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Solvent effects on the ionic decomposition of t-butylperoxyformate : and empirical correlation of rate… Kiovsky, Thomas Elstun 1965

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S O L V E N T E F F E C T S ON THE I O N I C D E C O M P O S I T I O N OF t - B U T Y X P E R O X Y F O R M A T E . A N E M P I R I C A L C O R R E L A T I O N OF R A T E W I T H S O L V E N T • P R O P E R T I E S b y THOMAS E . K I O V S K Y B.A., U n i v e r s i t y o f C o l o r a d o , 1962 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T OF THE R E Q U I R E M E N T S FOR THE DEGREE OF M A S T E R OF S C I E N C E i n t h e D e p a r t m e n t o f C h e m i s t r y We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE U N I V E R S I T Y OF B R I T I S H COLUMBIA A p r i l , 1965 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f • B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r -m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i -c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n * D e p a r t m e n t o f QhSJDlSJTJ The U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r 8, C a n a d a D a t e A p r i l , 23,1965 A B S T R A C T Rate constants f o r the pyridine catalyzed i o n i c decom-po s i t i o n of t-butylperoxyformate (TBF) are measured i n 15 non-hydroxylic solvents. The second order rate constants varied by a factor of 40 from the "slowest" solvent, t e t r a -chloroethylene, to the "fa s t e s t " , 1,2-dichloroethahe. -Ten d i f f e r e n t empirical equations are found and t h e i r a b i l i t y to correlate the rate constants with bulk solvent properties i s compared. The best of the ten equations involves the p o l a r i z a b i l i t y and dipole moment of the solvent as follows., The rate constants f o r TBF decomposition i n other non-hydroxylic solvents are calculated by the empirical equations and are compared with values previously reported. The average deviation of the log k i s 0.22. The rate con-stants for the reaction of methyl iodide with triethylamine are calculated from solvent properties and the values compared to l i t e r a t u r e values. In t h i s case the average deviation of the log k i s 0.31. + 3.99K + 0.003 ACKNOWLEDGEMENT I would l i k e to thank Dr. R. E. Pincock f o r his help and encouragement throughout the course of t h i s work. I also wish to thank the National Research Council, the University Research Committee and the st a f f of the UBC:Computing Center. T A B L E O F C O N T E N T S page Introduction 1 Results 7 Discussion 14 Experimental 26 L i t e r a t u r e Cited 33 Appendix 35 \ LIST OF TABLES page I Rate Constants for Decomposition of 10 TBF i n Various Solvents II Regression Co e f f i c i e n t s for Ten 12 Different Combinations of Solvent Parameters I l l i . Solvent Parameters Used i n Compu- 13 t a t i o n of Regression Coefficients IV Comparison of TBF Rate Constants 16 with Various Proposed Measures of Solvent P o l a r i t y V Computed Rate Constants Calculated Rate Constants f o r the Mensehutkinr: Reaction VI 20 24-INTRODUCTION 1 2 "5 4 5 Various proposals ' ' ' ' have been made over the years f o r means of c o r r e l a t i n g reaction rates with the solvents i n which the reactions are carried out. One rather successful proposal, developed by Kirkwood 1, for ap p l i c a t i o n to dipolar or i o n i c reactions i s based on t h e o r e t i c a l considerations alone. Kirkwood has given for the free energy change for transfer of a strong dipole of moment M. from a vacuum to a continuous medium of d i e l e c t r i c constant D_ an expression which, when the charge d i s t r i b u t i o n within the molecule i s symmetrical, becomes, D - I Since polar solvents increase the rate of a reaction i n which the t r a n s i t i o n state i s more polar than the i n i t i a l state, t h i s d i e l e c t r i c constant function, 2p+-\— ' should be d i r e c t l y proportional to the logs of the rate constants., A number of empirical proposals f o r c o r r e l a t i o n of 2 rates of dipolar reactions have also been made. Kosower has proposed using the charge-transfer t r a n s i t i o n energy between states of some 1-alkyl-pyridinium s a l t s as a measure of solvent p o l a r i t y . The t r a n s i t i o n i s between states repre-sented by l a and l b . He c a l l e d the molar t r a n s i t i o n 2 energies, calculated from the pos i t i o n of the absorption maxima, "Z" values. Kosower calculates the dipole moment Z = VxcxM = 2.859 * \ 0 - 3T*J CH i 1 l a l b of l a to be 13.9D and that of lb to be 8.9K. Since there i s a f a i r l y large change i n dipole moment the ease of t r a n s i t i o n should be sensitive to the p o l a r i t y of the solvent. The main d i f f i c u l t y with t h i s proposal i s that these complexes are insoluble i n any but highly polar solvents. The le a s t polar solvent for which he was able to obtain a "Z" value was chloroform. 