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The thermal decomposition of cyclobutane at low pressures Ogawa, Rosalind 1962

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THE THERMAL DECOMPOSITION OF CYCLOBUTANE AT LOW PRESSURES by ROSALIND OGAWA B.Sc.The University of Exeter,I960 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September,1962 In presenting this thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of C k W * ^ The University of British Columbia, Vancouver 3, Canada. Date ABSTRACT The thermal decomposition of cyclobutane i s a homogeneous,unimolecular reaction;ethylene being the only product.The rate law :-k = l O 1 5 ' 5 e - 6 l ' 7 0 ° / R T sec." 1 was found to he obeyed i n the pressure region 10 to 40 mm. and temperature range 398" to 450 C. Cyclobutane undergoes a wall reaction to form propylene and 1-butene. The high pressure rate constant f a l l s o f f at low pressures and reaches a l i m i t i n g low pressure rate when activation i s maintained by c o l l i s i o n with the walls of the reactor.The low pressure l i m i t i n g rate decreases as the size of the reactor increases. The f a l l o f f curves gave best agreement with values of the Slater parameter,n,between 5 and 8,and values of the Kassel parameter,s,between 3 and 7. It was concluded that the ring vibrations are of major importance i n the dissociation,and that the C—H bond vibrations are r e l a t i v e l y unimportant. No evidence for a tetramethylene b i r a d i c a l intermediate was found.The reaction mechanism probably involves the simultaneous s p l i t t i n g of two opposite G—C bonds. i i i ACKNOWLEDGEMENT I wish to express my gratitude to Dr.Butler for his advice and encouragement during the course of this work. i v TABLE OF CONTENTS page INTRODUCTION 1 1. Previous work 1 2. This work 3 EXPERIMENTAL 4 1. Materials 4 2. Furnace,and temperature measurement 7 3. Pressure measurement 10 4. Sampling 11 5. Analysis 12 RESULTS 15 1. Calculation of results 15 2. High pressure results 17 3. Lower pressure results 20 DISCUSSION ° 30 1. Unimolecular reaction theories 30 a. The Lindemann-Hinshelwood Mechanism 30 b. The Kassel theory 33 c. The Slater theory 35 d. Comparison of the Kassel and Slater f a l l o f f parameters;.-38 2. The pre-exponential factor 40 3. Minor products 43 4. The low pressure l i m i t i n g rate,k^ 46 5. Comparison of the theoretical and experimental f a l l o f f curves 48 V TABLE OF CONTENTS (continued) page 6. Related reactionist 56 7. Mechanism of the decomposition of cyclobutane 61 BIBLIOGRAPHY 69 LIST OF TABLES page TABLE I High pressure data obtained i n the 100 ml. reactor 18 TABLE II Low pressure data obtained i n the o n e - l i t r e reactor 23 TABLE I I I Low pressure data obtained i n the 100 ml. reactor 25 TABLE IV Low pressure data obtained i n the f i v e - l i t r e reactor 27 TABLE V Data from ethylene pyrolyses i n the o n e - l i t r e reactor 29 TABLE VI Experimental values of n and s 50 TABLE VII The thermal decomposition of cyclobutane derivatives 58 TABLE VIIIExperimental values of n and s for a number of compounds 62 v i i LIST OF FIGURES page FIG.I The apparatus 8 FIG.II The temperature dependence of the high pressure r a t e constant 19 F I G . I l l k " 1 vs. p " 1 ^ 2 51 FIG.IV F a l l o f f p l o t ^ o g k / k ^ vs. l o g p mm.,in the o n e - l i t r e r e a c t o r 53 FIG! V" F a l l o f f p l o t , l o g k/kgp vs. l o g p mm. , i n the 100 ml. r e a c t o r 54 FIG.VI F a l l o f f p l o t , l o g k/k vs. l o g p mm.,in the CO f i v e - l i t r e r e a c t o r 55 FIG.VII The s i x normal modes of v i b r a t i o n of the cyclobutane r i n g 64 INTRODUCTION 1.Previous work. The thermal decomposition of cyclobutane i s a homogeneous, unimolecular reaction;ethylene being the only product.The f i r s t order rate constant f a l l s o f f at low pressures,as expected for a unimolecular reaction.The low pressure rate constant can be restored to i t s high pressure value by the addition of an inert gas. Genaux and Walters 1 studied the decomposition i n the temperature range 430° to 480°C.and at i n i t i a l pressures from about 30 to 400 mm.They carried out the reaction i n several packed and unpacked Pyrex vessels,with various surface treat-ments, and observed no difference i n rate.They concluded the reaction to be f i r s t order and homogeneous. Kern and Walters^ studied the reaction at 449°C.and at i n i t i a l pressures from 0.2 to 80 mm.They observed a f a l l o f f i n rate constant with decreasing pressure;the rate constant at 0.2 mm.being approximately h a l f that at 80 mm.They concluded that the reaction did not involve a free rad i c a l chain mechanism as i t was not inhibited by the addition of radical scavengers such as n i t r i c oxide,toluene or propylene. Genaux,Kern and Walters-^ studied the decomposition over the temperature range 420° to 468°C. with i n i t i a l pressures from 1 to 99b mm.They found the rate law k = 4 . 