5.74 5.35 247.5 6.48 250.0 5. 80 5-87 252.5 255.0 8.36 260.0 6.59 265.0 • 8.71 * ^.75 270.0 * 4.74 6.56 275.0 280.0 6.21 * not included in the s t a t i s t i c a l analysis. k^' - ( 6.62 1 0.86 ) x 10 7 1 mole"1 sec" 1, based upon 22 measurements in the range from 220 to 280 nm. \ * = ( 6.59 1 0.28 ) x 10 7 1 mole"1 sec" 1, based upon 5 measurements in the range from 232.5 to 240 nm. - 272 -direct determination of Co and the evaluation of £(A) from the equation £(A) = A o / Co 1. These values are listed in Table-6.6 and represented by the black circles i n Pigure-6.5. This spectrum possesses a maximum at 235 nm, with £(235) = 1.02 x 10^ 1 mole1 cm1. This i s in good quantitative agreement with the report by Parkes, Paul, Quinn and Robson of a broad absorption band with a maximum near 230 nm; unfortunately they did not determine the extinction coefficient ( 38 ). The absorption spectrum of the ethylperoxy radical i n aqueous solution was characterized by Hickel in 1975 ( 28 ), and is included in Figure-6.5 for comparison. The maximum l i e s 250 3 -1 -1 nm with £(250) = 1.25 x 10^ 1 mole cm and the characteristics of the two curves are remarkably similar considering the difference in phase. The absorption spectrum of the methylperoxy radical i n the gas phase was discussed in Section C.4.b of Chapter 5 and i s included in Figure-6.5 for comparison with the spectrum of the ethylperoxy radical. The two spectra are qualitatively similar but differ i n intensity; the oscillator strengths of the methylperoxy and ethylperoxy radicals curve estimated as 6.3 x 1 0 2 and 3.4 x 1 0 2 respectively. (b) Determination by the kinetic method. A relative absorption spectrum was obtained by plotting values of £(A)/kl+' against A as shown in Figure-6.4. An absolute spectrum was obtained by calibrating the right hand ordinate, using the experimental value of k^' as the normalizing factor. The validity of the kinetic analysis was listed by comparing the values of £(A) obtained by the kinetic method with those obtained - 273 -Figure-6.5 The absolute absorption spectrum of the ethylperoxy radical 0'—1 1 • 1 1 i i 210 220 230 240 250 260 270 A ( n m ) - 274 -by the direct method. Accordingly the curve f i t t e d to the direct results of Figure - 6 . 5 was superimposed on Figure - 6 . 4 . The superimposed curve i s reasonably consistent with the experimental points, and thereby supports the validity of the kinetic procedure. (5) The value of k... (a) The output of the computer programme. The principal purpose of the programme was to calculate an appropriate value of the ratio k^'/k^ for each experiment so that a value of the fundamental rate constant k^ could be deduced from the experimental value of k^'. The main characteristics of the programme have been described in Section C.5«a of Chapter 5« The method consists of successively entering t r i a l values of kj^ in the input u n t i l the experimental value of k^' emerges from the output. The input also comprises the selected value of the ratio k^/k^, the values of the rate constants k^ to inclusive given in Table - 6 . 3 . the experimental values of C0 and [ o , J , and the period of reaction. (b) The evaluation of k The experimental value of k^' measured with [ o 2 J a 3'8 x 10^ mole l 1 i s i k^' = ( 6 .6 ± 0.3 ) x 10 7 1 mole 1 sec 1. This result i s based upon five values of k^'/E(X) measured near maximum absorption from 232-5 to 240 nm. Two values of k^/k^ were selected. With k^ /k^ = 0.50 the programme gives k^'/k^ = 1.124, yielding the result « k^ = ( 5 .87 ± 0.27 ) x 1 0 7 1 m o i i 1 s e S 1 . w i t h k ^ / f y = 0.33 the - 275 -programme gives k^'/k^ = 1 * 0 9 , yielding the result » k^ = ( 6 . 0 5 i 0.28 ) x 1 0 7 1 mole 1 sec 1. The f i n a l estimate of kj^ i s not affected significantly when the value of /Tn^ i s varied from 0 . 3 3 to 0 . 5 0 , which spans the same range as the published values of k^/k^ for the methylperoxy radical. The value t k^ = l o 7 * 7 7 1 0 * 0 3 = ( 6 . 0 + 0.4 ) x 1 0 7 1 mole1 sec 1 i s probably a f a i r assessment of our knowledge of this quantity. This estimate i s approximately one sixth of value of H —1 —1 ( 3 . 5 ± 0 . 3 ) x 10 1 mole sec estimated for the rate constant for the corresponding reaction of the methylperoxy radical in Chapter 5 ' The disparity i s greater than that observed between the rate constants for the mutual interaction of methyl radicals and of ethyl radicals, which were evaluated a s ( 3 « 2 ± 0 . 5 ) x 1 0 1 0 and ( 1.41 + 0 . 2 6 ) x 1 0 1 0 1 mole1 sec 1 respectively in this investigation. The greater disparity for the interaction of alkylperoxy radicals may be due to the participation of displacement reactions of the type 1 CKjQQ' + CH^ OO* - CH^ OOCR^  + 0 2 CH^ CHgOO* * CH^ CHgOO' *" CH^ CHgOOCHgCH-j + 0 2 and to the greater steric hindrance offered by the CH^ moiety of CH^CHg group. - 276 -D. Conclusions. Reviewing the spectra shown in Figure-6.5 and discussed i n Section C .4 and the kinetic results discussed in Section C 3 and C.5.b, three main conclusions may be drawn* (i) the results of this investigation are reasonably consistent with the limited amount of relevant data in the literature; ( i i ) the characterization of the absorption spectrum of the ethylperoxy radical i s supported by an independent qualitative study and by i t s similarity to the methylperoxy radical spectrum; ( i i i ) the rate constant for the mutual interaction of ethylperoxy radicals in the gas phase at 29ti K i s estimated to 7 —1 - 1 be ( 6 . 0 1 0 . 4 ) x 1 0 ' 1 mole sec , and i s therefore significantly lower than the value of ( 3 - 5 ! 0 . 3 ) x 10 1 mole sec* e s t a t e , , „ t h . corresponding reaction o L e ^ I p e r o x y radical in Chapter 5. X 0 4 - 2?7 -CHAPTER 7 THE SPECTRUM AND KINETIC 3SHAVIQUR OF THE  ACETYL RADICAL A, I n t r o d u c t i o n . (1) The p h o t o c h e m i s t r y o f ke t o n e s . I t has been known f o r some time t h a t the u l t r a v i o l e t i r r a d i a t i o n o f c e r t a i n o r g a n i c compounds ( p a r t i c u l a r l y dye pigments c o n t a i n i n g c o n j u g a t e d double bonds ) causes the e m i s s i o n o f l i g h t , w h i c h may p e r s i s t f o r some time a f t e r the e x t i n c t i o n o f the e x c i t i n g r a d i a t i o n . T h i s phenomenon was d e s c r i b e d by Wiedemann and Schmidt i n I895 ( 1 0 3 ) f o r dye pigments o f the q u i n i n e type d i s t r i b u t e d i n a g e l a t i n m a t r i x . S i n c e t h e n the t e c h n i q u e o f s t u d y i n g the luminesc e n c e o f o r g a n i c compounds by d i s t r i b u t i n g them i n r i g i d m a t r i c e s has been w i d e l y employed. I n 1 9 1 1 K o w a l s k i and G o l d s t e i n d i s c o v e r e d the d e l a y e d ( 1 0 4 , I 0 5 ) e m i s s i o n o f l i g h t from i r r a d i a t e d l i q u i d s o l u t i o n s o f a r o m a t i c compounds i n g l y c e r i n and i n a l c o h o l . The d e l a y e d e m i s s i o n o f l i g h t from b i a c e t y l , b o t h i n the gas phase and i n the pure - 278 -l i q u i d , was reported by Budin i n 1 9 3 0 . Carbonyl compounds have oft e n been the subjects of photochemical s t u d i e s of " slow fluorescence ", which i s temperature-dependent, and of normal fluorescence and phosphorecence, which are not. Three d i s t i n c t types of luminescence have been observed i n organic molecules, and the molecular enviroment i s c r u c i a l i n determining the r e l a t i v e extent of each type. For example, most organic compounds do not f l u o r e s c e s t r o n g l y i n the pure l i q u i d s t a t e or i n s o l u t i o n , and no luminescent a f t e r glow i s observed ( except i n e x c e p t i o n a l cases, l i k e that of b i a c e t y l ). However, when a s o l u t i o n i s cooled to form a c l e a r g l a s s , the normal fluorescence i s u s u a l l y enhanced, and two d i s t i n c t types of a f t e r glow may be i d e n t i f i e d : ( i ) slow fluorescence, with the same spectrum as normal fl u o r e s c e n c e , but w i t h a r e l a t i v e l y long l i f e t i m e that i s temperature dependent, and ( i i ) phosphorescence, with a spectrum d i s p l a c e d i n r e l a t i o n to fluorescence to longer wavelengths, and with a r e l a t i v e l y long l i f e t i m e that i s independent of temperature. The o r i g i n of the three types of luminescence i s i l l u s t r a t e d by the modified J a b l o n s k i diagram of Figure-7.1. The primary photophysical act of absorption of l i g h t by a molecule r e s u l t s i n i t s e x c i t a t i o n from the ground state S 0 to the f i r s t e x c i t e d s i n g l e t state S^. The excess energy of the photon i s converted i n t o v i b r a t i o n a l ( and r o t a t i o n a l ) energy, which i s represented by the s u p e r s c r i p t v i n the symbol 3^ on the diagram. Fluorescence i s emitted when the molecule f a l l s from the e x c i t e d s t a t e 3, to ground stat e S 0. The lowest t r i p l e t s t a t e T, l i e s - 2 ? 9 -Figure-7.1 Modified J a b l o n s k i diagram F i g . 4-10 Modified Jablonski diagram showing the origin of "slow fluorescence," phosphorescence, and triplet-triplet absorption. Radiationless transitions are indicated by wavy lines ( IC = internal conversion, ISC = intersystem crossing). 7", is Jablonski's "metastable state." ( 1 3 6 ) - 2 8 0 -at a lower energy than the e x c i t e d s i n g l e t state S^, and intersystem c r o s s i n g from the state S-, to the state T-^  i s u s u a l l y e f f i c i e n t by s p i n - o r b i t i n t e r a c t i o n . Phosphorescence i s emitted when the molecule f a l l s from the t r i p l e t s t a t e to the ground s t a t e So . Each process shown on the modified J a b l o n s k i diagram of Figure-7.1 i s represented by a t r a n s i t i o n i n t h i s scheme: ( i ) So + hv Sj" a b s o r p t i o n and e x c i t a t i o n ( i i ) + M + M' v i b r a t i o n a l r e l a x a t i o n ( i i i ) *• So + hVf fluorescence ( i v ) So" n o n r a d i a t i v e r e l a x a t i o n or i n t e r n a l conversion (v) S 0 y + M «- So + M" v i b r a t i o n a l r e l a x a t i o n ( v i ) S 1 T-^  intersystem c r o s s i n g ( v i i ) + M T 1 + M' v i b r a t i o n a l r e l a x a t i o n ( v i i i ) »- So + hVp phosphorescence ( i x ) T-^  »- SQV intersystem c r o s s i n g (x) T l + hy - T2V t r i p l e t absorption ( x i ) T 2 y + M T 2 + M v i b r a t i o n a l r e l a x a t i o n ( x i i ) T 2 *• T-j" i n t e r n a l conversion - 2 8 1 -The lowest t r i p l e t s t a t e , T-^ , of most ketones has a r e l a t i v e l y long l i f e t i m e , e s p e c i a l l y i n comparison w i t h the l i f e t i m e of the f i r s t e x c i t e d s i n g l e t s t a t e , S^. The t r i p l e t s t a t e T^ i s formed from the s i n g l e t s t a t e by the intersystem c r o s s i n g ( v i ), which i s normally very much f a s t e r than the competing t r a n s i t i o n s ( i i i ) and ( i v ) that degrade the s t a t e to the ground stat e So. The t r i p l e t s t a t e T^ formed by t r a n s i t i o n ( v i ) i s i n i t i a l l y v i b r a t i o n a l l y e x c i t e d , but i t lo s e s t h i s v i b r a t i o n a l energy r a p i d l y i n c o l l i s i o n s ( v i i ). As a r e s u l t the reverse intersystem c r o s s i n g from T^ to ^^"V^) has an appreciable energy of a c t i v a t i o n , and i s very slow. A c c o r d i n g l y , the o v e r a l l quantum y i e l d f o r the formation of the t r i p l e t s t a t e T-^  i s o f t e n e i t h e r u n i t y or close to t h a t value. A molecule i n the t r i p l e t s t a t e T^ normally returns to the ground stat e S» e i t h e r by the phosphorescent emission of l i g h t ( v i i i ) ( r a d i a t i v e t r a n s i t i o n ) or, more probably, by the no n - r a d i a t i v e r e l a x a t i o n ( n o n - r a d i a t i v e t r a n s i t i o n ) from T-^  to So" ( i x ); both intersystem c r o s s i n g s are r e l a t i v e l y slow t r a n s i t i o n s . The long l i f e t i m e of the t r i p l e t s t a t e i s t h e r e f o r e due to a combination of e f f i c i e n c y of