2 3 2 4 Dimroth, Reichardt, Slepmann, and Bohlmann ' have proposed using the molar t r a n s i t i o n energy, E^, calculated i n the same way as "Z" values, of a pyridinlum Nr-phenolbetalne I I or I I I as an empirical measure of solvent p o l a r i t y . This compound has the advantage that the s h i f t of the absorption maximum i s large upon changing solvent and I I I i s soluble i n hydrocarbon solvents. These authors have obtained E^ values f o r 6 2 solvents and f i v e solvent mixtures. Smith, Falnberg and Winstein'' have measured the rate of i o n i z a t i o n of p_-methoxyneophyl toluene sulfonate i n various solvents and propose the log of t h i s rate constant as a measure of solvent p o l a r i t y . This reaction has the advantage of being measurable In both hydroxylic and non-hydroxylic solvents. A plo t of log k, versus P~ x— gives a rough ° ion 2 D 4- \ straight l i n e i f hydroxylic solvents are omitted, while a plot of log k versus Z values gives a rather good straight l i n e . In some solvents, benzene f o r instance, autocatalysis takes place and k. varies with the extent of reaction. ^ ion A parameter,XL, defined as the log of the r a t i o of the 4 per cent endo to exo adduct i n the reaction between cyclopenta-diene and various dienophiles i s proposed as a measure of 4 solvent p o l a r i t y by Berson, Hamlet and Mueller . The arrangement, N, which leads to endo product would be favored by polar solvents more than the arrangement X, which leads to exo products. The l o g ^ j r - j should then be sensitive to solvent p o l a r i t y . A plot of f l versus Kosower's Z values i s a rather good straight l i n e , the c o r r e l a t i o n being about as good as that between k. and Z. ion Grunwald and Winstein^ proposed i n 1948 t h e i r famous l i n e a r free energy r e l a t i o n s h i p for c o r r e l a t i n g s o l v o l y s i s rates. X l o g Y s mY o 5 k i s the rate constant f o r s o l v o l y s i s of a compound i n anyy solvent, k Q i s the rate constant f o r s o l v o l y s i s i n the standard solvent {60% aqueous-ethanol), m i s a measure of the s e n s i t i v i -measure of the i o n i z i n g power of the solvent. The f a c t that plots of logs of the rate constants In d i f f e r e n t solvent pairs give d i f f e r e n t l i n e s Indicates that more than one property of the solvent i s Involved In determining the rate . In order to overcome t h i s d i f f i c u l t y Winstein, Grunwald 7 and Jones developed a two parameter equation i n which ,Y is. a measure of solvent i o n i z i n g power and N.'Is a measure of the n u c l e o p h i l l c i t y of the solvent. The p a r t i a l d i f f e r e n t i a l quantities were estimated by measuring the change i n In k when Y was changed but N was constant and when N: was changed but Y was constant. A s i m i l a r approach i s possible using any combination of properties of the solvent. In order to correlate and predict the rates of dipolar reactions i n various solvents, I have attempted to set up an equation similar to Winstein's but using physical properties of the solvent instead of the vague properties of n u c l e o p h i l l c i t y and i o n i z i n g power. The ty of the substrate to changes i n the solvent and Y i s a 6 p a r t i a l d i f f e r e n t i a l quantities were determined i n my tre a t -ment by multiple regression analysis c a r r i e d out on an IBM 7040 computer. The potential value of such a treatment Is p summed up by L a l d l e r i n the following quotation. Empirical relationships may be useful i n allowing r e l i a b l e estimates to be made of the properties of systems fo r which no experimental data are av a i l a b l e . Another and more important use of an empirical treatment i s that i t may lead to a valuable t h e o r e t i c a l i n t e r p r e t a t i o n . I t i s important i n developing an empirical treatment to have due regard to whatever theories are available i n order that the empirical treatment be of most value. The rate constants used i n thi s i n v e s t i g a t i o n of s o l -vent e f f e c t s were those of the base catalyzed decomposition of t-butylperoxyformate (TBF). This decomposition goes through a very polar t r a n s i t i o n state and i s ea s i l y studied i n a wide variety of solvents. There are perhaps more data p o t e n t i a l l y available than there are for establishing Z,fL , and k, (but not for E m) discussed above. The mechanism for ion T the base catalyzed decomposition of TBF has been established 9 by Pincock and proceeds as shown. The highly polar tran-s i t i o n state r e s u l t s from the charges formed being separated by the neutral C0 2. This charge separation causes the reaction to be very sensitive to changes In solvent p o l a r i t y . H / O - O - O C H 3 T B F o 7 RESULTS The base catalyzed decomposition of TBF follows pseudo f i r s t order k i n e t i c s , since the base i s regenerated and thus has a constant concentration. d(TBF) = Rate= -k 2(Base)(TBF) dlTBF) ( B a g e ) / d t (TBF) 2 ' In(TBF) = -k 2(Base)t+ const, .TBF) Q _ +k^(Base)t log (TBF) ~ * 2.303 Since the decomposition was followed by measurement of the l o s s of i n f r a r e d carbonyl absorption the function A _ A • L oS ~7\ 7T~ w a s Plotted versus t i n minutes, where A<» i s the absorbance of a sample l e f t f o r more than ten half l i v e s , A Q i s the absorbance of the sample taken at. t = 0 and A i s the absorbance of a sample at any time. The f i r s t order plots were good straight l i n e s followed usually to 80% decomposition with slope of k 2 ^ B a s e ^ . k 0 In l/mole sec. i s 2.303 2 found by d i v i d i n g the slope by (60)(Base) and multiplying i t by 2.303. The rate constants i n various solvents found i n t h i s way are l i s t e d In Table I. 8 The decomposition of TBF can also proceed by a free r a d i c a l chain mechanism, but Pincock^ has shown that the rate of thermal decomposition at 9 0 ° i s slow. According to W a l l i n g 1 0 free r a d i c a l s are