0 x 1 0 ^ e" 6 2 ' 5 0 ° / E 1 s e c . " 1 to be obeyed down to about 20 mm.pressure.Below this the rate decreased with decreasing pressure.The rate constant at low pressures was raised by the addition of hydrogen,ethylene or ethane.Additional evidence for the absence of free radicals was provided by the fact that cyclobutane had no effect on the rate of decomposition of formaldehyde or the rate of polymerization of ethylene;two reactions which are known to be accelerated by the presence of free ra d i c a l s . 4 Pritchard,Sowden and Trotman-Dickenson studied the decrease i n rate constant over the pressure range 100 to 0.057mm at temperatures between 448.2° and 448.6°C.They obtained a lower value for the l i m i t i n g high pressure rate constantjk^, than Genaux,Kern and Walters;3.9 x 10~^sec. - 1 compared to 4.86 x 10"^ sec." 1,at 449°C.They also measured the e f f i c i e n c y of various gases i n maintaining the high pressure decomposition rat There i s considerable disagreement i n the values of n,the effective number of normal vibration modes that contribute to extension of the reaction coordinate i n Slater's theory,and s, the effective number of o s c i l l a t o r s contributing to dissociation xji Kassel's theory,that have been reported for cyclobutane . Rabinovitch and Michel 5 give a value of n t = 20, (which i s equivalent to s = 20);whereas Powell^ gives a value of s , = 5 (which i s equivalent to n = 8).Both values are based on the 3 experimental data of Walters and his coworkers,and of Pritchard, Sowden and Trotman-Dickenson. 2.This work. The main purpose of this work was to obtain a more accurate estimate of the values of n and s for cyclobutane.By observing the rate constants down to lower pressures than had been previously reported,it was hoped to obtain a more accurate idea of the shape of the f a l l o ff curve and hence to reduce the uncertainty i n the comparison of the experimental curves with the tneoretical curves for n and s. No unambiguous evidence for the occurrence of any side reactions i n the decomposition of cyclobutane has been reported. But completely clean unimolecular reactions are rare and i t i s possible that a second unimolecular reaction i s taking place concurrently to form traces of G^,C^ and compounds.This reaction may occur to a very small extent at hign pressures but i t might become more important as the pressure i s lowered. In this experiment the reaction products were analysed on a Golay column using a flame ionization detector.This system i s —13 th e o r e t i c a l l y capable of detecting 10 g./cc.of sample i n the ca r r i e r gas.Therefore i t was hoped to find evidence for or against the occurrence of any side reactions. Genaux,Kern and Walters measured the rate by following the pressure change during the reaction,which i s a more accurate 4 method than gas chromatographic a n a l y s i s , h u t g i v e s no i n d i c a t i o n of minor s i d e reactions.They analysed the products from a few runs at about 120 mm.pressure,on a mass spectrometer and found t r a c e s of p r o p a n e , c o m p o u n d s and C^Hg . Pritchard,Sowden and Trotman-Dickenson^assumed that there were no minor s i d e r e a c t i o n s and measured the r a t e by a b s o r p t i o n o f the ethylene on a mercuric acetate bead. Genaux and W a l t e r s 1 have shown that there i s no s i g n i f i c a n t s u r f a c e e f f e c t on the r e a c t i o n at high p r e s s u r e s . T h i s may not be true at low pressures,however.Therefore i n t h i s experiment the r e a c t i o n was c a r r i e d out i n s e v e r a l r e a c t o r s with d i f f e r e n t surface-to-volume r a t i o s , t o see i f there was any su r f a c e e f f e c t on the r a t e o f the r e a c t i o n o r on the products formed. 