formation w i t h slowness of degradation. The l i f e t i m e i s o f t e n long enough to a l l o w the observation of an absorption spectrum of the t r i p l e t s t a t e T^ due to the t r i p l e t - t r i p l e t e x c i t a t i o n from T^ to T^ ( x ) . Porter and Windsor ( 1 0 6 ) reported the t r i p l e t - t r i p l e t a bsorption spectra of acetone and b i a c e t y l , with maxima at 324 nm and 317 nm r e s p e c t i v e l y , a n d s i m i l a r r e s u l t s were obtained by Singh et a l i a ( 1 0 ? ). The t r i p l e t state may be de a c t i v a t e d by the t r a n s f e r of i t s energy to a quenching molecule Q on - 282 -c o l l i s i o n : 3 D + 1 Q l D + 3 Q An e f f i c i e n t quencher must have a lower t r i p l e t energy than that of the donor species D. The excited states and T^ of a ketone may undergo secondary photochemical reactions to form d i s t i n c t chemical species. The p r i n c i p a l classes of secondary reaction are: (i) Type 1 d i s s o c i a t i o n to r a d i c a l s : CH 3COCH 3* - CH-jCO* +-CH3 ( i i ) Type 2 d i s s o c i a t i o n to molecules: CH 3CH 2CH 2COCH 3* » CH 2=CH 2 + CH3COGH3 ( i i i ) E n o l i z a t i o n : (iv) Abstraction of a hydrogen atom from another molecule: The long l i f e t i m e s of the t r i p l e t states of c e r t a i n ketones allow them to act as photochemical ox i d i z i n g agents; i n t h i s role t r i p l e t ketone molecules may successively abstract two hydrogen atoms from a molecule of a suitable substrate. Thus 2-propanol may be photochemically oxidized i n solution to acetone by benzophenone, which i s i t s e l f reduced to benzopinacol i n the process. - 2 8 3 -(2) The p h o t o d i s s o c i a t l o n of acetone. (a) I n t r o d u c t i o n . E l e c t r o n i c a l l y e x c i t e d acetone undergoes a Type 1 d i s s o c i a t i o n to r a d i c a l s as i t s main secondary photochemical r e a c t i o n . The mechanism f o r the formation and consumption of the primary methyl and a c e t y l r a d i c a l s was proposed by Noyes and Dorfman ( 10 ), and incl u d e s the r e a c t i o n s : CH 3COCH 3 CH3COCR3 CR^CO' 2 GH* GH* + CHjCO' 2 CR^CO* 2 GH 3 + CO CH3C0* + CH^ CH 3 + CO C„H 2n6 CH 3COCH 3 CH3COGOCH3 CH 3 + CH 3COCH 3 CH4 + CH 3COCH 2 ( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) ( 7 ) This mechanism does not d i s t i n g u i s h the S 1 and T i s t a t e s of acetone. The m e t a t h e t i c a l r e a c t i o n ( 7 ) i s n e g l i g i b l e during 1 the r e a c t i o n time of i n t e r e s t i n the present work as k-p = 31 - 1 - 1 1 mole sec a t 2 9 8 K, which i s too low to al l o w i t to compete f o r a s i g n i f i c a n t f r a c t i o n of the methyl r a d i c a l s . Consequently the CH3COCH2 r a d i c a l does not c o n t r i b u t e s i g n i f i c a n t l y to the mechanism of t h i s study. A number of aspects of t h i s mechanism have been the subjects of controversy i n the l i t e r a t u r e . These i n c l u d e : ( i ) the i d e n t i t y of the e x c i t e d s t a t e or s t a t e s of acetone - 2 8 4 -which undergo the primary d i s s o c i a t i o n r e a c t i o n s ( 1 ) and ( 2 ) ; ( i i ) the p r o p o r t i o n of spontaneous primary d i s s o c i a t i o n ; ( i i i ) the p r o p o r t i o n of primary d i s s o c i a t i o n that r e q u i r e s a c t i v a t i o n , and the corresponding energy or energies; ( i v ) the p a r t i c i p a t i o n of the v i b r a t i o n a l energy i n the d i s s o c i a t i o n of the species S^" and T^v ; (v) the proportions of the primary d i s s o c i a t i o n which occur by the simultaneous process ( i ) and which occur by the consecutive process ( 2 ) and ( 3 ) ; ( v i ) the pressure dependence of unimolecular d i s s o c i a t i o n of the a c e t y l r a d i c a l , r e a c t i o n ( 3 ); ( v i i ) the p a r t i c i p a t i o n of heterogeneous processes i n the mutual combination of a c e t y l r a d i c a l s , r e a c t i o n ( 6 ). Each of these problems w i l l be discussed i n the f o l l o w i n g s e c t i o n s . (b) Simultaneous and consecutive processes of d i s s o c i a t i o n . CH^COCH^ + hv CH^COCH^* ( e x c i t a t i o n ) CH 3COCH 3* 2 GH^ + GO ( 1 ) CH 3COCH 3* CH 3 + CH3CO* ( 2 ) CH3CO* • GH^ + GO ( 3 ) Reaction ( 1 ) represents the simultaneous formation of two methyl r a d i c a l s and one carbon monoxide molecule from an e x c i t e d acetone molecule i n a s i n g l e step. Reactions ( 2 ) and ( 3 ) represent the stepwise formation of the same products i n consecutive steps. The r a t i o : - 285 -(X = k1 / ( kx + k 2 ) a <D 1 / ( 4 > 1 + «D2 ) has been measured i n an attempt to e l u c i d a t e the primary decomposition process. The p r i n c i p a l r e s u l t s w i l l be summarized, ( i ) Noyes and Dorfman, 19^8 ( 10 ): (X(313) = 0.07, They studied the mechanism of the photochemical d i s s o c i a t i o n of acetone under s e v e r a l c o n d i t i o n s of temperature and of l i g h t i n t e n s i t y . The quantum y i e l d s of methane and ethane were measured. In the a n a l y s i s of t h e i r data they found that (X was dependent on wavelength at constant temperature, and tha t the primary quantum y i e l d <D, defined as.O^ + <D2,was dependent on temperature and on pressure. Their r e s u l t s are given i n Table-7.1. The temperature dependence f o r <J> was al s o s t r o n g l y Indicated by the decrease i n the fluorescence e f f i c i e n c y w i t h increase i n temperature when the wavelength of the e x c i t i n g r a d i a t i o n was held constant at 313 nm. An explanation of the temperature dependence of <t> was o f f e r e d . At 253«7 nm, where d> = 1 at each temperature, d i r e c t d i s s o c i a t i o n of the acetone molecule was assumed to occur upon abso r p t i o n o f r a d i a t i o n . At 313 nm the f o l l o w i n g steps were proposed: (X(253-7) = 0.22 a t 298 K. A + hv> A R A* CHn + CHoCO R K 9 [ A * ] 2 A R *10 t A*] [ A l This mechanism y i e l d s an expression f o r Table-7.1.A The dependence of the primary quantum y i e l d <t> = <D^  + <r>2( and of the f r a c t i o n 0<= <t>^/( d>1 + <t>2), upon the temperature and the wavelength of the e x c i t i n g r a d i a t i o n i n the p h o t o l y s i s of acetone Quantity Temperature 273 K 298 K 393 K <M313) 0.5 0.7(100 t o r r ) 1. 0 0.8( 25 t o r r ) *(253.7) 1.0 1.0 1.0 CX(313) 0.07 (X(253.7) 0.22 Ref: Noyes and Dorfman, 1 9 4 8 ( 10 ). Table-7.1.B The dependence of o<= <J>1/{ 4^ «• <D 2 ), upon the wavelength of the e x c i t i n g r a d i a t i o n at 295 K A (nm) C* X (nm) X (nm) cX 255 0.25 280 0. 04 305 0.00 260 0.18 285 0.04 310 0.00 265 0.14 290 0.03 315 0.00 270 0. 04 295 0.03 275 0. 04 300 0.00 Ref: Gandini and Hackett, 1977 ( 12 ) - 288 -4> = k 9 / ( k 9 + k 1 Q [ A j ) - 1/ [ 1 + ( k 1 Q [ A ] / k Q )] and therefore the value of <t> should depend upon the pressure. However, i t was estimated that Eg = 5 k c a l mole 1 and E ^ Q = ° » so that a s u f f i c i e n t increase i n temperature should make ^9 ^ k l o t A l * —** This i s c o n s i s t e n t w i t h the increase i n the value of <t> from 0 . 5 a t 273 K to 1 .0 at 393 K. ( i i ) Martin and Sutton, 1952 ( 108 ) i (X(313) — 0 as p-~°° at 298 K. The p h o t o l y s i s of acetone i n the presence of the vapour of 131 iodine l a b e l l e d w i t h r a d i o a c t i v e J I was s t u d i e d at 298 K, using r a d i a t i o n i n the neighbourhood of 3 i 3 nm. The io d i n e quenched the secondary r e a c t i o n s of the r a d i c a l s produced i n the p h o t o l y s i s almost completely. They found (X to be pressure dependent, and approximate e x t r a p o l a t i o n shows that at i n f i n i t e acetone pressure the a c e t y l r a d i c a l d i s s o c i a t i o n should be l e s s than 1 %. ( i l l ) O'Neal and Benson, 1962 ( 109 ): (X(313) = 0 Acetone was photolyzed w i t h l i g h t of 313 nm i n the presence of small amounts of hydrogen iodide over a range of pressure and temperature, 12 ~ 150 t o r r and 399 — 5 6 8 K r e s p e c t i v e l y . The primary process was found to be a G-C s p l i t to form the a c e t y l and methyl r a d i c a l s . Hydrogen iodide acted an e x c e l l e n t r a d i c a l " trap " f o r these r a d i c a l s . No spontaneous d i s s o c i a t i o n of a c e t y l r a d i c a l s was observed. The a c t i v a t e d d i s s o c i a t i o n of the a c e t y l r a d i c a l was measured above 473 K and the r a t e constant was observed to be pressure dependent, as described i n Section 4.a. - 289 -( i v ) Gandini and Hackett, 1977 ( 12 ). These authors r e i n v e s t i g a t e d the photochemistry and photophysics of acetone i n the u*-— n t r a n s i t i o n at v a r i o u s e x c i t a t i o n wavelengths ( 330 - 250 nm ), and at va r i o u s pressures ( 0 - 100 t o r r ) at room temperature. They measured the quantum y i e l d s of phosphorescence, intersystem c r o s s i n g , b i a c e t y l production, and carbon monoxide production. B i a c e t y l production was monitored by d e t e c t i n g i t s s e n s i t i z e d phosphorescence, and CO production was followed by monitoring i t s A( * n ) — X ( *E + ) resonance fluorescence. Their r e s u l t s are r e l a t e d to s e v e r a l areas of the present i n v e s t i g a t i o n , and w i l l be quoted i n s e v e r a l s e c t i o n s of t h i s i n t r o d u c t i o n . Gandini and Hackett presented evidence f o r two modes of p h o t o d i s s o c i a t i o n of acetone, w i t h the corresponding energy thre s h o l d s : GH^COCH^ + hv CH^COCH^* <I>1 CH3COCH3 2 CH 3 + CO E m l n = 104 K c a l mole 1 *>2 _ i CH 3 + GH3C0* E m l n = 95 K c a l mole The species CH 3COCH 3 represents the v i b r a t i o n a l l y e x c i t e d acetone molecule, e i t h e r i n the f i r s t e x c i t e d s i n g l e t s t a t e formed i n the primary photophysical act of l i g h t a b s o r p t i o n , or i n the i s o e n e r g e t i c t r i p l e t s t a t e formed by intersystem c r o s s i n g . They a l s o measured (X= 0^  / ( + <j>2 ) at 295 K at 5 nm i n t e r v a l s over the range of wavelength from 255 to 315 nm, and t h e i r values are l i s t e d i n Table 7.I.B. - 290 -The value of (X d e c l i n e d mono t o n i c a l l y from 0.25 at 255 nm to 0.00 a t A ^ 300 nm i n good agreement w i t h the corresponding r e s u l t s of Noyes and Dorfman ( 1 0 ) . The r e s u l t that (X ^ 0.04 f o r A ^ 280 nm i s s i g n i f i c a n t i n r e l a t i o n both to the c h a r a c t e r i z a t i o n of the spectrum of the a c e t y l r a d i c a l and to the k i n e t i c study of the r a d i c a l i n t e r a c t i o n s of the a c e t y l r a d i c a l ; and these are the p r i n c i p a l t o p i c s of t h i s chapter. Their r e s u l t i m p l i e s that the p h o t o l y s i s of acetone vapour enclosed i n a " P y r e i " v e s s e l a t room temperature w i l l generate a c e t y l and methyl r a d i c a l s i n s u b s t a n t i a l l y equal numbers. (c) D i s s o c i a t i o n from the s i n g l e t and t r i p l e t s t a t e s . The d i s s o c i a t i o n of the acetone molecule from the f i r s t e x c i t e d s i n g l e t s t a t e , S ^ t and from the lowest t r i p l e t s t a t e , T^ may be represented by the scheme below. V i b r a t i o n a l e x c i t a t i o n i s denoted by the s u p e r s c r i p t u, and some as s o c i a t e d r e a c t i o n s are i n c l u d e d : ( i ) So + hv »- S±v absorption and e x c i t a t i o n ( i i ) + M Sj_ + M' v i b r a t i o n a l r e l a x a t i o n ( x i i i ) V 2 CH3 + CO or CHo + CHoCO* d i s s o c i a t i o n from (xiv) Sj_ 2 CH^ + CO or CHo + CHQC0* the s i n g l e t s t a t e ( v i ) S V intersystem c r o s s i n g - 2 9 1 -( v i i ) + M T1 + M* v i b r a t i o n a l r e l a x a t i o n (xv) TY' CE'j + CH^CO* or 2 CH*. + CO J d i s s o c i a t i o n from ( x v i ) Tj_ - CH^ + CH^CO' the t r i p l e t s t a t e or 2 CH* + CO The p r i n c i p a l s t u d i e s of the d i s s o c i a t i o n of e x c i t e d s t a t e s w i l l be summarized. ( i ) Cundall and Davies ( 110 ). A mechanism f o r the gas phase p h o t o l y s i s of acetone was der i v e d from experimental data, i n c l u d i n g s t u d i e s of the ph o t o s e n s i t i z e d i s o m e r i z a t i o n of o l e f i n e s . Acetone was i l l u m i n a t e d by 313 nm l i g h t . D i s s o c i a t i o n i n t o methyl and a c e t y l r a d i c a l s occured from both the f i r s t e x c i t e d s i n g l e t and t r i p l e t s t a t e s ; the corresponding r a t e constants are: k| = 2 . 