sometimes produced from polar t r a n s i t i o n states i n amine peroxide reactions. For example r a d i c a l s are produced i n the reaction between phenyldlmethyl-amine and dlbenzoylperoxide. CH 3 o o-C - 0 o O KK A. </>- k*—o I CVA, 0 — N * o c-<t> O w . • O - C - 0 In order to insure that no free r a d i c a l chain decompo-s i t i o n was occuring i n solvents from which oxygen had been removed by degassing, runs were made i n solutions of about .02M quinone. Since the addition of quinone did not affect! the rate, i t was concluded that no such r a d i c a l decomposition was taking place. I t was found that degassing of the solvent was necessary i n some cases In order to get reproducible k i n e t i c s . The procedure used was to freeze the solution i n a low temper-ature bath and allow I t to melt under vacuum produced by a rotary vacuum pump. The ampoules were then refrozen and 9 sealed under vacuum. Halogenated solvents may react with the pyridine used as a catalyst i n TBF decomposition by elimination or displacement reactions. For example, I t was noted during the course of t h i s research that n-butylchloride reacts with pyridine even under the mild conditions used. In order to f i n d out whether pyridine was reacting with the solvents runs were made at d i f f e r e n t pyridine concentrations. Since the second order rate constants, f o r solvents l i s t e d i n Table I, did not change with changes In pyridine concentration i t was concluded that there was no such reaction taking place.. Rate constants f o r the base catalyzed decomposition of TBF are l i s t e d i n Table I along with the number of runs made i n the solvents and the average devi-a t i o n from the mean. An empirical c o r r e l a t i o n of the rate constants with various combinations of solvent parameters, the choice of which i s explained i n the discussion section, was made using an equation of the form, log k 2 = A(P 1) + B(P 2) ... N(P n) + Const. represents some solvent parameter such as p o l a r l z a b l l l t y , P 2 some other parameter such as dipole moment and so f o r t h . The c o e f f i c i e n t s A, B, etc. were determined using multiple regression analysis. This procedure r e s u l t s i n a set of c o e f f i c i e n t s which minimize the error i n log Ts. . It i s further explained i n the appendix. 10 TABLE I Rate Constants f o r Decomposition of TBF i n Various Solvents Solvent Notes No. Runs k 0 x10^l./molesec. Tetrachloroethylene a 2 4 . 8 9 0.1 trans-Dichloroethvlene a,b 2 12.0 + 0.0 1 ,1 ,1-Trichloroethane a,b 4 20.2 + 1.4 Trichloroethylene a,b 2 22.6 + 1.8 JD-D1 chlorobenzene c 2 2 8 . 7 + 1.7 Fluorobenzene 3 30.2 + 1.1 m-Dlchlorobenzene 3 3 7 . 6 + 1.3 Chlorobenzene 3 4 6 . 6 + 0.6 Bromobenzene 3 4 9 . 6 + 0.7 Iodobenzene 2 63.2 2.0 cis-Dlchloroethylene a,b 2 72.7 0.6 £-Di chlorobenzene a 2 75.8 + 0.6 Te trachloroe thane a 3 7 9 . 5 6 .7 1,1-Dichloroethane a 2 105 4.0 1,2-Dichloroethane a,b 2 207 + 3.0 a Degassed b Run with .02M quinone c Allquots taken instead of sealed tubes 11 In Table II are l i s t e d the values found f o r the c o e f f i -cients under the parameter for which they were determined; f o r example, Equation 6 would read, where k g i s r e l a t i v e to k 2 f o r tetrachloroethylene. The actual log k 2 i s calculated by adding 0.69 to l o g . k 2 e l , since k 2 f o r tetrachloroethylene i s 4.89x 10 l/mole sec. In Table III are l i s t e d the values of solventtparame-ters used to determine the c o e f f i c i e n t s . Unless otherwise noted the values were taken either from Weissberger 1 1 or 12 from the "Handbook of Chemistry and Physics" + . r e l TABLE I I R e g r e s s i o n C o e f f i c i e n t s F o r Ten D i f f e r e n t Combinations o f S o l v e n t Parameters - 1 *\% + 2 n o - I M b.p. M e * AW V D - l 2&-H Const. i -4.708 0.376 0.004 0.154 1.282 2 -10.63 0.314 0.006 0.009 3.412 3 -0.306 0.462 0.154 -0.055 0.034 4 -0.043 0.475 0.004 0.161 -0.251 5 -0.001 0.472 95.52 0.145 -1.945 6 -0.030 0.405 0.138 -0.023 7 -0.108 0.552 - 10.28 -0.498 8 -0.496 0.550 9.54 -0.596 9 3.278 3.995 -1.541 10 1.207 0.399 0.003 TABLE I I I S o l v e n t Parameters Used I n Computation Of R e g r e s s i o n C o e f f i c i e n t s S o l v e n t y M.W. b.p. " D M e A H V D T e t r a c h l o r o e t h y l e n e 165.8 121.2 1.507 0.00 1.623 8.299 2.30 0.888 t r a n s - D i c h l o r o e t h y l e n e 96.5 47.6 1.452 0.00 1.255 6.905 2.14 0.404 1,1 , 1 - T r i c h l o r o e t h a n e 133.4 73.9 1.438 1.79 1.349 7.692 7.52 0.681 T r i c h l o r o e t h y l e n e 131.4 87.2 1.477 0.90 1.468 7.521 3.42 0.566 j>-Dichlorobenzene 147.0 174.1 1.528 0.00 1.247 13.6 2.41 1 . 0 l a Pluorobenzene 96.1 84.85 1.465 1.47 1.024 7.695 5.42 0.707* mJ ) i c h l o r o b e n z e n e 147.0 173.0 1.546 1.48 1.288 „ _ ,b 9.36 5.04 a 1.13 Chlorobenzene 112.6 132 1.525 1.56 1.106 8.735 5.70 0.799 Bromobenzene 157.0 155 1.562 1.73 1.495 9.049 5.40 1.090 Iodobenzene 204.0 188 1.621 1.80 C 1.832 9.90 b 4.63 1.02 a e i s - D i c h l o r o e t h y l e n e 96.95 60.36 1.449 1.89 1.282 7.225 9.20 0.467 _o—Dichlorobenzene 147.0 180.4 1.551 2.26 1.306 9.48 9.93 1.16 a T e t r a c h l o r o e t h a n e 167.9 146.2 1.497 1.85 1.595 9.236 8.20 1.715 1,2-Dichloroethane 98.97 83.5 1.448 2.06 1.252 7.654 10.36 0.835 a C a l c u l a t e d from the Papov e q u a t i o n = ^ M/p) Chem. A b s t r a c t s 54 6239h (\94»o) b C a l c u l a t e d from Trouton's r u l e H = 21T v c The gas phase v a l u e o f 1.80 was used i n s t e a d o f the