5 x 1 0 1 6 exp ( - 1 6 9 0 0 / RT ) s e c " 1 rn i n _1 Kg = 2 . 5 x 10 exp ( -6400 / RT ) sec They found no pressure dependence f o r the t r i p l e t s t a t e d i s s o c i a t i o n . At low i n t e n s i t i e s of ab s o r p t i o n , d i s s o c i a t i o n of a c e t y l r a d i c a l s predominated over r a d i c a l - r a d i c a l i n t e r a c t i o n s , and the t r i p l e t s t a t e was e x t e n s i v e l y populated at moderate temperatures, the quantum y i e l d a t 321 K being 0 . 9 8 . ( i i ) O'Neal and Larson, 1969 ( I I I ). These authors s t u d i e d the p h o t o l y s i s of acetone by 315 nm l i g h t i n the presence of hydrogen bromide. They concluded that - 292 -a l l photodissociation of acetone occurred from the t r i p l e t manifold one of two ways. (a) Spontaneous dissociation of molecules in the vibrationally excited t r i p l e t state T^'' formed isoergotically after light absorption by intersystem crossing from the excited singlet state S± . The rate constant k(£)* for the reaction: Tj/' • C H ^ + C H ^ C O * ( xiv ) was expressed in terms of the Rice-Ramsperger-Kassel theory by the equation: k ( E ) * « A * [ < E - E e ) / E ] 8 - 1 • -1 The parameters were evaluated, giving: A w = 11.1 sec , E c = 9.1 ~-10.3 kcal mole1 and s = 5.7 ~?.2. (3) Thermally activated dissociation of those molecules in the t r i p l e t state which have been thermalized by the collisional deactivation process ( v i i ). The processes of activation and dissociation were described by the equations: k 0 r T t + M ^ T i y + M ; Z log k 0 ( 1 mole"1 sec" 1 ) = 9.81 - ( 5.95 / 2.3 R T ) T ^ - CH3 + C H ^ C O * ; k(e) The overall process of dissociation is therefore pressure-dependent, with a rate constant: k d = k0[M] / { 1 + ( z [M] / k ( S ) )} which has a limiting value at high pressure given by - 2 9 3 -log k £ (sec" 1) = l o g ( ko k(E) / Z ) = 10.14 - ( 9.6 / 2.3 R T ) ( i i i ) Recent publications. This section w i l l present a summary of the ideas i m p l i c i t in Sections ( i ) and ( 11 ), and show how these ideas have been developed i n recent investigations. Let us suppose that a ba r r i e r to d i s s o c i a t i o n e x i s t s at a c e r t a i n c r i t i c a l energy i n the t r i p l e t state manifold, such that t r i p l e t state molecules formed with v i b r a t i o n a l energies above th i s barrier decompose with unit e f f i c i e n c y , whereas those formed with energies below th i s b a r r i e r can decompose only afte r thermal a c t i v a t i o n . The existence of such a b a r r i e r was discovered by Hackett and Kutschke i n 197? i n a study of the photochemistry of hexafluoroacetone ( 112). The l i f e t i m e of a molecule i n the t r i p l e t state would depend c r i t i c a l l y upon i t s v i b r a t i o n a l energy. A molecule formed with an energy i n excess of the c r i t i c a l value would possess a l i f e t i m e very much shorter than the l i f e t i m e of a molecule in a thermally equilibrated t r i p l e t state. This idea was developed by Gandini and Hackett i n r e l a t i o n to the photochemistry of acetone ( 12 ). They attempted to detect an excited state of acetone with a l i f e t i m e intermediate between the l i f e t i m e of the excited singlet and thermallzed t r i p l e t states, but could f i n d no evidence for such a state. This negative r e s u l t i s consistent with the view that an acetone molecule i n the t r i p l e t state with an energy in excess of a c r i t i c a l value would have a l i f e t i m e shorter than the l i f e t i m e of the excited s i n g l e t state due to - 294 -d e p l e t i o n by spontaneous decomposition, and Gandini and Hackett o f f e r e d f u r t h e r evidence to support t h i s view. An a l t e r n a t i v e e x p l a n a t i o n of the r e s u l t i n the previous paragraph would be that e x c i t e d s i n g l e t s t a t e i s more e f f e c t i v e l y depleted at higher i n t e r n a l energies by a n o n - r a d i a t i v e process other than intersystem c r o s s i n g . In t h i s connection, G i l l e s p i e and Lim proposed i n 1975 t h a t i n t e r n a l conversion to e x c i t e d ground s t a t e s should p l a y a dominant r o l e i n a l i p h a t i c ketone photochemistry ( 1 1 3 )• They showed t h e o r e t i c a l l y t h a t the sharp decrease i n the fluorescence l i f e t i m e of c e r t a i n halogenated ketones w i t h i n c r e a s i n g e x c i t a t i o n energy can be r a t i o n a l i z e d i n terms of a r a p i d l y i n c r e a s i n g r a t e of the i n t e r n a l conversion —- S0V as the v i b r a t i o n a l energy content of S^ i s increased. I f the i n t e r n a l conversion S^ — - So" can be a competitive process i n the photochemistry of acetone then d i s s o c i a t i o n of v i b r a t i o n a l l y e x c i t e d ground s t a t e molecules to r a d i c a l s must be considered. G i l l e s p i e and Lim quote the i n c r e a s i n g production of c h l o r i n e atoms at s h o r t e r e x c i t i n g wavelengths i n the gas phase p h o t o l y s i s of chloropentafluoroacetone observed by Majer et a l i a i n 1969 ( 1 1 4 ). In t h i s molecule the e x c i t a t i o n energy was i n s u f f i c i e n t to d i s s o c i a t e the C-C 1 bond i n the S^ s t a t e , but i t exceeded the C-Gl bond st r e n g t h i n the i s o e n e r g e t l c So" ground stat e i n d i r e c t r e l a t i o n s h i p to the energy of the e x c i t i n g quantum. Unfortunately, a systematic l n v e s t g a t l o n of the c o n t r i b u t i o n of molecules i n the v i b r a t i o n a l l y e x c i t e d ground s t a t e to the p h o t o d i s s o c i a t i o n of acetone has not yet been published. - 2 9 5 -(3) The absorption s p e c t r a of the a c e t y l r a d i c a l and of k e t y l  r a d i c a l s . The a b s o r p t i o n spectrum of the a c e t y l r a d i c a l has not been reported In any phase i n the l i t e r a t u r e ; e i t h e r i n s t u d i e s of the p h o t o l y s i s of acetone or i n the p h o t o l y s i s of any other probable source of the a c e t y l r a d i c a l . In c o n t r a s t , the absorption spectrum of the k e t y l r a d i c a l (CH-j)2G(OH) was detected among the products of the p h o t o l y s i s of acetone i n var i o u s s o l v e n t s by G.Porter et a l i a i n 1973 (115 )• The absorbance of such s o l u t i o n s increased monotonically as the wavelength was decreased from 475 to 315 nm without passing through a maximum. O p t i c a l a bsorption s p e c t r a f o r a v a r i e t y of k e t y l r a d i c a l s were measured down to 210 nm by Simic, Neta and Hayon i n 1969 ( 116 ), who generated the k e t y l r a d i c a l s by the pulse r a d i o l y s i s of aqueous s o l u t i o n s of v a r i o u s primary, secondary and t e r t i a r y a l c o h o l s . Absorption maxima were obtained f o r f i v e k e t y l r a d i c a l s i n the range from 222 to 238 nm. The formation of the k e t y l r a d i c a l i n the p h o t o l y s i s of acetone i n the l i q u i d phase was discussed by Po r t e r e t a l i a ( 1 1 5 ) . The t r i p l e t s t a t e of the acetone molecule i s formed w i t h high e f f i c i e n c y and v i b r a t i o n a l r e l a x a t i o n i s r a p i d i n the l i q u i d phase. The d i s s o c i a t i o n of the thermalized t r i p l e t s t a t e r e q u i r e s thermal a c t i v a t i o n , and i s a r e l a t i v e l y slow r e a c t i o n i n t h i s system. The k e t y l r a d i c a l may be formed by the a b s t r a c t i o n of a hydrogen atom from a solvent molecule by an acetone molecule i n the t r i p l e t s t a t e : ( CH 3 ) 2 CO* + RH ( CH 3 ) 2 C ( OH ) + R - 296 -and this reaction i s comparatively fast i f the strength of the R-H bond is sufficiently low. Under favourable conditions in the liquid phase the formation of the acetyl radical by the photodissociation of the t r i p l e t state is replaced by the formation of the ketyl radical by the metathetical reaction of the t r i p l e t state. In the gas phase the balance between the reactions is reversed because the concentration of the hydrogen atom donor is too low to allow the bimolecular metathesis to compete favourably with the dissociation. The possiblity of detecting the absorbance of the acetyl radical, generated by photolysis of acetone in the gas phase in the new flash system, was supported by calculations based on the CNDO/2 method and published by White et a l i a ( 117 ). They calculated that the f i r s t excited state of the acetyl radical is a 2A" state, lying 0 . 1 3 eV above the 2A* ground state. A search was made for the absorption spectrum of the acetyl radical in the gas phase between 200 and 500 nm. A variety of l i k e l y photochemical sources of the acetyl radical was used for this search including: CH^COCH^, CH^COCgH^ and CH^COCOCH^. (4) The dissociation of the acetyl radical. k. CH"3C0 CH 3 + CO ( 3 ) (a) O'Neal and Benson, 1962 ( 109 ); k^ = 0 . 2 0 sec 1 at 298 K. The rate of dissociation of the acetyl radical, CH 3 C0, was studied by photolysing acetone in the presence of small amounts of hydrogen iodide over the range 508 - 568 K. The dissociation - 297 -was typical of an unimolecular reaction in i t s M f a l l off " region, with a correspondingly pressure dependent rate coefficient. They obtained the following Arrhenius equations for the dissociation at infinite pressure and at low pressure respectively: k~ = 10.3 - 61.8 ( kj mole1 ) / 2.303 RT sec 1 = 10.3 - 15000 ( cal mole 1 ) / 4.575 T sec 1 k^ 0 = 11.5 - 50.21 ( kJ mole1 ) / 2.303 RT 1 mole1 se = 11.5 - 12000 ( cal mole1 ) / 4.575 T 1 mole1 se (b) Prey and Vlnall 1973 ( 118 ); k^ = 1.03 x l O - 1 sec" 1 k^0 = 3.09 x 1 0 2 1 mole"1 sec" 1 at 298 K. They studied the photolysis of 3.3-dlmethylbutane-2-one ( methyl t-butyl ketone ) in the gas phase at 408 and 326 K, mainly with 313 nm lig h t . At the higher temperature of 408 K the major products were methane, ethane, isobutane, isobutene, neopentane, tetramethylbutane and carbon monoxide. At 326 K, in addition to these products, appreciable quantities of acetaldehyde, acetone, and biacetyl were detected. Quantum yields were determined using acetone and pentan-3-one as actinometers, and they explained most of the experimental data by a conventional mechanism as follows: CH3COC(CH3)3 + hV • CH3C0 + (CH^C* ( 1 ) - CH3 + (CH3)3CCO* ( 2 ) - 298 -CH-jCO' - CH^ + CO ( 3 ) (CH 3) 3CCO* +> (CH 3) 3C* + CO ( 4 ) 2 CH 3 " C 2 H 6 ( 5 ) CH 3 + ( G H 3 ) 3 C — - neo-C^H 1 2 ( 6 ) - CH^ + lSO-C^Hg ( 7 ) 2 ( C H 3 ) 3 C " C 8 H 1 8 ( 8 ) i s o - C ^ H 1 0 + iso-C^Hg ( 9 ) 2 CH3CO* - CH3COCOCH3 ( 10 ) CH3GO* + CH 3  — - CH 3COCH 3 ( 11 ) GH3CO' + (C H 3 ) 3 C l  - CH3CHO + iSO-C^Hg ( 12 ) — - MTBK ( 13 ) CH* + MTBK — - CH^ + R* ( 14 ) GH 3 + R* — - C H ^ ( 15 ) ( C H 3 ) 3 C + R* — * (CH 3) 3CR ( 16 ) (GH 3) 3C* + R* — - iso-CH^Hg + MTBK ( 17 ) They measured the cross-combination r a t i o k^(kg + kg/ V k ^ between the methyl r a d i c a l and the t - b u t y l r a d i c a l , and the d i s p r o p o r t i o n a t i o n / combination r a t i o , k^/k^, of these r a d i c a l s , using the mechanism above. Values of ky^k^Q- were a l s o obtained. From the p l o t of k^ Q^/k^ against the r e c i p r o c a l of pressure at - 2 9 9 -3 2 5 . 7 K, the leas t - s q u a r e s value f o r k^ at high pressure was expressed by the equation: 1 - 6 k~ / sec = ( 4 . 0 6 + O.63 ) x 10 x ( k 1 Q / 1 mole 1 s e c 1 ) They obtained the value of k* to be 19.1 t 3 . 0 s e c 1 at 325.7 K assuming the value of k^ Q to be the same as the value o f k^, 2.2 x 1 0 1 3 1 mole 1 s e c 1 , given by Shepp ( 1 1 9 ). In a d d i t i o n they reevaluated the Arrhenius equation given by O'Neal and Benson, using the i n t e r c e p t s and slopes of O'Neal and Benson's data, and gave the r e v i s e d v a l u e s : l o g U ^ / s e c 1 ) = ( 1 0 . 4 + 1.8) - (64 . 4 t 19.2) k j n o l e 1 / 2 . 3 0 3 RT log(k 3°/l mole 1 s e c 1 ) = (11.6? t 0 . 2 9 ) - ( 5 2 . 3 8 + 3.01 ) kJ mole 1 / 2 . 3 0 3 ST These r e s u l t are i n reasonable agreement w i t h O'Neal and Benson" own f i g u r e s . (c) Watklns and Word, 1974 ( 120 ); k^ = 7.61 s e c 1 at 298 K. These authors studied both the a d d i t i o n of the methyl r a d i c a l to the carbon monoxide molecule and the d i s s o c i a t i o n of the a c e t y l r a d i c a l . The products observed from the p h o t o l y s i s o f azomethane i n the presence o f carbon monoxide were ethane, acetone and b i a c e t y l . These products and t h e i r dependence on temperature and pressure are c o n s i s t e n t w i t h the f o l l o w i n g mechanism: CH^NgCH^ + hv 2 CH3 + N 2 ( 1 ) - 300 -CH* + CO — CH3CO** ( 3 ) CH3CO** + M — - CH3GO* + M ( 4 ) CH^CO* CH^ + CO ( 5 ) CH3CO* + M , CH 3C0 , f + M ( 6 ) CH3CO'+ - CH^ + CO ( 7 ) CH3CO' + CH3 - CH 3COCH 3 ( 8 ) 2 CH3CO* - CH3COCOCH3 ( 9 ) where k a i s the average r a t e constant f o r the unimolecular d i s s o c i a t i o n of the a c e t y l r a d i c a l , and co i s the frequency of c o l l i s i o n a l s t a b i l i z a t i o n of c h e m i c a l l y a c t i v a t e d a c e t y l r a d i c a l s The a s t e r i s k denotes chemical a c t i v a t i o n , whereas the dagger denotes c o l l i s i o n a l a c t i v a t i o n . The study of the a d d i t i o n of the methyl r a d i c a l to the carbon monoxide molecule between 260 and 296 K was based on a steady stat e treatment of the thermalized a c e t y l r a d i c a l , which y i e l d the r e s u l t : / x , -1/2 3/? -1/2, l o g k3/>;> ' (mole cm ' sec ) = (4.5 + 0.2) - (25.0 t 0.1) k j raole 1/2.3 RT ~\ -1 -1 Using l o g k (cm-' mole sec ) = 13*3^ given by Basco, James and Suart ( 33 ) and E9 = 0, the ra t e constant of the a d d i t i o n of methyl r a d i c a l s to carbon monoxide was found to be: " l o g k (cm 3 mole 1 s e c 1 ) = 11.2 - 25(kJ moleV2.3 RT, or: - 301 -log k ^ l mole1 sec 1) = 8.2 - 6.0(kcal mole1)/2.3 RT The chemically activated acetyl radicals formed by the addition of methyl radicals to carbon monoxide possessed an excitation energy of 78 kJ mole1 or 18.7 kcal mole1. For the study of the dissociation of the acetyl radical at sufficiently high pressures and temperatures, reaction ( 5 ) can be neglected and reactions ( 6 ) and ( 7 ) must be Included. As p — oo , the steady state treatment for the acetyl radical gave: k_ k Goo — ~ 3 J ± R ( acetone ) R ( C 2H 6 ) [CO] p-»oo were k o o i s the high pressure l i m i t i n g value of the unimolecular r a t e constant f o r the d i s s o c i a t i o n of the a c e t y l r a d i c a l . The corresponding Arrhenius p l o t , combined w i t h the value of k^ quoted above, and the assumption that kg = k 2 y i e l d e d the l i m i t i n g v alue: l o g kooCsec1) = 13.5 - 1 7 . 2 ( k c a l m o l e 1 ) / 2 . 3 RT Thermochemical p r o p e r t i e s of the a c e t y l r a d i c a l were d e r i v e d from the Arrhenius parameters f o r i t s r e v e r s i b l e d i s s o c i a t i o n as f o l l o w s : A H J = - ( 4 .1 t 0 . 7 ) k c a l mole 1 and S ° = 6 2 . 7 c a l K " 1 mole" 1. The p r i n c i p a l l i m i t i n g high pressure values of the Arrhenius parameters are c o l l e c t e d i n Table - 7 . 2.A (d) Gandini and Hackett, 1977 ( 12 ) - 302 -These authors evaluated k d / k c - f o r the r e a c t i o n s CH-jCO' CH* + CO ( k d ) 2 CH3C0* CH~3COCOCH3 ( k c ) at 295 K. over a wide range of pressure, and ex t r a p o l a t e d t h e i r values to i n f i n i t e pressure. Representative r e s u l t s are given i n Table-7.2.B, w i t h the corresponding estimates c a l c u l a t e d from the r e s u l t s of the p r i n c i p a l i n v e s t i g a t i o n s i n t h i s f i e l d . Values were a l s o c a l c u l a t e d f o r k d, using the estimate of 3.2 x 1 0 1 0 1 mole 1 s e c 1 f o r k Q, as no d i r e c t measurement has been made. The d i s p e r s i o n of these values i s co n s i d e r a b l e , but Gandini and Hackett*s estimate w i l l be s e l e c t e d as re p r e s e n t a t i v e of the s e t . The h a l f l i f e of the a c e t y l r a d i c a l w i t h respect to d i s s o c i a t i o n at 295 ft i s probably of the order of one second. C l e a r l y , t h i s imposes no l i m i t a t i o n upon the measurement of the f a s t r e a c t i o n s of the a c e t y l r a d i c a l a t room temperature. Gandini and Hackett argued that the constancy of t h e i r i values of k d / k c ? c o n s t i t u t e d evidence that " hot " a c e t y l r a d i c a l s were not formed under t h e i r experimental c o n d i t i o n s . (5) Patterns of cross combination of the a c e t y l r a d i c a l and r e l a t e d r a d i c a l s . CH 3 + CH3C0* - CH 3COCH 3 ( 4 ) CH^ + CH 3COCH 2 - CH 3COCH 2CH 3 ( 7 ) (a) Noyes and Dorfman, 1948 ( 10 ). Table-?.2.A L i m i t i n g high pressure values of the Arrhenius parameters, k°°(298) and t|°(29a) f o r the d i s s o c i a t i o n : C H ^ C U ' C H ; + C O Authors year log A°° sec''' l k c a l mole 1 1cJ mole 1 K°°(298) 1 mole 1 s e c 1 t j ( 2 9 8 ) sec O'Neal and Benson Kerr and C a l v e r t 1962 1965 10.3 15.0 6 2 . 0 0.20 3-5 O'Neal and Benson r e c a l c u l a t e d by Frey and V i n a l l 1962 1973 1 0 . 4 * 1 . 0 15.4 64.41 19.2 0.13 5 . 3 Frey and V i n a l l 1973 14 .35* 01 0 .15* 4 - 5 S z i r o v i c z a and halsh 1974 1 3 . 3 * 0 . 5 21.8 91. * 7- 2.24 x 15 3 309. Watkins and Word 1974 1 3 . 2 * 0 . 3 17.3 72 ± 2 3-8 0.18 Gandini and Haclcett 1977 - - - 1 .6 0.44 O Note 1 * based on k°Yk2* » ( 1.28 t 0.20 ) x 10 ^ ( 1 mole" 1 sec 1 E " = 81 kJ mole" 1 and kP = 3.2 x 1 0 1 0 1 mole" 1 s e c " 1 . - 304 -Table-7.2.B Values of the r a t e constant at room temperature, f o r the d i s s o c i a t i o n of the a c e t y l r a d i c a l : C H - C O * — - C H : + co \ Authors yea r T K e t o r r ( l 1 mole s e c 1 ) * k d s e c 1 t j . (b) sec Ref Noyes and Dorfman 1 9 4 8 2 9 8 1 0 0 1 . 5 x 1 0 " 6 0 . 2 7 2 . 5 10 Wijnen 1 9 5 7 3 0 3 3 0 - 6 0 1 . 2 x 1 0 " 5 2 . 2 0 - 3 2 122 G a n d i n i and Hacke t t 1 9 7 7 2 9 5 13 2 . 5 x 1 0 " 6 0 . 4 5 1 . 5 12 G a n d i n i and Haclcett 1 9 7 7 2 9 5 2 0 4 . 1 x 1 0 " 6 0 . 7 4 0 . 9 4 12 G a n d i n i and Hacke t t 1 9 7 7 2 9 5 00 8 . 9 x 1 0 " 6 1 . 6 0 . 4 4 12 O'Nea l and Benson r e c a l c u l a t e d by Prey and V i n a l l 1 9 7 3 2 9 8 00 0.13 5.3 118 S z i r o v i c z a and Walsh 1 9 7 4 2 9 8 00 0 . 0 0 2 2 3 0 9 . 121 Watkins and Word 1 9 7 4 2 9 S 00 3 . 8 0 . 1 8 120 (a) expe r imen ta l v a l u e s i k c f o r the mutual i n t e r a c t i o n o f a c e t y l r a d i c a l s assumed to be 3 . 2 x 1 0 1 0 1 m o l e " 1 s e c " 1 to c a l c u l a t e k J . d (b) t j = O . 6 9 3 / k d , the h a l f l i f e w i t h r e s p e c t to d i s s o c i a t i o n . - 3 0 5 -These authors i n v e s t i g a t e d the secondary r e a c t i o n s of the methyl and a c e t y l r a d i c a l s i n the o v e r a l l photochemical d i s s o c i a t i o n of acetone at 298 and 3 9 5 K. They proposed that the s i g n i f i c a n t secondary r e a c t i o n s were l i m i t e d to the set given below, on the ba s i s of t h e i r measurements of the quantum y i e l d s of methane and ethane, and carbon monoxide at 2 9 8 K only; the quantum y i e l d of carbon monoxide was assumed to be u n i t y at 3 9 5 K. CH3C0* CH* + CO ( 1 ) 2 CH3C0* - CH3COCOCH3 ( 2 ) 2 CH 3 C 2H 6 ( 3 ) CH 3 + CH3CO* - CH 3COCH 3 ( 4 ) CH^ + CH 3COCH 3 - CHzj. + CH"3C0CH2 ( 5 ) 2 CH 3COCH 2 ( CH 3COCH 2) 2 ( 6 ) CH 3 + CH 3COCH 2 CH 3COCH 2CH 3 ( 7 ) CH^CO* + CH 3 C 0 C H 2 CH^COCHgCOCH-, ( 8 ) They derived values of the r a t e constant r a t i o s ki,,Vk 2 &3 and 2 k 3 k^/kr, , which are r e l a t e d to the i n t e r a c t i o n of r a d i c a l s , of k 1 / k 2 ? , which i n v o l v e s the d i s s o c i a t i o n of the a c e t y l r a d i c a l and of k 3/k^ , which Involves the m e t a t h e t i c a l r e a c t i o n ( 5 ); t h e i r r e s u l t s are l i s t e d i n Table - 7 . 2.B. Experiments were conducted a t two r e p r e s e n t a t i v e temperatures, 298 and 3 9 5 K; the former to examine r e a c t i o n s of the a c t y l r a d i c a l , and the l a t t e r to examine the formation and r e a c t i o n s of the acetonyl r a d i c a l CH^COCHg* At 395 & the value of the r a t e constant r a t i o : k^ k£ / kr, 2 = 2.0 + 2.4 i f a l l e i g h t r e s u l t s are included = 1.5 t 1.2 i f the two most deviant r e s u l t s are r e j e c t e d . was determined from the quantum y i e l d s of methane and ethane. Of s p e c i a l i n t e r e s t i n the present study i s the question whether the r a t e constant f o r the cross i n t e r a c t i o n between such d i s s i m i l a r r a d i c a l s ,as the methyl and acetonyl r a d i c a l s i s s t a t i s t i c a l l y r e l a t e d t o the r e s p e c t i v e r a t e constants f o r mutual i n t e r a c t i o n ; the corresponding value of k 3 k^/k^ would be 0 . 2 5 . Unfortunately the p r e c i s i o n of the experimental value of t h i s r a t i o i s too low to give even a general i n d i c a t i o n whether a s t a t i s t i c a l r e l a t i o n s h i p i s approximately v a l i d . At 298 K the a c e t y l r a d i c a l has a s u f f i c i e n t l y l o n g l i f e t i m e to allow i t s r e a c t i o n to become dominant. The r a t e constant f o r i t s thermal d i s s o c i a t i o n was c a l c u l a t e d from the r e s u l t s of Noyes and Dorfman. The value k 1 / k 2 - = 1.5 x 10 1 mole^ sec' may be combined w i t h an estimate: k 2 ^ k-^  = 3.2 x 1 0 1 0 mole 1 s e c 1 from Chapter 3 to give the estimate: k^ = 0.27 s e c 1 at 298 K, but at a pressure f a r too low to y i e l d a l i m i t i n g value. Of greatest i n t e r e s t i n r e l a t i o n to the present i n v e s t i g a t i o n i s the e s t i m a t i o n of the cross combination r a t i o f o r the a c e t y l and methyl r a d i c a l s . The r e s u l t : k^ 2 / k 2 k 3 = 1.1 may be compared w i t h the value of 4 p r e d i c t e d by simple - 3 0 ? -c o l l i s i o n theory. (b) Gandini and Hackett, 1977 ( 1 2 ). These authors obtained the value k i + 2 / k 2 k 3 = 1.0 f o r the cross combination r a t i o of the a c e t y l and methyl r a d i c a l s , i n c l o s e agreement w i t h the value of 1.1 measured by Noyes and Dorfman. Gandini and Hackett discussed the d e v i a t i o n of t h e i r value from the value p r e d i c t e d by simple c o l l i s i o n theory and suggested that the mutual combination of two a c e t y l r a d i c a l s may occur along a t r i p l e t p o t e n t i a l s u r f a c e . The r a t e constant f o r the cross combination of a c e t y l and methyl r a d i c a l s : CH3C0* + CH^ CH 3C0CH 3 ; ^ = 2.5 1 mole 1 s e c 1 may be c a l c u l a t e d from the r a t i o : k^ / k 2 k 3 = 1.0 and the other r a t e constants: 2 CH 3 C 2H 6 ; k 3 = 3.2 x 1 0 1 0 1 mole 1 s e c 1 2 CH3C0* CH 3C0C0CH 3 ; k g = 2.0 x 1 0 1 0 1 mole 1 s e c 1 i f the value of k 2 assumed by Gandini and Hackett i s accepted. (6) The mutual combination of a c e t y l r a d i c a l s . 10 -1 - l 2 CH 3C0 - CH 3C0C0CH 3 ; k 2 = 2.0 x 10 1 mole sec This value was assigned by Gandini and Hackett ( 12 ) i n the absence of an experimental value. I t Is reasonably c o n s i s t e n t w i t h the values of r a t e constants of s i m i l a r r e a c t i o n s which have been adopted i n t h i s work. A value of k ? i s r e q u i r e d f o r - 308 -the computer programme which simulates the generation and consumption of the a c e t y l r a d i c a l d u r i n g the p h o t o l y s i s of a mixture of azomethane and carbon monoxide; t h i s programme i s discussed i n Section B . 