l i q u i d phase v a l u e o f 1.27 14 DISCUSSION In Table IV are l i s t e d values of log k2 for the decom-po s i t i o n of TBF along with A » Z, E^, and log k i Q n for solvents i n which data for both are available. The agreement with log k 2 f o r T B F i s 'best with log ^ , which i s not sur-p r i s i n g since both are rate constants for polar reactions. Unfortunately not enough data i s available to make a r e a l l y meaningful comparison except for values. The f a c t that the c o r r e l a t i o n between log k 2 and E^ i s not very good i s no doubt because the solvent Interacts d i f f e r e n t l y with d i f f e r e n t substrates. Any treatment which r e l i e s on a measure of the i n t e r a c t i o n of the solvent with a c e r t a i n substrate w i l l suffer from t h i s d i f f i c u l t y . The more si m i l a r the substrates i n two treatments the greater w i l l be the c o r r e l a t i o n . This r e s u l t makes one wonder about the usefulness of trying to correlate rate data with such empir-i c a l measures of solvent p o l a r i t y . For a comparison of a l l the parameters mentioned above except log k 2 see H e i c h a r d t ^ . A plot of log k 2 f o r the decomposition of TBF versus the Klrkwood function, — » i s shown i n Figure 1. The plot y i e l d s a rough straight l i n e with the exception of 1 , 1 , 1-trl-chloroethane. The reason for t h i s solvent being so f a r o f f the l i n e i s probably that due to the odd shape of the molecule i t s dipole axis i s prevented from becoming p a r a l l e l to that of the TBF t r a n s i t i o n state. Since the plot i n Figure 1 i s 15 only a rough straight l i n e there must be other factors which a f f e c t the rate constant. The parameters used i n the equations of Table II were chosen because i t was f e l t these quantities had some chance of being r e l a t e d to properties of the solvents which a f f e c t the rates. The Kirkwood parameter i s j u s t i f i e d because i t i s so often used and seems to work f a i r l y w e l l . However, Wiberg 1^ states, " I t i s evident that d i e l e c t r i c constant i s not a useful value for describing the e f f e c t of the solvent on a dipolar species except i n c e r t a i n special cases, such as a mixture of two solvents." Many functions of the index of r e f r a c t i o n are related to the p o l a r i z a b i l i t y of the molecule. r\*~ ~± ?. w a s *"ound Q by Pincock to correlate the rate of TBF decomposition f a i r l y well i n solvents with no permanent dipole moment. A si m i l a r function, !2° . \ ^ > the molar r e f r a c t i o n , was used because i t i s a measure of the deformabillty or p o l a r i z a -14 b i l l t y of the electron clouds i n a molecule i n an e l e c t r i c f i e l d . I t was thought that the t r a n s i t i o n state dipole would be s t a b i l i z e d by f i e l d s r e s u l t i n g from dlpoles induced i n the solvent molecules and the more polarizable the solvent molecules the greater the s t a b i l i z a t i o n . The b o i l i n g point was used because i t i s related to the l a t e n t heat of vaporization. The latent heat of vaporization i s a measure of the energy of a t t r a c t i o n between solvent molecules and so may be related to the a b i l i t y of solvent 16., TABLE IV Comparison of TBF Rate Constants with Various Proposed Measures of Solvent P o l a r i t y Solvent log k 2+3 n. Z E T 1,2-Dichloroethane 2.32 0.552 63.2 10. 37 Nitrobenzene 2.32 34. 6 Nltromethane 2.22 0.642 38. 57 Dlchloromethane 1.84 8. 9 A c e t o n i t r i l e 1.71 0.634 71.3 37. 5 Bromobenzene 1.70 5. 39 Chlorobenzene 1.66 5. 61 Chloroform 1.66 63.2 4. 70 Tetrahydrofuran 1.45 7. 39 p_-Dloxane 1,36 2. 21 Benzene 1.33 2. 27 Toluene 1.25 2. 38 Carbontetrachloride 0.78 2. 23 l Q S k i o n + 7 3.08 2.78 0.93 Note: TBF rate constants not reported i n t h i s thesis were taken from Pincock (Ref. 9). + Q C M 50 .40 .30 .20 1,1,1-trichloroethane © O-dichlorobenzene cis-dichloroethylene fluorobenzene p-dichlorobenzene-^j> m-dichlorobenzene 1,2-dichloroethane 1,1-dichloroethane 1,1,2,2-tetrachloroethane chlorobenzene bromobenzene iodobenzene trichloroethylene tetrachloroethylene © trans-dichloroethylene ±_ i ; L o .0 2.0 3.0 Log k„ + 3 at 90' 18 molecules to solvate the t r a n s i t i o n state. Direct dipole-dipole Interaction "between the t r a n s i t i o n state dipole and the dlpoles of solvent molecules which have permanent dipole moments was thought to be an important f a c t o r . The magnitude of the i n t e r a c t i o n i s given by M a * ^ c 0 * 9 where r i s the distance between the centers of the dipoles and 9 i s the angle between them. The dipole moment of the t r a n s i t i o n state was assumed to be the same i n a l l the solvents and cos8 was assumed to be a constant since there was no way of taking i t into account. The rate should then be proportional to the dipole moment of solvent mole-cules and probably to r . It was hoped that the dependence of dipole-dipole i n t e r -action on r-' could be accounted for by using molar volume or i t s r e c i p r o c a l as a separate v a r i a b l e . The molar volume i s defined as The larger the molar volume (the volume of a solvent molecule) the l e s s should be the e l e c t r o s t a t i c i n t e r a c t i o n . The molar volume was also used i n a quantity c a l l e d the i n t e r n a l pressure 1^, defined as ^  which i s approximately equal to M / ^ > * i n t e r n a l pressure of a l i q u i d a r ises from the balance of a t t r a c t i v e and repulsive forces between molecules of the l i q u i d . I t was thought that t h i s quantity might be a good measure of the a b i l i t y of solvent molecules to be packed around the t r a n s i t i o n state dipole. 19 The f l u i d i t y , the r e c i p r o c a l of the v i s c o s i t y , was used because i t was f e l t that the a b i l i t y of the solvent molecules to rearrange themselves to accommodate the newly formed t r a n s i t i o n state dipole might be proportional to i t . The v i s c o s i t y i s also r e l a t e d to the latent heat of vapori-zation 1'''. The combination of parameters i n the various equations was more or le s s a r b i t r a r y since i t was impossible to t e l l beforehand what combination would give the best equation. The equations were tested by c a l c u l a t i n g the rate constants f o r TBF decomposition i n solvents which had not been used i n f i n d i n g the c o e f f i c i e n t s . In Table V are l i s t e d the calcu-l a t e d rate constants both for solvents used i n determining the c o e f f i c i e n t s and for others not used. The average deviation of the calculated values from the measured ones fo r the solvents not used i n determining the c o e f f i c i e n t s i s l i s t e d under each column. In terms of average deviation Equations 9 and 10 are the best, having respectively average deviations of 0.23 and 0.22. Eq. 9 log k £ e l = 3.278 [^f^] + 3 .995(|g^- 1-541-3 Eq. 10 log k j e l = 1.207( n t "I ^ + 0.399R - 0.003 -3 This r e s u l t i s surprising since these equations have only two variables. The reason why these two variable equations <D ti © © i N ' <D •A O u o 3 c© © 0 © N © a ti N © © $3 ts» P © ti O,Q © ti o A o s o , H o «d H .titi O OXQ M 3 J o o ° • • E p i r ° " - . »- « o -p © o ti o •£* O o ; *-« ro t OC CM © H ti i>> © © &.r-i ti >» cd .C .ti +> " © O H ti .ti o O r H • H . t i O o I «H *-{ C 1 1 cd t d o j ti H « -Pi C | •r-03 «*d p © o ti o rH . t i O © ti © © © H ti ti > > © © cd • t i . t i H . t i +3 aj >-,p © ,ti ,ti © O -P -P O in © © O O O o © O O * - * - " -ON >*• oc in 00 00 00 OC UN 00 1 -P in > § o is d 0> •P •oc 00 oc o CO IP oc in 00 •4" OO ro co oc oo co IN UN 0C c* CM CM I ™ ' —* ro oc cr> I UJ L L > r v l - I Z O L U ; UN ro m C* 00 -4-o> o 0> IP - H r » <NJ CO >fr rO O —* O H O l O H H INI 00'ON '**•:•*• vO o>:o—• 0> INJ UN o> o o • o o O —1 —I O, r-l «H ON fH INI INJ 0> o 00 IN) <NI f~ (NJ O -H O O rH rH c*> <-H O 00 0> ON UN O —I O 0> rH p» rH ro O O O O rH rH I N • O I N oo a «0 O -H O C M - * r~ ro rH O O O O rH UN ro cr> o oo ro o H r- * 0s IN IN O »-l O O —< — 4 vj- ro -o CN «0 ro I N n to <t r- I N « N O O O O rH rH o o - H vO o> o» CT> rH r -O IN "-H O O O O r H r H 0> UN UN 0* ro ro N O O o m o C M in I N CM tN IN —I CN IN UN O >0 O 00 O rH 00 rH >t C O O o o a> IN O IN rH rH O O •—' .—< 0C O LU O IN U B M 1/1 M H N J M N Z Q J Z Z Z < i ^ O LU 1X1 LU OC - « M CO CO 30 h- O O u o o cd ti -P © EH o ^  o «p.9 <S ti H .ti o • H )% EH © © ti ti © © IS) to ti ti © © O O o o iH H -ti .ti 0 o « Q 1 I OI Bl 00 rO ro (MUN -O O «0 •O r0 'O t> ON ffi o N o I N a* O r l ; 0 H H O ro *r ro UN «o 0^ o I N r- rH m ro I N o o I N cr O rH O rH —I O UN r\l rH ro O s0 O O un U*l rH v}-rH'fjMCr -^!IN «0 O rH O rHjrH O UN IN C* rH rH CO o o m <t « C O O IN O IN UN C rH O rH rH O O O 00 IN O IN ( M O O N O * oo ro * O r H UN O rH O rH rH O co >0 ro vO IA H r H CT> O >o oo ro o >fr r H m r--O O O rH rH O O * ro ( M M IP i H H r- >j- o o in o IN IN vO O »H O rH rH O O O f-<o ro a> - H o m CO IP o vO o> o H r l in O rH O rH rH O r - N}- m co ro O 00 UN o O r - O 0> ( M r H O ao co -H CM I N I N I N I N O UO O rH >o * o a> oo >r rH o> * o NO I N * o O rH O rH rH rH O < L U <X C O CO < L U L U < _ J _ J OC u o OC u o LU OC 0C LU O Q .1- a s: © ti © ti © fit o U r-j O . t i r H O ^ «H 0 O •rH I 1 • «o pi o — © ti © © © © Ctirti 0J o o •P H r l Pi o o ©(>>>» m o o e»oo ^ © ti 0} 4H  © •H r< O r - l rti O r< cd © -p -P © © © •P H ti ti > > © o -P a £k p >>>>© ^ cq o K B c3 I I I 3 O C| P» PJO © 6 O O o ( f I in in in ro vO »t r-. I N co -* ro ro ro O I N ro >J- ro O rH o o O O i rO rH ON IN O O xt CO O rH (\| >o ON 00 O -H CM IN o o o o o o r- r- r- CO IN Ifl N H CO H ^ rO rH IN O rH O O r H o O O O I I ro vt ro in in O O ro «-H o in rO IN rO rH rH o O rH O O O O I I - f co H co co s CO N r) * IP r - rH O rH CN rH O rH O O O O in ro r— *o o * o in N >t >0 N 00 O IN O rH O O rH O O O O I I «r co »»• m iv >o m <t- co >j- o <NI oo ro o rH ro rH O rH O O O O ro CO UN <o UN 00 •J- in oo r - co f- CM r H O IN O O r H o O O O I 0* -* O 00 r H 0"N rO oo ro rO oo UN CM 0> 00 rH O 00 CM CM CM CM CM r H in O 1 >}• O O >t co in o C M o ro in ro vO m ro O rH O O O O CO _) Z < LU h -O < X X LU U H h U J U J h rH Q CL I X OC Q H UJ > >. < 0 . rH X O U O © © ti ti © © rH C O © En « V) If) -vC o o 0 ° o o O n ifl H H f> o m in o 'm r» ro ro m m i ro o o o o o o n o m a UN UN - 4 i O ro >o r-•4* ro rO ro ro ro o o o o o o o o ro m ao c*> •T O N N o m ^ • 0 0 0 - 4 0 o o o o o o in oo r» * o o> ro oo -o r- o UN rO CM rH O rH o o o o o o o I I I in rH C M ro O N oo rH o «o CM o UN rH rH rH rO CM o o o o o o oo in * CM UN o \0 >0 <t N r - IP «J- r H O -* CM O O O O O O in rH ro ro rH ro C M in co co C M in f— rH O rH C O —I o o o o o o stNtOMAvOC oo C M rH in * C M - f O O O N H o o o o o o I I ro co co r H ro -o rH CM * CM "J" O UN 00 CM vO o in rO CM CM CM CM rH rH ON >0 CM CO O fM sO 0> O ro <r CM <0 * *~ UN CM rH O O O O O I Z Z U J Z Z L U L U 2? L U L U U J £ J U J O N 3>->-r J Z s «5 .ti © © •p ti ti © cd © B A N o -P ti © © B P o o .ti u u O -P -P -H - H «H 0 8 15 — 10 S* r< O B ti O © 4H ti O cd ti X O O H •H X! « o 0*0* — — — O ti o «H •P cd © © © ti to © cd ti ti >> © •P > CQ < rJ 00 0> UN ON r - — 4 UN coico CM * 00 rO -»M?int>>t O O O - 4 r H O CM O rH CM vO O CO tj1 CO >t M s N 0> H <t sT O O O rH rH O O rH rH O "-H rH to co nj o m * * CO rH UN ro O O O r H C M C M O <* (M 00 O * CM o * o> ro >t m o* N o «i o O O rH C M C M O I o co C M o rH m O <0 ro r*- in O 0 3 O O 0 > H O O rH CM rH O rO fM ro r- UN o O O CM rH m N . >0 CT> I N in CM - 4 O O rH CM CM O r - O ro CM OO r -N f H -( O H O r» O 1 H M M r 4 O O rH CM CM O IP « 00 M P CO -t B m rn s ^ * - 00 O CM rH o O O - 4 C M C M O C M o> O C M co r -r<10 0 < f >f N (M O 1 O O \ t ? tN <-H CM ro ro rH in ro C* O rO 00 C M P CO >C 0> «t -O r— 00 00 <-H O O O r H tN O Z SI U l UJ UJ z < oc s : 2: 33 L U X O J Ct cc cc O U , U r (- > f4 o of ro <0 ro ro 00 C 0 O X 3 O L U r H _ l i - H i - . r - e r -z a a. o »- co o_a_o_^z_ c o 21 are the best i s probably because they include only parameters which are important i n determining the rates. If other parameters are included they either are not important or they are important only because they are related to parameters which have already been included. The next best equation, Eq. 6 with three variables, has an average deviation of 0 . 3 2 . The A, B, ... of the equations of Table II are related to c e r t a i n t h e o r e t i c a l quantities as follows. If log k Is a function of the physical properties of the solvent i t i s possible to write the t o t a l d i f f e r e n t i a l giving the change i n log k with respect to changes In the solvent parameters P. In order to eliminate the d i f f e r e n t i a l s , dlog k and dP^, a standard i s chosen and the d i f f e r e n t i a l s set equal to differences between the quantities for the solvent and f o r the standard. log k = f ( P 1 ( P 2, ... P n) dlog k = log k - log k std dP, = P, - P i i i s t d log k - log k s M = t ( 0 P i " R * 1 ) By taking a l l the rate constants r e l a t i v e to the rate r e l constant of the standard log k ^, i s made zero. std 22 r e l constant = log k ^ log k r e l = + constant The p a r t i a l d i f f e r e n t i a l quantities, » were deter-mined using multiple regression analysis carried out on an IBM 7040 computer and are the same as the A, B, ... mentioned above. In order to further test the usefulness of the equations an attempt was made to predict the rate constants f o r another reaction. Assuming that the solvent e f f e c t s i n the two reactions w i l l be proportional, the changes i n the free ener-gies of a c t i v a t i o n upon changing solvents can be made pro-p o r t i o n a l . Then, assuming that k i s correctly represented by the Eyrlng equation, the constant c can be found as follows: k^ = A exp(- AF A/RT) k^ = A exp(- AF B/RT) (2) RT log & = - A . A . F , * and s i m i l a r l y f o r reaction 2 i n the two solvents A and B, RT log •=? = - A A F 2 (3) then c can be found from Equation 4- using the known values. 23 log k A - log k? °= 1 W ( 4 ) log k| - log kg Instead of using only two solvents as above as many as possible should be used and c determined from the slope of a plot of l o g k^ values versus log kg values. The slope was found using values for the reaction of triethylamine with ethyl iodide i n six solvents, l i s t e d i n the f i r s t part of Table VI, by the method of least squares. The rate constants f o r the Menschutkin reaction are those of 1 ft Ruf, Grimm, and Wolff . c turns out to be approximatelyy 1.1 and the predicted values f o r the rate constants along with measured rate constants and the average deviation are l i s t e d i n Table VI. The values are predicted by taking the rate constants f o r TBF decomposition calculated by Equa-t i o n 10 and using the following equation, which follows from (4). The average deviation of the values calculated lo g k A = c log k^ + (log k B - c log k|) i n t h i s way from the experimental values i s 0.31 for 8 solvents. This work has accomplished two things; f i r s t , the TBF rate constant empirical solvent p o l a r i t y scale has been extended and second, equations which can be used to predict the rate of a polar reaction have been found. There are now available rate constants for i o n i c TBF 24 TABLE VI Calculated Rate Constants f o r the Menschutkin Reaction Solvent log k ™ l o s ^ l o g ^ l o g ^ Fluorobenzene ?1. 52 -3.04 Chlorobenzene -1. 32 -2.86 Bromobenzene -1. 30 -2.80 Iodobenzene -1. 20 -2.57 o-DIchlorobenzene -1. 12 -2.60 rj-Dlchlorobenzene -1. 54 -2.95 Cyclohexane -2. 68 -2.62 -4 .26 -5.00 Toluene -1. 75 -1.79 -3 .36 -3.60 Benzene -1. 68 -1.94 -3 .52 -3.40 Nitrobenzene -0. 62 -0.32 -1 .72 -1.86 p_-Xylene -1. 86 -1.94 -3 .54 -4.10 m-Dlchlorobenzene -1. 17 -1.32 -2 .83 -3.16 Phenetole -1.54 -3 .08 -2.93 Benzonltrile -0.31 -1 .72 -1.95 Average Deviation 0.31 25 decomposition i n 34 non-hydroxylic solvents. I believe these rate constants should provide a better means of corre-l a t i n g rate data f o r polar reactions than systems based on solvatochromism, simply because the substrates are more si m i l a r . The equations allow the system to be extended to hydrox-y l i c solvents and i n fac t to any solvent whatsoever. Never-theless, t h i s treatment i s only empirical and w i l l hopefully be made unnecessary along with the others when the theory of the l i q u i d state has advanced s u f f i c i e n t l y . 