2 . e . i i . The d i r e c t determination of k i n t h i s i n v e s t i g a t i o n w i l l be described i n Se c t i o n B.3. - 309 -B. Experimental method. (1) General p r i n c i p l e s . (a) Generation of the a c e t y l r a d i c a l . The a c e t y l was generated by the p h o t o l y t i c d i s s o c i a t i o n of a s e r i e s of a c e t y l d e r i v a t i v e s , comprising C H 3 C O C H 3 , CH-^ COCH^ CH-}, CH3COCOCH3 and C D 3 C O C D 3 . The vapour of the chosen d e r i v a t i v e was d i l u t e d w i t h an excess of argon or n-pentane, to act as a moderating gas, and enclosed i n a " Pyrex " r e a c t i o n v e s s e l . " Pyrex " was used to l i m i t the p h o t o l y t i c r a d i a t i o n to > 280 nm. This l i m i t a t i o n ensured that the p h o t o l y t i c d i s s o c i a t i o n of acetone occurred by the process: C H 3 C O G H 3 + hv> CH^CO* + C H 3 w i t h a n e g l i g i b l e c o n t r i b u t i o n from the process: G H 3 G O C H 3 + hV 2 G H 3 + CO As w i l l be c l e a r from the r e s u l t s of Gandini and Hackett ( 12 ) l i s t e d i n Table-7.1.B. A c c o r d i n g l y , a c e t y l and methyl r a d i c a l s were generated i n equal numbers by the p h o t o f l a s h , and t h i s e q u a l i t y s i m p l i f i e s the e v a l u a t i o n both of the e x t i n c t i o n c o e f f i c i e n t of the a c e t y l r a d i c a l and of the r a t e constants f o r the r e a c t i o n s of the a c e t y l r a d i c a l . I t seems reasonable to assume that the a c e t y l moiety w i l l be re l e a s e d i n t a c t from the p h o t o l y s i s d i s s o c i a t i o n of each of the other a c e t y l r a d i c a l sources by p h o t o l y s i s i n a •* Pyrex " v e s s e l . (b) Mechanism f o r the p h o t o l y s i s of acetone. The s i g n i f i c a n t r e a c t i o n s o c c u r r i n g d u r i n g the p e r i o d of - 3 1 0 -observation of the a c e t y l and methyl r a d i c a l s are l i m i t e d to the se t : CH^COCH^ + hv 1- CH-jCO* + CH^ ( 1 ) 2 CK*3 - C 2H 6 ( 2 ) CH^CO* + CH* » GH3COCH3 + other products ( 3 ) 2 CH3C0* GH3GOCOCH3 + other products ( 4 ) The period of observation i s l e s s than 200 microsec, which i s f a r too short to allow a s i g n i f i c a n t consumption of r a d i c a l s by the processes: ^ CH 3 C0* CR'j + CO ; 1 s e c 1 ( Table-?.2.8 ) CH 3 + CH 3COCH 3 - 0 % + CH-3COCH2 ; k 6 = 31 1 mole 1 s e c 1 ( 9 ) A c c o r d i n g l y the k i n e t i c a n a l y s i s i n t h i s chapter i s based upon r e a c t i o n s ( 1 ) to ( 4 ) only. (2) The absorption spectrum of the a c e t y l r a d i c a l . (a) The nature of the absorbance. Acetone has a broad absorption spectrum, without f i n e s t r u c t u r e and w i t h a maximum at 2?5 nm, which i s assigned to the 77 - — n t r a n s i t i o n . The a c e t y l r a d i c a l was assumed to possess a s i m i l a r absorption spectrum, and the p r e l i m i n a r y search f o r i t spanned the range of wavelength from 200 to 460 nm. (b) Methods of measurement Two methods were used to explore the absorption spectrum - 3H -of the a c e t y l r a d i c a l . In each method the a c e t y l d e r i v a t i v e was enclosed i n a " Pyrex " r e a c t i o n v e s s e l , d i l u t e d w i t h the moderating gas, exposed to the photoflash and l e f t u n t i l the p h o t o f l a s h was v i r t u a l l y e x t i n c t before measurements of the absorbance were made over the d e s i r e d s p e c t r a l range. The computer programme described i n Sections B . 2 . e . i i and C.l.h shows that the emission should be 9 9 * 9 % complete a f t e r 37 microsec, so that the absorbance was measured only a f t e r t h i s i n t e r v a l . The p h o t o e l e c t r i c procedure described i n Chapter 2 was used f o r these measurements. ( i ) The Absorbance-40 method. This method depends upon the exact r e p l i c a t i o n of the value of the a c e t y l r a d i c a l c o n c e n t r a t i o n w i t h i n each s e r i e s of experiments w i t h each of the four a c e t y l r a d i c a l sources. Each experiment w i t h a p a r t i c u l a r sources was conducted so that the a c e t y l r a d i c a l s were generated by the p h o t o l y s i s of i d e n t i c a l r e a c t i o n mixtures under i d e n t i c a l c o n d i t i o n s , and t h e i r absorbance were measured at i d e n t i c a l times a f t e r the f i r i n g of the photoflash; only the wavelength chosen f o r the measurement of absorbance being changed. A delay time of 40 microsec was chosen f o r t h i s procedure, and the values of the absorbance, w e r e p l o t t e d against wavelength to give a r e l a t i v e absorption spectrum f o r the a c e t y l r a d i c a l . ( i i ) The k i n e t i c method. This method was r e s t r i c t e d mainly to the p h o t o l y s i s of acetone. I t was discovered that the absorbances of both the a c e t y l r a d i c a l and the methyl r a d i c a l conformed to a second order equation of the k i n d : - 3 1 2 -1/A = 1/Ao + ( 2 k / £ ( A ) l ) ( t - to ) i f measurement was confined to the dark period f o l l o w i n g the v i r t u a l e x t i n c t i o n of the p h o t o f l a s h . The d e v i a t i o n of the experimental values of 1/A from the s t r a i g h t l i n e f i t t e d by the method of l e a s t squares was small over the l a r g e r p a r t of the p e r i o d of observation. A value of k/£(A) was d e r i v e d from the gradient of the r e g r e s s i o n l i n e at each wavelength, and a p l o t of £(A)/k against A gave a second r e l a t i v e absorption spectrum f o r the a c e t y l r a d i c a l . The apparent r a t e constant k has no p r e c i s e s i g n i f i c a n c e , but i t may be used i n the e v a l u a t i o n of k^ and kz^ by an i t e r a t i v e process described i n S e c t i o n C.4.b. The k i n e t i c method was a l s o used f o r a supplementary study of the t r a n s i e n t species formed by the p h o t o l y s i s of b i a c e t y l . The absorbance of one these species overlapped the absorbance of the a c e t y l r a d i c a l and t h i s study allowed an appropriate c o r r e c t i o n to be made. (c) The nature of the spectra. The s p e c t r a are shown i n Figures 7 . 5 to 7 . 1 0 i n c l u s i v e , and each spectrum has two c h a r a c t e r i s t i c features which are described i n the next two subsections, ( i ) The methyl r a d i c a l spurs. Each of the spectra d e r i v e d from the p h o t o l y s i s of acetone, methyl e t h y l ketone or b i a c e t y l has a narrow spur centred on 216.4 nm, due to absorption by the concomitant methyl r a d i c a l . The prominence of t h i s spur v a r i e d w i t h t h e a c e t y l r a d i c a l source - 3 1 3 -P l g u r e - 7 . 2 E v a l u a t i o n of £ ( 2 1 5 ) f o r the a c e t y l r a d i c a l A: Absorbance near 2 1 6 . 4 nm f o l l o w i n g the f l a s h p h o t o l y s i s of acetone o ACH3(216-4) ACH3CO(216-4) 216.4 A n m 3 : E x t r a p o l a t i o n of the absorbances due to the methyl and a c e t y l r a d i c a l s CD o c o _o c_ o (/) < Time ( usee) - 314 -used. The spectrum d e r i v e d from the p h o t o l y s i s of acetone-d^ has an analogous spur centred on 214.5 nm which i s due to the methyl-djj r a d i c a l . These spurs allow the d i r e c t c a l i b r a t i o n i n absolute u n i t s of the spec t r a of the a c e t y l and acetyl-d-j r a d i c a l s d e r i v e d from acetone and acetone-d^ r e s p e c t i v e l y ; t h i s process w i l l be described i n Section B . 2 . C . i i . ( i i ) The absorbance of the a c e t y l r a d i c a l . A broad band w i t h a maximum near 215 nm was observed i n each of the three undeuterated systems and assigned to the a c e t y l r a d i c a l . A s i m i l a r band w i t h a maximum at 207.5 nm was observed i n the a c e t y l - d ^ system, and assigned to the acetyl-d3 r a d i c a l . No f i n e s t r u c t u r e was observed i n these bands. (d) The e v a l u a t i o n of A G H^ ( 2 1 6.4) and A G H ^ 0 ( 2 1 6 . 4 ) . The t o t a l absorbance at 216.4 nm i n the acetone system i s due to i n roughly equal parts to the a c e t y l and methyl r a d i c a l s . ?igure-7.2.A i s a sketch of that r e g i o n of the spectrum. A set of measurements of AQJJ^QQ(A) and A^otalt2 1 6.4) were made at a s e r i e s of times t . Each value of AQJ^CO^216.4) was obtained by i n t e r p o l a t i o n from values of A G H ^ G Q ( A ) measured outside the spur. The corresponding value of A £ H (216.4) was obtained from the d i f f e r e n c e : A ^ o t a l ( 2 l 6 . 4 ) - &QEJQQ(216.4). (e) The e v a l u a t i o n of £ G H 3 G Q ( 2 l 6 . 4 ) / E N W CQ(215)» The q u a n t i t y i s r e q u i r e d f o r the e v a l u a t i o n of r a t e constants from the k i n e t i c measurements, and i s equal to A * H ^ C 0 ( 2 l 6 . 4 ) / A^ H ^ G O ( 2 1 5 ) , w i t h a value of 0.9B. ( f ) The e x t r a p o l a t i o n to A g f ^ G Q ( 2 1 5 ) and Ag^(216.4). A c e t y l and methyl r a d i c l a s are generated i n equal numbers by the f l a s h p h o t o l y s i s of acetone vapour enclosed i n a " Pyrex " - 315 -r e a c t i o n v e s s e l . Let c m a x be the equal concentrations of the methyl and a c e t y l r a d i c a l s that would have been observed i f a l l the r a d i c a l s generated by the f l a s h had been simultaneously present i n the r e a c t i o n c e l l , and l e t the corresponding e x t r a p o l a t e d values of the absorbance be A m ^ ( 216.4) and Each e x t r a p o l a t i o n was performed on the appropriate set of values of absorbance measured duri n g the I n i t i a l p e r i o d of 48 microsec preceding the k i n e t i c measurements. The procedure i s i l l u s t r a t e d by F i g u r e - 7 . 2 . B and i s a modified from of the procedure described f o r the methyl r a d i c a l i n Section B.2.G of Chapter 3. Greater accuracy was obtained i n t h i s system by the used of an i t e r a t i v e method which w i l l be desceibed i n Section C.4.b. I t e r a t i o n gave A m g * c 0 ( 2 1 5 ) / Ag§ ^ ( 2 l 6.4) = 1.04; t h i s value was used to evaluate ^CH^CO^ 2 1^)* (g) The e v a l u a t i o n of g c ^ C Q ( 2 1 5 ) * The Beer-Lambert Law has been shown to be v a l i d f o r the methyl and a c e t y l r a d i c a l s i n the present apparatus, so that .max A •CH3CO ( 2 1 5 ) £ G H 3 G 0 ( 2 1 5 ) ' GCH^CO • 1 e C H 3 C o ( 2 1 5 ) 1 A ^ ( 2 1 6 . 4 ) £^(216.4) . . 1 6 ^ ( 2 1 6 . 4 ) From Chapter 3 we have £qh {216.4) = 9 . 5 x 10^ I mole 1 cm 1; since ^^Cq{Z1^) / £^(216.4) = 1.04, i t f o l l o w s that v - 1 - 1 eCH3C0^ 2 1 5 ) ~ 9 . 9 x 10-> 1 mole x cm . R e a l i s t i c l i m i t s ' of e r r o r l 3 i mole cm . give ^R3qQ{215) = ( 1 . 0 + 0 . 1 ) x 1 0 ^ 1 mole 1 cm 1. This value was used to c a l i b r a t e the absolute scales of Figures 7 . 5 to 7 . 8 and 7 . 1 0 . - 3 1 6 -No supplementary product a n a l y s i s was r e q u i r e d f o r t h i s e v a l u a t i o n . No assumption was made about the mechanism except the e q u a l i t y of the numbers of a c e t y l and methyl r a d i c a l s generated by the f l a s h . (h) The photosynthesis of the a c e t y l r a d i c a l . ( i ) General p r i n c i p l e . The c h a r a c t e r i z a t i o n of the absorption spectrum of the a c e t y l r a d i c a l r e s t s on the comparison of the absorption s p e c t r a of systems i n which the a c e t h y l r a d i c a l was generated by the p h o t o d i s s o c i a t i o n of four d i s t i n c t a c e t y l d e r i v a t i v e s . In p r i n c i p l e , the absorption spectrum of the a c e t y l r a d i c a l should be a l s o observed a f t e r a mixture of azomethane and carbon monoxide has been subjected to f l a s h p h o t o l y s i s . The a c e t y l r a d i c a l i s synthesized i n tha t system by the r e a c t i o n : CH^ + CO CH^CO* ; = 6 . 6 x 1 0 3 1 mole 1 s e c 1 at 2 9 8 K The r a t e constant was evaluated from the expression: l o g k 1 (1 mole 1 s e c 1 ) = 8 . 2 - ( 25 k j mole 1 ) / 2 . 3 RT due to Watkins Word ( 1 2 0 ) . This comparatively slow r e a c t i o n occurs i n competition w i t h four other r e a c t i o n s , three of which are f a s t : 2 CH 3 - CgHg ; k 2 = 3 . 2 x 1 0 1 0 1 mole 1 s e c 1 CH* + CH-jCO* a l l products; k^ ~ 2.5 x I 0 1 0 1 mole 1 s e c 1 2 CH-CO* a l l products; k/j, as 2 . 