26 EXPERIMENTAL A. Synthesis of t-Butylperoxyformate Two d i f f e r e n t methods were used, one by Pincock^ and one by Ruchardt^ . The method of Pincock involves f i r s t making formic acetic anhydride which i s then reacted with t-butylhydroperoxide. Ruchardt's preparation involves just the reaction of formic a c i d with t-butylhydroperoxide. 1) t-Butylhydroperoxide Lucidol t-butylhydroperoxide (500 ml) was d i s t i l l e d under vacuum i n an azeotrope d i s t i l l a t i o n aparatus u n t i l the d i s t i l l a t e no longer separated into two phases. Three f r a c t i o n s were then c o l l e c t e d a f t e r discarding the material which d i s t i l l e d below 39° at 22 mm. The f i r s t f r a c t i o n of about 50 ml b o i l e d at 39°-40° at 22 mm, the second of about 100 ml at 40° at 22 mm and the t h i r d of about 100 ml at 40-41° at 22 mm. * 9 2) Formic acetic anhydride Commercial formic acid, 100 ml of 9&%, was treated with a stream of ketene gas passed through a trap held at 0° f o r four hours. The ketene was generated by passing acetone over red-hot wires. The reaction mixture was then d i s t i l l e d under vacuum and three f r a c t i o n s collected; the fi r s t ' s 70 g., b o i l i n g at 25-34° from 80 to 20 mm, the second b o i l i n g at 34-38° at 20 mm, 67.7 g and a small t h i r d f r a c t i o n b o i l i n g 27 at 38-40°C at 20 mm. 3) t-Butylperoxyformate^ To 30 g of formic acetic anhydride i n 100 ml of l i g h t pet. ether was added a solution of 20 g t-butylhydroperoxide over about one hour at 0° with vigorous s t i r r i n g . The reaction mixture was held at 0° with s t i r r i n g f or 18 hours. A f t e r 18 hours the mixture had only one phase; i t was then washed with 150 ml of water i n 10 ml portions, dried over anhydrous magnesium sulfate and the solvent evaporated. The remaining l i q u i d was d i s t i l l e d under vacuum using shields and keeping the pot temperature below 55°. Three fractions were c o l l e c t e d a l l of which had good i n f r a r e d spectra com-pared to an authentic spectrum. The f i r s t f r a c t i o n , 4.6 g, was co l l e c t e d at 23-36° at 20 mm; the second from 36° at 20 mm to 30° at 10 mm; and the t h i r d at 34° at 20 mm., 21 4) t-Butylperoxyformate t-butylhydroperoxide, 30 g, and 30 g 98% commercial formic acid i n 200 ml I t . pet. ether were s t i r r e d at 50° overnight i n an apparatus for continuous extraction of water. A f t e r 24 hours there was only one phase, which was then washed about 30 times with water, dried over anhydrous magnesium sulfate and the solvent evaporated. The remain-ing l i q u i d was d i s t i l l e d under vacuum and two f r a c t i o n s , both having good Infrared spectra, were c o l l e c t e d . Both 28 b o i l e d at 41 at 22 mm, each was about 5 ml. B. Pyridine and Quinone Pyridine was used as the base i n a l l the runs. Eastman White Label grade was d i s t i l l e d from barium oxide and sodium hydroxide at atmospheric pressure, b.p. 1 1 5 ° . Quinone, used as a r a d i c a l i n h i b i t o r , was p u r i f i e d by sublimation. C. P u r i f i c a t i o n of Solvents 1) Fluorobenzene Eastman White Label grade was used without further p u r i f i c a t i o n . 2) Chlorobenzene Eastman White Label grade was washed with concentrated s u l f u r i c a cid, then with water and dried over calcium chloride. The solvent was then d i s t i l l e d through a two foot o Vlgreux column, b.p. 132 . 3) Bromobenzene P r a c t i c a l grade material was d i s t i l l e d f i r s t from phosphorous pentoxide then from anhydrous potassium car-bonate, b.p. 1 5 5 - 1 5 6 ° . 4) Iodobenzene Eastman White Label grade was washed with aqueous sodium t h i o s u l f a t e , dried over calcium chloride and then over phosphorous pentoxide, and f i n a l l y d i s t i l l e d under vacuum, b.p. 5 0 ° at 4 mm. 29 5 ) trans-Dlohloroethylene Eastman P r a c t i c a l grade was d i s t i l l e d at atmospheric pressure, b.p. 48°. Gas-liquid chromatography showed that t h i s trans isomer contained about 8% c i s isomer. 6) cls-Dlchloroethylene Eastman White Label grade was d i s t i l l e d at atmospheric pressure, b.p. 60°. Gas-liquid chromatography showed that t h i s solvent contained about 3% trans Isomer. 7) 1,2-Dlchloroethane Eastman Spectrograde material was used without further p u r i f i c a t i o n . 8) Tetrachloroethylene Eastman Spectrograde material was used without further p u r i f i c a t i o n . 9) 1,1,1-Trichloroethylene Eastman Technical grade was shaken with concentrated hydrochloric acid, then with 10$ potassium carbonate solu-t i o n and f i n a l l y with saturated sodium chloride solution. The solvent was then dried over anhydrous magnesium sulfate and d i s t i l l e d , b.p. 74-75°. 10) Trichloroethylene Eastman White Label grade was d i s t i l l e d at atmospheric pressure and the f r a c t i o n b o i l i n g at 85.7° at 751 mm col l e c t e d . 11) o-Dichlorobenzene Eastman White Label grade was d i s t i l l e d at atmospheric 30 _ o pressure, b.p. 180 . 12) m-Diehlorobenzene P r a c t i c a l grade was washed with 10$ sodium hydroxide and then with water u n t i l the washings were no longer basic. The solvent was then dried over anhydrous magnesium sulfate o and d i s t i l l e d at atmospheric pressure, b.p. 173 . 13) p_-DlchloPobenzene Chemically pure material was used without further p u r i f i c a t i o n , m.p. 55°. 