0 x 1 0 1 0 1 mole 1 s e c 1 CH^CO* - Cllj + CO ; k^ « 1.0 s e c 1 - 31? -The values of the l a s t three r a t e constants are estimates assigned f o r use i n the computer programme. The p o s s i b i l i t y of observing the absorption spectrum of the a c e t y l r a d i c a l was i n v e s t i g a t e d both by d i r e c t experiment and by a computer programme designed to c a l c u l a t e the concentration of the a c e t y l r a d i c a l over the p e r i o d of i n t e r e s t . -2 Two concentrations of carbon monoxide were used: I.83 x 10 and -2 -1 4.0 x 10 mole 1 . ( i i ) The s i m u l a t i o n of the photosynthesis of the a c e t y l r a d i c a l . The computer programme was based upon of f o u r t h order Runge-Kutta i n t e g r a t i o n of two r a t e equation. d [CH«] / dt = ( G m t / t m 2 ) exp ( - t / t m ) - k 1 [ CH^] [ CO] - 2 k 2 [ C H ^ ] 2 - k 3 [cR^CO*] + k^ [CH3C0*] d [cH^CO*]/ dt = k 1 [CH 3] [ c o ] - k 3 [ c H - ] [cH-jCO'] - 2 k^ [ C H 3 C 0 ' ] 2 - k^ [cH^CO*] The p r i n c i p a l data r e q u i r e d f o r these i n t e g r a t i o n s comprised: (1) the values of k^, k 2, kj* k^ and k^ l i s t e d above; (2) the value of t m , the time r e q u i r e d f o r the i n t e n s i t y of the f l a s h to reach i t s maximum value ( measured as 4 microsec ) ; (3) the value of C m = C m a x , the c o n c e n t r a t i o n of methyl r a d i c a l s that would have been observed i f a l l the methyl r a d i c a l s generated by the f l a s h had been simultaneously present i n the r e a c t i o n v e s s e l , ( estimated as 2.33 x 10^ mole 1 1 under the c o n d i t i o n s ) ; (4) the values of [ c o l l i s t e d above; - 318 -(5) the time p e r i o d of i n t e r e s t , u s u a l l y 50 miorosec. The output of the programme i s i l l u s t r a t e d i n S e c t i o n G.l.h by Figures-?.1 1 .A and 7.11.3 and TabIes - 7 . 1 2 .A and 7.12.B, which were computed f o r [ c o ] = I . 8 3 x 1 0 2 and 4 . 0 x 1 0 2 mole I 1 r e s p e c t i v e l y . The concentrations are normalized i n F i g u r e s - 7 . 11.A and 7.11.3, so that the symbol " 0 " represents [ c H ^ ] / C m and the symbol " X " represents 100 [cH^CO*] / C m. (3) The k i n e t i c measurements. (a) The e m p i r i c a l second order equations. - 3 -1 - 3 A mixture of 2.73 x 10 mole 1 of acetone and 5.46 x 10 -1 mole 1 n-pentane was enclosed i n a " Pyrex " r e a c t i o n v e s s e l and photolysed w i t h a f l a s h energy of 1080 J . The values of the absorbances A G j j^ c 0 ( 2 1 5 ) and A t o t Q ^ ( 2 1 6 . 5 ) were measured d i r e c t l y over the i n t e r v a l from 48 to 156 microsec. The corresponding values of A C ij^ CQ(216.4) were obtained by i n t e r p o l a t i o n from measurements of A Q J ^ C Q ( / \ ) made outside the methyl r a d i c a l spur. Values of ^ ^ ( 2 1 6 . 4 ) were c a l c u l a t e d from the d i f f e r e n c e : A t o t a l ( 2 1 6 . 4 ) - A C H ^ G 0 ( 2 1 6 . 4 ) . These procedures were described i n S e c t i o n 2.d. The values of each set of absorbances, A^ H (216.4) and A C H ^ C 0 ( 2 l 6 . 4 ) , conformed to a corresponding second order r a t e equation of the k i n d : 1/A = 1/Ao + ( 2 k / £ ( A ) 1 ) ( t - to ) A l i n e a r r e g r e s s i o n l i n e was f i t t e d to each p l o t of 1/A against time, and i t was found that the d e v i a t i o n s of the observed values of 1/A from the r e s p e c t i v e r e g r e s s i o n l i n e were not - 319 -s t a t i s t i c a l l y s i g n i f i c a n t . Each r e g r e s s i o n l i n e has a g r a d i e n t : G = d ( l / A ) d t = 2 k / 6 ( A ) . 1 S t a t i s t i c a l a n a l y s i s y i e l d e d a value of / k ^ r ( 2 1 6 . 4 ) f o r the methyl r a d i c a l and a value of k a / k C j j c o ( 2 1 6 . 4 ) f o r the J a c e t y l r a d i c a l from the r e s p e c t i v e values G m and G a of the gra d i e n t s . (b) The approximate r a t e equations. The exact forms of the r a t e equations a re: -d [C H ^ ] / dt = 2 k 2 [CE'}] 2 + k3 [CEj] [ G H ^ C O * ] -d [cH^CO*] / dt = 2 k^ [cH^CO'j 2 + [ CR3 ] [ C H 3 C Q ' ] which may be r e w r i t t e n i n the form d ( 1/[CH 3] ) / dt = 2 k 2 + k 3 [cH-^CO* ] / [CH3] d ( 1/[CH 3C0*] ) / dt = 2 k^ + k 3 [ c H j ] / [CH^CO*] Each equation corresponds to a second order r a t e equation only i f the concent r a t i o n r a t i o remained constant throughout the pe r i o d of measurement. The r a t i o has the i n i t i a l value of u n i t y i f the r a d i c a l s were generated e x c l u s i v e l y by the p h o t o d i s s o c i a t i o n : O H COCH^ + hv CH^CO' + GH* ( 1 ) The value of u n i t y could be maintained i f the r a t e s of consumption of the methyl and a c e t y l r a d i c a l s were equal thronghout the period of obser v a t i o n . This r e q u i r e s that k ? = k^, and that c o n d i t i o n i s l i k e l y to be no more than - 320 -approximately t r u e . Even so, the d e v i a t i o n of i n d i v i d u a l values of the r a t i o from i t s average v a l u e : ^[cH^ C O * ] / [ C H 3 ] ^ > was found to be small over the p e r i o d of k i n e t i c measurement. Ac c o r d i n g l y the r a t e equations were r e w r i t t e n i n the approximate form: d ( 1 / [ C H ' ] ) / dt = 2 k 2 + k 3 < [ G H 3 C O , j /[QE'3]y d ( 1 / [ C H 3 C 0 * ] ) dt = 2 k^ + k 3 / <( [cH 3C0*]/.[cH 3] ^> These are f o r m a l l y equations of the second order as the average value i s a constant, so that they may be r e l a t e d to the second order r a t e equations of p a r t ( a ) , y i e l d i n g the r e l a t i o n s h i p s : 2 ic^ = 2 k 2 + k 3<([cH 3 C<r] / [ C H ^ ] ^ 2 k a = 2 k^ + k 3 / < ( [ C H 3 C 0 * ] / [ c H ' J ^ (c) The measurement of ^l"cH 3C0'1 / [cR" 3]^>_ P a i r s of values of A* H c 0 ( 2 l 6 . 4 ) and A * H 3 ( 2 l 6 . 4 ) were measured at six-microsecond i n t e r v a l s between 48 and 156 microsec. Their r a t i o s u f f e r e d o n l y a minor decrease over that time, as the mean and standard d e v i a t i o n show: ^ A C H 3 C O ( 2 L 6 , / | ) / A G H 3 ^ 2 L 6 ' Z J ' ) ) > = ° ' 8 M - ° * 0 ^ 8 M u l t i p l i c a t i o n by the f a c t o r : £^^(216.4) / €QP QQ{216.4) y i e l d e d the corresponding mean co n c e n t r a t i o n r a t i o ^ [ C H ^ C O * ] / [cH 3]y>. This value may be s u b s t i t u t e d i n t o the f i n a l p a i r equations of the previous subsection to o b t a i n eatimates'of the values of k 3 and k^. (d) The e v a l u a t i o n of k^ and k^. - 321 -An i t e r a t i v e procedure was adopted f o r the e v a l u a t i o n of and k^. This procedure was based on the i n v a r i a b l e q u a n t i t i e s : k 2, from Chapter 3; k m / EcH^CO^ 2 1^*^ from Section B.3.a; and <A£ H^ C O(216.4) / A G H ; 3(2l6.4)^> from B . 3 . C . The e x t i n c t i o n c o e f f i c i e n t ^cH-^Cot 2 1^*^) 9X1(1 ^CR^21^A) were tr e a t e d as adjustable parameters f o r the purpose of i t e r a t i o n . The i n v a r i a b l e q u a n t i t i e s and the adjustable parameters vrere used i n conjunction w i t h the equations: 2 1^ = 2 k 2 + k 3 ^ [cH-jCO*] / [CH 3]^> 2 k a = 2 k 4 + k 3 /<([CH 3C0'] / [CE'3])> The f i r s t c y c l e of i t e r a t i o n employed the i n i t i a l estimates: E G H ^ C 0 ( 2 1 6 . 4 ) = 9.8 x 10 3 1 mole 1 cm 1 £ C H^(216.4) = 9.5 x 10 3 1 mole 1 cm 1 to c a l c u l a t e the f i r s t estimates of the q u a n t i t i e s : <[CH 3C0'] / [CH 3]> , k m, k a, k 3 and k^. I t was then p o s s i b l e to c o r r e c t an anomaly i n the determination of A m^(216.4) and A G a^Q 0(2l6.4) by the e x t r a p o l a t i o n procedure described i n Sect i o n 3.2.f. The values of G m and Ga were measured over an i i i a, i n t e r v a l d u r i n g which <([cH3CO*] / [ c H ^ 1 = 0.857, according to the f i r s t c y c l e of i t e r a t i o n , and then a p p l i e d to the e x t r a p o l a t i o n over an i n t e r v a l d u r i n g which <^[cH3C0*] / [ C H 3 ] ^ > ^ 1. A c c o r d i n g l y , G m and G a were replaced i n the e x t r a p o l a t i o n procedure by: Gm I X = G n ( 2 k 2 + k 3 ) / ( 2 k 2 + 0.857 k 3 ) - 322 -G-aI][ = G a ( 2 k 4 + k 3 ) / ( 2 k 4 + k 3 / 0.657 ) f o r the second c y c l e of i t e r a t i o n . This refinement of the c a l c u l a t i o n increased both £ C H^(2l6.4) and ^ cH 3C0^216.4) °y 5 which i s approximately equal to and l e s s than the r e s p e c t i v e standard d e v i a t i o n s , so i s not s i g n i f i c a n t i n i t s e l f . The use of these r e v i s e d values increased k 3 by 12 % and k^ by 0.2 %, I t a l s o gave the new estimate ^[cH-^CO*] / [ c H ^ ] ^ ? 1 , which i n turn y i e l d e d the new values G^ and G^- f o r the e v a l u a t i o n of E Q J J (216.4 ) M and ^ c ^ C O ^ 2 1 6 * ^ 1 f o r t h e t h i r d c y c l e of i t e r a t i o n . I t e r a t i o n was continued u n t i l the values of k 3, k^ and the e x t i n c t i o n c o e f f i c i e n t s became s t a b l e ; the corresponding f u r t h e r change was l e s s than 1 % i n each case. An a n a l y s i s of s i x c y c l e s of i t e r a t i o n i s given i n Table-?.15 i n Section c.3»C. (e) The computer programme. The v a l i d i t y of second order procedure was te s t e d by a computer programme which used k 2 and the f i n a l values of k^, k^ and <^[cK3C0* ] / [cH"3]^> from the i t e r a t i v e method i n i t s input, solved the d i f f e r e n t i a l r a t e equations of p a r t ( b ) by a f o u r t h order Runge-Kutta method, c a l c u l a t e d Co/C f o r each species and p l o t t e d the corresponding p a i r of second order graphs. T y p i c a l output i s shown i n Tables-?.3, 7.4 and 7.5 and Figures-7.3.M and 7.4.A f o r the c o n d i t i o n s : - 7 -1 - A Co ( CH 3 ) = 1.0 x 10 mole 1 , Co ( CH3C0* ) = 8.5 x 10" -1 mole 1 and a period of observation of 150 microsec. The l i n e a r i t y of each p l o t was tested by computing the corresponding r e g r e s s i o n l i n e and the standard d e v i a t i o n of the p o i n t s , and c a l c u l a t i n g the d e v i a t i o n DY and the q u a n t i t y TY = DY A r f o r - 323 -each p o i n t . The output i s given i n Tables-?.4 and 7.5. The magnitude of the values of TY show that the curvature i s n e g l i g i b l y s m a l l . Furthermore, values of k 2 and k^ were c a l c u l a t e d from the gradients of the r e g r e s s i o n l i n e s and compared w i t h the values entered i n the i n p u t . The r e s u l t s appear i n Tables-?.4 and 7.5 as K 2(CALC) / K 2 = ° « 9 9 6 and i'C^  / ivi4.(CALC) = 1.00 3, showing a n e g l i g i b l e d i s t o r t i o n by the computing procedure. ( 4 ) Apparatus and method. The apparatus was s i m i l a r to that used f o r the study of the mutual combination of methyl r a d i c a l s , which was de s c r i b e d i n Section B of Chapter 3 . A l l experiments were c a r r i e d out i n " Pyrex " r e a c t i o n v e s s e l s which were f i t t e d w i t h end windows of " S u p r a s i l " quartz to transmit the monitoring l i g h t . The double gas f i l t e r c o n t a i n i n g C l 2 and B r 2 was used to transmit the wavelength range from 200 to 270 nm, the g l a s s f i l t e r s 7.54 and 7.59 were used to transmit the wavelengths from 250 to 360 nm and from 330 to 460 nm r e s p e c t i v e l y , and each f i l t e r removed s t r a y l i g h t from the p h o t o f l a s h . The absorption spectrum of the double gas f i l t e r and the tr a n s m i s s i o n curve of these g l a s s f i l t e r have been described i n Se c t i o n C 9 of Chapter 2. The p u r i f i c a t i o n of a c e t y l r a d i c a l sources, acetone-h^, acetone-d£, methyl e t h y l ketone and b i a c e t y l , and of the moderating gases, argon and n-pentane, has been described i n Section C . 1 9 of Chapter 2. A c e t y l r a d i c a l s were generated by the p h o t o l y s i s of the vapour of one of these sources enclosed Table-7•3 Material balance ratios for the methyl and acetyl radicals T «IC«M«C 12. I ) . IS. ~nr ?«. O . l O O F 01 6.963. oo 0.929E 00 Q.»9T; oo »IT i ro 10» Y m . r i c i / . m f IT i - xo i /a i r i JO. 93. O.660F 00 0.B40E 00 0.8I4F 00 ~ ~ f 90. "OO 0.T67E 00 0.746' 00 O.BSIE oo 0.814F 00 0.7 79F 00 0.T48F 00 . T76F 00 O.rOTE 00 _0.6«95 00 0.7I« OC 0.69IE 00 0.664E 00 " 0.643E 00 0.62IE 00 Q.600f 00 0. 100E 01 0.I04E 01 0.1OBE 01 " • l i l t 01 6.fc T ] >* oo O . H M 00 0.64CE 00 51. 54. "TT7" t o . ____ .625E 00 0.6I1E 00 0.398! 00 0.585E 00 0.573! 00 Q.5»IE 00 0.5IK 00 0.563E 00 _ 0 . 3 4 6 ! J | 0 _ 0^3)OF 00 0.514! 00 0.50C! 00 . 115E 01 0.II9E 01 0.123E 01 0.I2TE 01 0.1 JOF 01 1.000E 00 1.046E 00 1.C92F 00 l . l l l i 00 • 9. 77. J l l . 0.530E 00 0.539! 00 0.529! oo 0.486E 00 0.473! 00 __._4»1!_00_ 0.449F 00 0.438E 00 o.«.w 00 0.1 ME 01 o. I«;E OI Q.I*;E OI 0.149* oi o . m e oi Q.I36! 0' .184E 00 1 . 1 )1! 00 I. 77 IE 00 1. 324E 00 1 . 1 1 1 ! 00 i . m t oo .5I9E 00 0.509? 00 0.5 OOF oo • 7. 90. 107. 103. - 1 0 8 t 111. l i t . " I . 0.49IE 0.483! 00 0.474E_00 "TT.46EF 00~ 0.459F 00 0.43IF 0° 0.«1IE 00 0.408E 00 0.398E 00 0.389! 00 0.381! 00 0.3T3! 00 0.I60E 01 0.164! 01 _O.J87E_01_ 0.I7IE 01 0.1791 01 0.IT88 01 465E 00 3I2E 00 I.559E 00 I.607E 00 1.655E 00 I.702! 00 »IPM»I Tl 8.510F-01 B.449E-01 8.191E-0I -4 i ! 3 S U S L _ 8.2B2E-01 B.211E-0I 8.162E-01 8.I35E-0I 8.090E-01 8.05TE-01 «3»ETHITI/K3 .3.CETITI / .3 8.878E-01 B.94 2E-01 9.004E-01 9.064F-0| 170. 173. _JZ6. 129/ 132. 0.444! 00 0.4I7E 00 _0.43 |E_00_ 0.474! 00 0.418! 00 0.4I7E 00 .365! 00 0.35TF 00 _0.350€ 00 0.343E 00 0.337! 00 0.330E 00 0. I I I ! 01 0.184! 01 0.I89E 01 0.193! 01 0.196! 01 0.200! 01 I3B. 141. _144. 14 7. 150. 3.B2? 03 0.406F 00 0.400E 00 _0.395E 00 6.S89 e 90 0.384F 00 0.3 7°E 00 .324E 00 0.318E 00 O.JI2E_00 0.30 IF OO 0.301E 00 0.296E 00 0.204! 01 0.207! 01 _ 0 . 2 l l ! 01_ 0.214E 01 o. nee o i .t.lllt 01 I. T3CF 1.798E 00 _I .84 6E 00 1. B94E 00 I.942E 00 1.99IE 00 2. CUE 00 2.08SE 00 _ i . | 1 6 E 00 _ 2.IB3E 00 2.234E 00 .003E-01 7.964E-0I 7.925E-01 T.887E-01 T.830E-01 r.«nt-oi 9. 12 3E-0I 9.179E-01 9.234C-0I_ 9.2B7E-OI 9.339E-0I 9. 390!-01 1.129! 00 I.121! 00 1.113! 00 _Jjl«iEjo_ 7.7BOE-OI 7.T47E-0I T.7I4£-0I_ T.682E-01 7.631E-0I T.MIC-OI 9.419E-01 9.4S7E-0I _ 9 . 5J4E-01_ 9.5B0EH1I 9.624!-01 9. 64 BE-01 .099E 00 1.092E 00 1.085E 00 1.0I9E 00 1.073E 00 l . M T t 00 .374 = 0.369! 00 0.364. "0 ~0.360E 00 ' 0.35?. 00 9.80E 01 0.29IE 00 0.286E 00 0.28IE 00 0.277F 00 0.272F 00 0.26BE 00 0.275! 01 0.229E 01 _0 . l32 t 01_ 0.736E 01 0.239E 01 0.143E 01 2.332E 00 2.38]E 00 .2.4S0E 00_ 2.479E 00 2.32BE 00 _tl5.18.E_M_ .592E-01 7.564E-0I J . S J 6 E - 0 1 _ T.509E-0I 7.4B2E-0I T.437E-01 9.711E-01 9. 753!-01 _J.794E-0I 9.8S5E-01 9.875E-01 t . ?H{ -01 I.062E 00 1.036! 00 _1.03IE 00_ I.046E 00 1.041! 00 I. 037! 00 SUHI . 12E 02 0.264F 00 0.260F 00 .2 36E 00 .252E 00 .248F 00 C"4 1.21E-02 0.246E 01 0.230! 01 0.253E 01 0. 237E 01 0.2ME 01 0.264E 01 7.677E 00 1 . 1 1 1 ! 00 _2.T26E 00 2. 776! 00 2.826E 00 t . t ' t j 00 T.431E-0I 7.407E-0I 7.3B3! -Ol_ 7.359T--01 7.336E-0I 7.3I3E-01 9.952E-0I 9.969!-01 _l.0°3_00_ 1.006! 00 I.OIOE 00 l . O U t 88 • 1.032E 00 I.028E 00 _l.023£ 00_ 1.019E 00 I.019E 00 • I t O l U 00 1.007E 00 I.003E DO _ _ . ' ' 4 t - 0 l _ 9.960E-OI .9251-01 9.890E-01 0.2bSE 01 0.2TIE 01 0.275J 01 0.27BE 01 0.282E 01 2.924E 00 2. 976E 00 3.026E 00 3.07AE 00 3.126E 00 _3UJ « t _ 5 0 _ 3.227E 00 3.277E 00 3.328E 00 3.37BE 00 3.429E 00 7.29IE-0I 7.269E-01 T.248E-0I_ 7.727E-0I 7.207E-OI -LtitJE-Ol 7.I6TE-01 T.I47E-0I 7.I2SE-01 7.1106-01 T.09IE-01 01 7.0566-01 7.O3BE-01 7.02IE-01 7.004E-01 6.918F-01 1.036E 00 1.039E 00 1.042! 00 I.045E 00 I.048E 00 1.03 IE 00 1.054E 00 1.057E 00 I.060E 00 1.063E 00 1.065E 00 1.068E 00 1.071E 00 I.073E 00 I.076E 00 1.079F 00 I. 08 IE 00 9.67IE-0I 9.6421-01 «.614E-01_ 9.9B6E-01 9.559E-0I *.332E-OI 9.5O6E-0I 9.4B0E-0I 9.453E-01 9.430E-01 9.4O6E-0I _-u3»f-01 9.359E-01 9.336E-01 9.313E-01 9.291E-01 9.269E-01 1.62E-02 INT I.OIE 00 IN( .79F-01 .2ICBLCI/K2 9. 96 3.-01 «4|C«lCI/«4 1.003E 00 - 3 2 5 -Figure-7.3 «M A simulated second order p l o t f o r the decay of the methyl r a d i c a l c o n c e n t r a t i o n o c 4 I H time Table-7.4 A f i t t i n g a second order regression lines to values o: Co/C = Y computed for the decay of the CH^ concentration SMNJARt) 'jlvMTIiN 01- H2ICAIC. ANL> l i . O 24.0 27.0 _30.0_ ii'.O )6.0 42.0 45.0 69.0 72.0 I S O . • /:o 96. 0 99.0 _102.0 105.0 ' loa.o I I I . 114.0 117.0 _120.0_ 121.0 126.0 1 21.0 1)2.0 119.0 1>6,0_ 141.6 144.0 1*7.0 1.000 1.01H 1 .077 I . I K 1.151 1.190 1.226 1.26t 1.015 I-05L. 1.30) 1.141 _ l . )76_ 1.415 1.452 l .4«9 1.526 1.5.) _i .600_ 1.6)7 ' 1.671 K746 1.78) 1.819 1.855 1.892 1-928 1.087 1.124 1.1 60 1.196 1.2)2 l .?69 -0.014*4 -O.J12a^  .964 2.000 _2.0)6_ 2.072 2.108 2.144 2.570 130.0 Gmoiem >T.oev 2.605 2.640 _2.675 7.710 2.745 2.761 2.613 1.305 l .)41 1.377 1.414 1.4 50 1.486 1.522 1.559 _l-595_ U6 31 1.66? .704 -0.01090 -0.00908 -0.007*7 -0.00579 -0.00412 -0.00295 -0.00169 -0.00052 0.00054_ 0~.00132 0.00240 0.00)20 -1.9«,8 _ H . i i . l 9 _ -1.458 -1.214 -0.986 -0.774 -0.577 -0.195 0.0 ).0 15.0 16.0 1.740 1.776 _ l . 61J . 1.649 1.665 I ••>-! 0.00)91 0.00454 _ 0.00510_ 610O557 0 . 0 0 59 6 0.00626 -0.226 -0.070 0.07) 0.20) 0.122 9-1H .957 1.994 _2.0W> 2.066 2.102 ^•1)9 0.00654 0.00672 _0.00684_ 6^00669 0.0066 6 0.0068 1 2.173 2.211 _2.247_ 2.26) 2.120 2.) 56 0.0066 6 0.0064 6 0.00624_ 0.00599 0.0055 7 0.00513 2.192 2.426 _2,465 2.501 2.517 0.00469 0.00417 _0.00160 6.00296 0.00211 0.00160 0.323 0.607 0.681_ 0. 744 0.79? ° . » < Q 0.674 0.699 -0_.?|J 0.922 0.920 0.911 0.691 0.66? 0.614 0.79) 0. 745 <M69 2.610 2.646 2,662 2.718 2.7 55 .791 0.00084 0.0000) .-O t00082_ -0.00172 -0.00266 -0.00)64 2.627 -0.00467 -0.0037) -0,00664 _ -0.00796 -0.00914 -0 . 010)9 0.62? 0.39? 0.461 0.396 0.309 0.21) 0.112 0.004 - 0 ,I |0 -0 . 2)0 -0.196 -0.467 -0.0114) -0.624 -0.766 -0.914 -1.047 -1.225 -1.369 0.012062 0.000024 i_tf«Ci(>T st.oev 1.0145 0.0021 M r r n — SIO.DEy.Of,< 0.0073 13.0 )6.0 39-0 42.0 45.0 -6.1. «_ 31.0 34.0 - l i -.O 61.0 _*» .4_ 49.0 72.0 73.0 J « , 0 _ 67.0 93,0 „ -|O»i0_ 103.0 • 00.0 111.0 116.0 117.0 120.0 • 21.0 126.0 129.0 1)2.0 1)3.0 136.0 141 .0 144.0 I 6 ' . 0 «2<C»LCI S?.0f» -«JltHt|«j l.!66f-02 1.1644-04 9.96) 36-01 - 32? -Figure-?.4.A A simulated second order p l o t f o r the decay of the a c e t y l r a d i c a l c o n c e n t r a t i o n time Table-7 . 5 A f i t t i n g a second order r e g r e s s i o n l i n e s to values of Co /c = Y computed f o r the decay of the CH^CO' concentration He AN AAD STAVJfl 07VI A M J N O F ( U K A i o AN. l^TtHCtfl * I 2 1 C.tC 1 01 T2 7|HE >  0.0 1.0 1 .000 I .n<.& 0.47*) 1.0>H 0.0?114 0. 01(3 . .1 .7 1 - -44 0.0 3 .0 6.0 9.0 1 2.0 1.092 1.1)8 1. 1 B4 1 .0 76 1. 1 29 1.11) 0.01566 0.01.15 O.ulOdO 1. 5)6 1.124 1.087 6.0 ' 9.0 12 .0 15.0 i s .o -1.0 U231 1.277 1.32* 1.222 1.271 1.319 0.00859 0.0065 3 0. 00460 0.865 0.657 0. 4t3 13.0 16.0 21 .0 21.0 27.0 30.0 1.121 1.416 1.469 1 .168 1.417 1.463 0.00261 0.00114 -0.00040 0. 28) 0. 1 15 -0.040 24.0 27.0 30.0 33.0 36.0 39.0 11.0 16.0 39.0 1.912 I.55S 1.601 1.314 1.961 1.611 -0.00182 -0.OOJI1 -0.00429 " -0.18) " -0. 313 -0.412 42.0 45.0 48.0 1.693 1.702 1 .790 1.660 1.709 1.757 -0.00535 -0.00631 -0.00715 -0.5 39 -0.635 -0. 719 42.0 43.0 48 .0 51.0 54.0 57.0 1.796 1.846 1.894 1.806 1.894 1 .901 -0.00786 -0.00851 -0.00903 -0.79) -0.856 -0.909 31 .0 34 .0 37.0 60.0 61 .0 66.0 1.942 1.991 2.039 1.992 2.000 2.049 -0.0094S -0.00977 -0.00999 -0.951 -0.98) -1.006 60.0 4 3 .0 66.0 69.0 T2.0 75.0 2.086 2.136 2.189 2.098 2.146 2.199 -0.01012 -0.01015 -0.01009 -1.019 -1.022 - 1.016 49.0 72 .0 79.0 71.0 81.0 • 4.0 2.234 2.26) 2.332 2.244 2.292 2.141 -0.00994 -0.00970 -0.00937 -1.001 -0.977 -0.94) 76.0 61.0 64.0 • 7.0 90.0 91.0 2.)8I 2.4)0 2.479 2. 190 2.416 2.461 -0.00896 -0.00846 -0.00787 -0.902 -0.851 -0.792 67.0 90.0 91.0 96.0 99.0 102.0 2.326 2.376 2. 62 T 2.339 2.384 2.611 -0.00720 -0.00645 -0.00562 -0.72. -0.649 -0.566 94.4 9 9 . 0 102.0 105.0 toa.o 111.0 2.677 2.726 2. 776 2.661 2.710 2.7 79 -0^00471" -0.00373 -0.00266 -0.4 74 -0.375 -0.2 68 103.0 106.0 1II .0 114.0 117.0 120.0 2.626 2.876 2.926 2.627 2.676 2.923 -0.00152 -0.000)0 0.00099 -0. 15) -0.0)1 0.099 114.0 117.0 120.0 123.0 126.0 129.0 2.976 3.026 ).076 2.9)1 1.022 1.071 0.002)5 0.00379 0.005 2 9 0.2 37 0. 181 0. 53) 121.0 126.0 129.0 132.0 135.0 1)8.0 ).126 ). 176 1.227 1.119 1.166 1.217 0.00687 0.00852 0.0102) 0.641 0. 857 1.030 1.209 ~ 1. 395 1, 588 1)2.0 113.0 1)0.0 141 . 0 144.0 1 47 .0 141.0 144.0 147.0 ).277 1 . )2B ).)78 1.269 3.314 1.362 0.01201 0.01)86 0.01578 150.0 1 . 4 1 * 1 . 4 1 1 0 . 0 1 1 7 * 1 . 7 8 8 1 3 0 . 0 cjAoiewr s t .otv IN7EKCEP? ST.OEV 0.0099 «4<C«IC| 4.933E-02 ... Sl.OtV «4fC4lCI/«4 1.6316-04 1.00)46 0 0 0.016215 0.000032 0.9769 0.0027 - 329 -i n a r e a c t i o n v e s s e l having w a l l s of " Pyrex " and end windows of " S u p r a s i l ". Some photolyses were conducted on the pure vapour, others on the vapour d i l u t e d w i t h an excess of the moderating gas, argon or n-pentane; the pressures ranged from 50 to 630 t o r r . The s t a b l e products of the f l a s h p h o t o l y s i s of acetone include carbon monoxide and ethane. These products were i s o l a t e d at the end of some experiments, and t h e i r y i e l d s were estimated. The procedure was s i m i l a r to t h a t described i n Sect i o n 3 . 3 of Chapter 4 f o r the separation of N 2 and of the C 2 f r a c t i o n from C ^ H ^ Q and r e s i d u a l s . The products were separated by f r a c t i o n a l d i s t i l l a t i o n a t c o n t r o l l e d temperatures under vacuum; CO a t 73 K and C 2H^ at 112 K. The y i e l d of each f r a c t i o n was measured by a McLeod gauge. The CO f r a c t i o n contained a l l the CH^ , and H 2 formed by the p h o t o l y s i s , and these i m p u r i t i e s may c o n s t i t u e 10 mole % of t h i s f r a c t i o n ( 123 ) . The s y n t h e s i s of the a c e t y l r a d i c a l by the r e a c t i o n : CH3 + CO -CH^CO*; k 7 = 6 .6 x 1 0 3 1 mole 1 s e c 1 ( 120 ) v;as attempted by the f l a s h p h o t o l y s i s of two mixtures of 10 t o r r azomethane w i t h 335 and 735 t o r r carbon monoxide r e s p e c t i v e l y i n a standard " pyrex " v e s s e l f i t t e d w i t h " S u p r a s i l " end vrindows to allow a search f o r the spectrum of the a c e t y l r a d i c a l . A computer programme was w r i t t e n to simulate the course of t h i s r e a c t i o n , and has been described i n Se c t i o n B . 2 . e. i i . - 330 -C. R e s u l t s . (1) Absorption spectrum of the a c e t y l r a d i c a l ,  (a) Acetone-h^ as the p h o t o l y t i c source. The absorption spectrum of the a c e t y l r a d i c a l was obtained by the f l a s h p h o t o l y s i s of pure acetone-h^ vapour and of i t s mixture w i t h argon at room temperature. The absorption s p e c t r a obtained f o r the a c e t y l r a d i c a l i n the absence and presence of argon do not d i f f e r s i g n i f i c a n t l y i n shape. Values of the absorbance-40 f o r v a r i o u s wavelengths are l i s t e d i n Tables - 7 . 6 and ? . 7 and are shown i n F i g u r e s - 7 » 5 and 7.6 r e s p e c t i v e l y . Three maxima were observed i n each absorption spectrum. The f i r s t maximum was due to the methyl r a d i c a l and was lo c a t e d at 216.4 nm; the r e s o l v i n g power of the apparatus was i n s u f f i c i e n t to show i t s d e t a i l e d s t r u c t u r e . The second and t h i r d maxima were assigned to the a c e t y l r a d i c a l and were l o c a t e d at 207*5 and 215.0 nm. The lower value of the absorbance observed when 59 t o r r acetone-h^ i s d i l u t e d w i t h 580 t o r r of argon i s probably due to the c a p a c i t y of that gas to promote the v i b r a t i o n a l r e l a x a t i o n of the e l e c t r o n i c a l l y e x c i t e d s t a t e s of the acetone molecule: According to Gandini and Hackett ( 12 ) the v i b r a t i o n a l l y e x c i t e d s t a t e s s | and T£ undergo spontaneous d i s s o c i a t i o n , whereas a f t e r v i b r a t i o n a l r e l a x a t i o n the d i s s o c i a t i o n of the and T^ sta t e s i s slow because i t r e q u i r e s thermal a c t i v a t i o n . I f the presence of argon promotes v i b r a t i o n a l r e l a x a t i o n : Sj + Ar s j + Ar - 331 -Table - 7 . 6 Absorbance of the a c e t y l r a d i c a l : measured 40 microsec a f t e r f i r i n g the ph o t o f l a s h on 50 t o r r of pure acetone vapour Photo f l a s h energy: 1080 J ( 12 kV, 7.5 P )*2 X(nm) A40 A40 H-188-A H-192-A 2 0 2 . 