14) Tetrachloroethane Eastman White Label grade was washed with concentrated s u l f u r i c a c i d once, then with water u n t i l the washings were no longer a c i d i c . The solvent was then dried over anhydrous magnesium sulfate and d i s t i l l e d at atmospheric pressure, b.p. 146°. I>. K i n e t i c Procedure 9 The method was similar to that of Pincock . A small amount of a mixture of TBF and pyridine i n the solvent under study was made up and s p e c i a l l y prepared test tubes having a c o n s t r i c t i o n were f i l l e d with one to two mis of the mixture. The tubes were then sealed and lowered into the o i l bath In a special sample holder. The samples were withdrawn a f t e r varying times and quenched i n an ice bath. Since p_-dichlorobenzene i s a s o l i d at!room temperature a special technique was necessary. A weighed amount of 31 pyridine was dissolved i n a known amount of solvent and t h i s o mixture was held at 90. i n a small f l a s k . A f t e r adding an appropriate amount of TBF, 1 ml aliquots were withdrawn with pipettes previously heated to 110° and discharged into 2 ml portions of benzene. These p_-dichlorobenzene-benzene mixtures were then analyzed lnthe usual manner. Analysis of the samples was c a r r i e d out by measurement of the l o s s of carbonyl absorption at 1760 cm"*1 on an I n f r a -cord spectrophotometer. Before making any measurements of samples the machine was set to read zero absorbance with pure solvent i n both beams and i n f i n i t y with the sample beam completely blocked. The r e l a t i v e concentration at time t was calculated by the equation, P Ago - A Plots of log —2 versus time were straight l i n e s and the P decomposition was usually followed to about 75$. Second order rate constants were obtained by d i v i d i n g the slope by the concentration of pyridine used i n the run and mu l t i -plying by 2.303. The best straight l i n e was f i t t e d v i s u a l l y to the points with due note taken that a constant error i n the extent of reaction, A, becomes an increasing error i n log (Aa - A ). 32 Streltwieser, Van Sickle and Langworthy state, "A careful analysis shows that t h i s procedure i s c l e a r l y superior to the usual l e a s t squares method." 33 LITERATURE CITED 1. Kirkwood, J. G., J. Chem. Phys., 2, 351 (1934) 2. Kosower, E., J. Am. Chem. S o c , 80, 3253 (1957) 3. Smith, S. G., Fainberg, A. H. and Winstein, S., i b i d , 8_3_, 618 (1961) 4. Berson, J. A., Hamlet, Z., and Mueller, W., i b i d , 84,, 297 (1962) 5. Grunwald, E. and Winstein, S., Ibid, 7.0, 846 (1948) 6. Wiberg, K. B., Physical Organic Chemistry, John Wiley and Sons Inc., New York, 1964, p. 420 7. Winstein, S., Grunwald, E. and Jones, H., J. Am. Chem. S o c , 73, 2700 (1951) 8. L a i d l e r , K. J., Solvation Phenomena, 1_, 2 (1963) Report of Symposium held by Chemical Institute of Canada (P. J. Krueger, ed. ) 9. Pincock, R. E., J. Am. Chem. S o c , 86, 1820 (1964) 10. Walling, C:., "Free Radicals i n Solution", John Wiley and Sons Inc., New York, 1957, p. 590 11. Weiesberger, A., ed., Organic Solvents, Intersclence Publishers, Inc., New York, 2 n d ed., 1955 12. Handbook of Chemistry and Physics, Chemical Rubber Publishing Co., Cleveland, Ohio, 3 4 t h ed. (1952-53) 13. Wiberg, K. B., l o c c i t . , p. 385 14. Glasstone, S., Textbook of Physical Chemistry, D. Van Nostrand Co., Princeton, New Jersey, 1946, p . 537 15. L a i d l e r , K. J., l o c . c i t . , p. 1 16. Glasstone, S., l o c c i t . , pp. 479-480 17. Glasstone, S., i b i d , p. 502 18. , Grimm, H. G., Ruf, Hi. and Wolff, H., Z. physik. Chem., 13B, 301 (1931) 34 19. Smythe, C. P., D i e l e c t r i c Behavior and Structure, Mc&raw-Hlll Book Co. Inc., New York, 1955 20. Menschutkin, N., Z. physik. Chem., 4, 41 (1890) 21. Rtichardt, C., Private communication 22. Streitwieser, A., Van Sic k l e , D. E. and Langworthy, ¥. Ci., J. Am. Chem. S o c , 84, 244 (1962) 23. Dimroth, E . , Reichardt, C , Slepmann, Ti and Bohi-mann, Fxi, Liebigs Ann. Chem., 661, 1 (19 63) 24. Reichardt, C:., Ang. Chem. internat. E d i t . , 4^ 29 (1965) 35 APPENDIX A. Regression Analysis The l og of the rate constant y i n a solvent j can. "be expressed as a l i n e a r combination of regression c o e f f i c i e n t s , b, , and solvent parameters, x., plus an error, £ . £• = (yj - 1L few,)1 7 T e J = Z ( v - - f b l x - l - ) 1 In order to minimize the error, the derivative of with respect to the regression c o e f f i c i e n t s i s set to zero. - 51 X-^ yj - 1L b-, 51 xTj £xv,yj =- Z t>i II Xtj The l a s t equation y i e l d s a set of l i n e a r equations i n b^ which can be solved for the regression c o e f f i c i e n t s which minimize the error. A s t a t i s t i c a l quantity c a l l e d the 11F r a t i o " and defined as ^ - ^ r ] 1 w a s also computed. If the Fr r a t i o of a regres-sion c o e f f i c i e n t i s l e s s than unity then the variable 36 associated with that c o e f f i c i e n t i s not related, according to t h i s method of c a l c u l a t i o n , to the log k. L i t t l e use of' F r a t i o s was made i n choosing varia b l e s . B. Computing A program from the University of B r i t i s h Columbia Computing Center l i b r a r y was used to calculate the regres-sion c o e f f i c i e n t s and F~- r a t i o s . A program was written for r e l computing the l o g k presented i n Table V. A l l computing was done on an IBM"7040 computer. 

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