5 0 . 042 0 . 064 2 0 5 .0 0 . 0 6 5 , 0.064 0 . 0 7 3 , 0 . 0 7 5 207.5 0 . 0 7 4 , 0 . 0 7 3 0 . 0 8 7 , 0 . 0 8 6 2 1 0 . 0 0 . 0 7 0 , 0 . 0 6 7 0 . 0 6 9 , 0 . 0 7 1 2 1 2 . 5 O . O 6 9 , 0 . 0 7 3 0 . 0 7 4 , 0 . 0 8 2 2 1 5 . 0 0 . 0 8 1 , 0.080 0 . 0 9 0 , 0 . 0 8 7 2 1 6 . ^ 0 . 1 6 0 , 0 . 1 8 1 , 0 . 1 7 9 , 0 . 1 5 6 , 0 . 1 5 1 0 . 1 6 5 , o ! o 6 9 , 0 . 1 7 2 , 0 . 1 6 8 2 1 7 . 5 0 . 0 6 7 , 0 . 0 6 8 0 . 0 8 6 , O . 0 7 5 2 2 0 . 0 0 . 0 5 3 , 0 . 0 5 0 0 . 0 6 2 , 0 . 0 5 6 2 2 2 . 5 0.042, 0.045 0.049, 0 . 0 5 1 2 2 5 . 0 0.048, 0.049 0.045, 0.047 2 2 7 . 5 0.043, 0.040 0.046, 0.044 1 ; 2 3 0 . 0 0 . 0 3 6 , 0 . 0 3 6 1 O . 0 3 5 , 0 , 0 3 4 2 3 2 . 5 0 . 0 3 2 , 0 . 0 3 1 0 . 0 3 6 , 0 . 0 3 6 2 3 5 - 0 0 . 0 2 3 , 0 . 0 2 5 0 . 0 3 0 , 0 . 0 3 1 i 2 3 7 . 5 0 . 0 2 1 , 0 . 0 2 1 0.028, 0.028 240. 0 0 . 0 2 5 0 . 0 2 7 , 0 . 0 2 7 242 .5 0 . 0 5 7 , 0 . 0 5 7 2 4 5 . 0 0 . 0 3 5 , 0 . 0 2 3 2 4 7 . 5 0 . 0 2 3 , 0.024 2 5 0 . 0 0 . 028 - 332 -Figure-?.5 Absorption spectrum of the a c e t y l r a d i c a l , formed by f l a s h p h o t o l y s i s of acetone at 50 t o r r - 3 3 3 -Table-7.7 Absorbance of the a c e t y l r a d i c a l : measured 40 microsec a f t e r f i r i n g the ph o t o f l a s h on a mixture of acetone and argon. P h o t o f l a s h energy: 1080 J ( 12 .KV, 7.5 uF )x2 X (nm) A 40 A 40 H-I89-A H-191-A Acetone = 50 t o r r Acetone - 50 t o r r Argon = 578 t o r r Aegon - 580 t o r r 202 .5 0. 040 0. 048 205.0 0 . 0 5 0 , 0.053 0 . 0 5 1 , 0.052 207.5 0 . 0 5 5 , 0 . 0 5 7 , 0.054 0.062, 0.068 210 .0 0 . 0 5 1 , 0.055 0.048, O .051 212 .5 0 . 0 5 2 , 0.052 0 . 0 5 2 , O .O55, 0.057 215.0 0.062, 0.062 0.066, 0. 068 216 .4 0.124, 0.124, 0.118, 0.121 0.134, 0 .135, 0.143, 0.136 217 .5 0 . 0 6 0 , 0.062 0 . 0 5 9 , 0.056 220 .0 0.043, 0.042 0 . 0 3 9 , 0. 040 222.5 0 . 0 3 9 , 0.038 0.041, 0.043 225 .0 0 . 0 3 1 , 0.034 0 . 0 3 6 , 0.035 227.5 0.033 0 . 0 3 6 , 0.034 2 3 0 . 0 0 . 0 2 9 , 0.029 0 . 0 3 1 , 0 . 0 3 2 , 0 . 0 3 4 , 0.035 232.5 0 . 0 3 4 , 0.032 0 . 0 3 3 , 0.032 2 3 5 . 0 0 . 0 3 2 , 0.031 0 . 0 3 6 , 0.034 237-5 0 . 0 3 4 , 0.036 0 . 0 3 2 , 0.030 240. 0 0 . 0 3 2 , 0.030 O . 0 3 2 , 0.031 242 .5 0.028, 0.039 0.035 245 .0 0.036 0.029 247 .5 0.025 - 3 3 4 -Figure -7.6 Absorption spectrum of the acetyl r a d i c a l , formed by f l a s h photolysis of a mixture of 50 torr acetone and 580 torr arson 0.15 0.10 o < 0.05 Acetone: Ar= 50 : 580 J — 1 — 1 — 1 1 1 • 1 20 15 200 210 220 230 240 250 X ( nm ) 0 £ o UJ 10 S°, note: normalised to give £(215) = 1.0 x 10^ 1 mole1 cm1 - 335 -T j + Ar - + Ar argon should reduced the d i s s o c i a t i o n of the e x c i t e d s t a t e s and the intersystem c r o s s i n g and promote the competing r a d i a t i o n l e s s r e l a x a t i o n to the ground s t a t e s £ • (b) Methyl e t h y l ketone, MEK, as the p h o t o l y t i c source. The absorption spectrum assigned to the a c e t y l r a d i c a l was obtained by the f l a s h p h o t o l y s i s of pure MEK. vapour, using the same experimental c o n d i t i o n s as f o r acetone. The r e s u l t s are l i s t e d i n Table-?.8 and shown i n Figure-?.7. The bond d i s s o c i a t i o n energies required to separate the methyl and e t h y l groups from the MEK molecule have been determined to be about -1 -1 bO k c a l mole and 75 k c a l mole r e s p e c t i v e l y : CH 3COC 2H 5 ^ C 2 H 5 + CRyjO ' j E1 * 75 k c a l mole 1 • CK~ + C2H^CO"; S 2 ~ 80 k c a l mole 1 so that k^> k 2 f o r the d i s s o c i a t i o n of the e x c i t e d s t a t e . A c c o r d i n g l y , the greater p r o p o r t i o n of the d i s s o c i a t i o n should proceed, by the former path, and the c o n t r i b u t i o n of the methyl r a d i c a l to the r a d i c a l spectrum should be smaller f o r t h i s ketone than f o r acetone; and t h i s i s found to be so. 'Two maxima were observed at 210.0 and 215.0 nm, and good q u a l i t a t i v e agreement e x i s t s between t h i s spectrum and that derived from the f l a s h p h o t o l y s i s of acetone at the same pressure and a f t e r the same delay. The i n t e n s i t y of the spectrum from MEK i s stronger than that from acetone, due to d i f f e r e n c e s i n the e x t i n c t i o n c o e f f i c i e n t s of the ketones, i n - 3 3 6 -Table-7.8 Absorbance of the a c e t y l r a d i c a l : measured 40 microsec a f t e r f i r i n g the photof l a s h on a 50 t o r r of pure methyl e t h y l ketone vapour Phoroflash energy: 1080 J X(nm) A 4 0 H-I98-A, H-165-A 202.5 0.048, 0. 040 2 0 5 . 0 O .O69, 0.063 207 .5 0 . 0 7 8 , 0.076 210. 0 0 . 0 9 2 , 0.088 212.5 0 . 0 8 9 , 0.087 215 .0 O . 0 9 8 , 0.093 216.4 0.104, 0.111, 0 . 1 0 8 , 0 . 1 0 3 , 0.109 217.5 0 . 0 8 7 , 0 . 0 9 1 , 0.082, 0.086 220. 0 0 . 0 8 5 , 0 . 0 8 7 , 0 . 0 8 0 , 0.081 222.5 0.086, 0 . 0 7 5 , 0 . 0 7 7 , 0.078 2 2 5 . 0 0 . 0 6 5 , 0 . 0 6 6 , 0 . 0 5 5 , 0.054 227 .5 0 . 0 5 1 , 0 . 0 5 0 , 0 . 0 5 1 , 0 .049 2 3 0 . 0 0.048, 0 . 0 4 5 , 0.042, 0.041, 0.049 232.5 0.044, 0 . 0 3 6 , 0.034 2 3 5 . 0 0 . 0 3 5 , 0 . 0 3 1 , 0.033 237.5 0 . 0 3 3 , 0.028 240 .0 0.032 242 . 5 0.028 - 337 -F i g u r e - 7 - 7 Absorption spectrum of the a c e t y l r a d i c a l , formed by f l a s h p h o t o l y s i s of methyl e t h y l ketone at 50 t o r r 0.15 0.10 o < 0.05 MEK = 50 torr 15 ^5 200 210 220 230 240 250 X ( nm ) 0 'E o o 10 !z UJ CO Note: normalized to give £(215) = 1.0 x 10^ 1 mole 1 cm 1 without c o r r e c t i o n f o r absorption by the e t h y l r a d i c a l . - 338 -the d i s s o c i a t i o n energies of the e x c i t e d s t a t e s , and i n the ra t e s of the r e a c t i o n s that consume the a c e t y l r a d i c a l . (c) B i a c e t y l as the p h o t o l y t i c source. The absorption spectrum assigned to the a c e t y l r a d i c a l was obtained by the f l a s h p h o t o l y s i s of a mixture of b i a c e t y l vapour and the moderating gas, argon. The photochemistry of b i a c e t y l has been i n v e s t i g a t e d many times, and sev e r a l aspects of i t are s t i l l i n d i s p u t e . The secondary photochemical r e a c t i o n s of b i a c e t y l i n c l u d e the f o l l o w i n g processes: CK^COCOCH^ + hv (B) 1* n o n - r a d i a t i v e r e l a x a t i o n IC i s c ^ 3 ) 1 (B )3** IC (B) J ISC 3* d e c o m p o s i t i o n spontaneous) n o n - r a d i a t i v e r e l a x a t i o n k (fluorescence) decomposition(primary) phosphorescence 0 Z I 3 OH e n o l i z a t i o n The orimary p h o t o d i s s o c i a t l o n of b i a c e t y l may y i e l d both a c e t y l and methyl r a d i c a l s : ( CH 3C0C0CH 3 ) : 2 CH 3C0' CH* + CH 3C0C0' 2 CH^ + 2 CO The s i g n i f i c a n t secondary r e a c t i o n s of these r a d i c a l s are probably l i m i t e d to mutual and cross combination. The geometry of b i a c e t y l makes every carbon-carbon bond of t h i s molecule - 339 -Table-7.9 Absorbance of the a c e t y l r a d i c a l : measured 40 microsec a f t e r f i r i n g the ph o t o f l a s h on a mixture of 10 t o r r b i a c e t y l and 190 t o r r argon Ph o t o f l a s h energy: 1080 J A(nm) Al+0 Al+0 Al+0 H-11+1+-A H-11+6-A H-191+-A 2 0 0 . 0 0 . 0 5 2 2 0 2 . 5 0 . 1 2 5 2 0 5 . 0 0 . 1 2 2 0 . 1 6 5 2 0 7 . 5 0 . 2 5 3 2 1 0 . 0 0.268 0 . 3 0 5 0 . 2 9 3 2 1 2 . 5 0 . 2 9 1(at 213 nm) 0 . 3 2 8(at 215.2 ran) 0.321+ 2 1 5 . 0 0.>+3, 0 . 3 5 2 0 . 3 5 3 . 0 . 3 5 5 , 0 . 3 5 2 0.31+0 216.1+ 0.1+33, 0.1+81+ 0.1+50, (at 0.1+77, 0 . 5 1 5 217.2 nm) 0.1+71, 0.1+83, O.1+88 2 1 7 . 5 0 . 3 2 6 , 0.351+ 0 . 3 5 0 , 0 . 3 3 2 0.3^-5 2 2 0 . 0 0 . 3 7 9 0 . 3 5 3 0 . 3 2 6 2 2 2 . 5 0 . 2 8 2 0 . 2 7 6 0 . 3 0 9 2 2 5 . 0 0 . 2 8 8 0.282, 0 . 2 7 0 0 . 2 5 9 2 2 7 . 5 0 . 1 9 9 0.218 0.221+ 230. '0 0.211+ 0 . 2 1 5 0 . 1 8 3 , 0 . 1 9 0 , 0.218 2 3 2 . 5 0 . 1 6 0 0.151+ 0 . 1 5 9 2 3 5 . 0 0 . 1 3 3 , 0 . 1 3 2 0 . 1 5 2 , 0 . 1 5 7 0 . 1 3 0 2 3 7 . 5 0 . 1 3 9 0 . 1 2 8 0 . 0 9 7 , 0 . 0 9 0 0.110, 0 . 116 u. luS u . u 7 u , 0 . 0 7 2 21+2.5 0 . 0 7 5 0. 082 0 . 0 7 0 21+5.0 0 . 0 7 3 0 . 0 7 7 , 0 . 0 7 5 0 . 0 5 5 21+7-5 0 . 0 6 0 5 0 . 0 7 0 0.01+1+ 2 5 0 . 0 0. 061+ 0 . 0 6 ? 0 . 0 2 7 2 5 2 . 5 0 . 0 5 7 - 340 -F i g u r e - 7 - 8 A b s o r p t i o n spectrum o f the a c e t y l r a d i c a l , formed by f l a s h p h o t o l y s i s o f a m i x t u r e o f 10 t o r r b i a c e t y l and 190 t o r r argon Note: n o r m a l i z e d to g i v e £(215) = 1-0 x 10 1 mole~~ cm " c o r r e c t e d a p p r o x i m a t e l y f o r the absorbance due to s p e c i e s C o f F i g u r e - 7 . ? . - 341 -Figure-7-9 Absorption due to s e v e r a l t r a n s i e n t species, formed by f l a s h p h o t o l y s i s of a mixture of 10 t o r r b i a c e t y l and 190 t o r r argon A, a c e t y l r a d i c a l B, methyl r a d i c a l C, unknown long l i v e d t r a n s i e n t species 0, t r i p l e t - t r i p l e t a bsorption of the b i a c e t y l molecule 200 220 2^ 0 260 280 300 320 3Z>0 A ( nm ) - 342 -weaker than the corresponding bond of acetone. This i s c o n s i s t e n t w i t h the greater i n t e n s i t y of the absorption spectrum observed f o r the t r a n s i e n t species when b i a c e t y l i s the p h o t o l y t i c source. The absorption spectrum corresponding to the a c e t y l r a d i c a l was overlapped by the absorption spectrum of an unknown long l i v e d t r a n s i e n t species l a b e l l e d C on F i g u r e - 7 . 9 . The absorbance due to the species G i n the r e g i o n from 220 to 250 nm was estimated by e x t r a p o l a t i n g to zero time those values of A which had been measured a f t e r the a c e t y l r a d i c a l had been consumed completely. Thus e x t r a p o l a t i o n i s accurate because the formation of t h i s long l i v e d species followed the p r o f i l e of the f l a s h c l o s e l y , whereas the h a l f l i f e of t h i s species i s of the order of s e v e r a l m i l l i s e c o n d s i n a t y p i c a l experiment. This procedure was repeated at a s e r i e s of wavelengths w i t h i n the i n t e r v a l of i n t e r e s t . This extrapolated absorbance was subtracted from the t o t a l a bsorption between 220 and 250 nm to give the a c e t y l r a d i c a l spectrum. The corresponding r e s u l t s are l i s t e d i n Table - 7 . 6 and the spectrum i s shown i n Figure-?.6. The spectrum shows only a s i n g l e maximum at 215.0 nm i n a d d i t i o n to the absorption of the methyl r a d i c a l . The minor d i f f e r e n c e s between the o u t l i n e of t h i s absorption curve and the o u t l i n e s of the previous curves are probably due to a l o s s of accuracy r e s u l t i n g from the s u b t r a c t i o n of the absorbance of another species ( C ). F i g u r e - 7 . 9 shows four peaks obtained from the f l a s h p h o t o l y s i s of a mixture of b i a c e t y l and argon. Peak C was due to an unknown long l i v e d t r a n s i e n t species w i t h a maximum at - 343 -about 250 nm, and peak D was assigned to a t r i p l e t - t r i p l e t absorption spectrum of b i a c e t y l w i t h a maximum at about 310 nm. This T-T absorption of b i a c e t y l was f i r s t r eported by P o r t e r and Windsor ( 106 ), who c h a r a c t e r i z e d i t by a maximum at 310 nm. Figure-?.9 shows that peaks A and C overlap each other i n the wavelength range from 220 to 250 nm, and a method, of c o r r e c t i n g peak A f o r absorption by by species C has been suggested above. (d) Acetone-d^ as the p h o t o l y t i c source. The absorption spectrum corresponding to a c e t y l - d ^ r a d i c a l was obtained by the f l a s h p h o t o l y s i s of pure acetone-d^. The values of absorbance and the spectrum are shown i n Table-?.10 and Figure-?.10 r e s p e c t i v e l y . The spectrum shows only a s i n g l e peak l o c a t e d at 20?.5 nm i n a d d i t i o n to the absorption of the methyl-d3 r a d i c a l at 214.5 nm, and therefore d i s p l a y s the expected s h i f t to a shorter wavelength i n r e l a t i o n to the p r i n c i p a l peak of the a c e t y l - h ^ r a d i c a l , which l i e s at 215 nm. The apparent absence of a second peak at