5 EXPERIMENTAL 1.Materials. Cyclobutane was prepared by the photolysis of cyclo-pentanone using a 450 watt,medium pressure,mercury arc lamp. The cyclopentanone was supplied by Eastman Organic Chemicals. The main products of the photolysis are carbon monoxide,ethylene 7 and cyclobutane.Blacet and M i l l e r have suggested the mechanism:-CH2CH2CH2CH2CO + CH2CH2C0CH2CH cyclo-C^Hg + CO CH2=CHCH2CH5 + CO CH 2CH 2CH 2CH 2 + CO 2 C 2H 4 + CO polymers The cyclobutane used i n the high pressure experiments was the by-product of an experiment on the photolysis of cyclopentanone by Dr.Butler and Mr.Drake-. It was purefied on cyclo-C^HgCO + h * CH 2Cii2CH2CH2CO CH2CH2C0CH2CH2 X CH 2CH 2CH 2CH 2 + Y C nH 2 n > * Unpublished work. 6 a Beckmann Megachrom Preparative Gas Chromatograph.The purity of the sample was 98.6$.It contained 0.7$ ethylene and 0.7$ of a Cj- compound,probably 2-pentene,together with traces of C^, and compounds. This sample was repurified for use i n the low pressure experiments,using a Perkin Elmer model 154-C Vapor Fractometer, with a four-metre polyethylene gly c o l column,(column R),at room temperature.The purity of the sample obtained was 99.1%,the ethylene impurity being reduced to 0.01$.This sample was used for the f i r s t thirteen runs i n the one- l i t r e reactor.lt was then repurified again,by the same method,and a 99.7$ pure sample obtained.This sample was used for the remainder of the runs i n the one- l i t r e reactor and for the runs i n the 100 ml. reactor. A second sample of cyclobutane was prepared for the low pressure experiments i n the f i v e - l i t r e reactor.Cyclopentanone vapour was photolysed for about half an hour and a l l the products,except for carbon monoxide,were condensed i n a trap cooled with l i q u i d nitrogen.The products collected from about forty photolyses were p u r i f i e d on the Perkin Elmer Vapor Fractometer under the under the same conditions as described above.The sample obtained was 99.9$ pure. Research grade ethylene was kindly donated by Dr.Halpern, who obtained i t from the Matheson Company of Canada Ltd.The ethylene used i n the low pressure pyrolyses was p u r i f i e d on 7 the Perkin Elmer Vapor Fractometer,under the same conditions as above.A 97$ pure sample was obtained,the main impurity being about 3% of benzene.There were no C^,C^ or compounds present. The gases were stored i n two-litre Pyrex vessels,with cold fingers,attached to the vacuum l i n e .(See Figure I on page 8.) Care was taken to exclude any non-condensable impurities when the gases were placed i n the storage vessels. 2.Furnace,and temperature measurement. Three different reaction vessels were used.They were made from spherical Pyrex flasks and were approximately 100 ml.,one-l i t r e and f i v e - l i t r e s i n volume.The reaction vessel was heated i n a furnace consisting of three concentric copper drums of diameters 24,28 and 40 cm., and heights 24,28 and 45 cm., respectively.The wall of the second drum was covered with asbestos paper and wound with nichrome heating wire.The space between the second and the outer drum was packed with vermiculite. The outer drum was wound with copper piping through which cold tap-water circulated.The temperature of the furnace was regulated by means of a variac and voltage regulating transformer.Usually i t did not change by more than 0.6°C. i n a two hour run. When the f i r s t reaction vessel was changed i t was found that the two inner drums were badly corroded.They were then replaced by steel ones. F I G . I T H E A P P A R A T U S 03 9 Ctoromel-alumel thermocouples were used to measure the temperature.They were placed i n wells,made of 8 mm. glass tubing,which projected about 3 cm. into the reactor.Only one thermocouple was used for the 100-ml. reactor.This thermocouple and three others were used for the one- and f i v e - l i t r e reactors. The four thermocouples were arranged tetrahedrally around the reactor.The reference junction was placed i n melting ice,and the e.m.f. was measured using a Leeds and Northrup student-type potentiometer,which gave readings to within 0.2 of a m i l l i v o l t (0.5°C.).The corresponding temperature was found from Leeds and Northrup conversion tables. The four thermocouples were tested o r i g i n a l l y by placing them i n the furnace(without a reactor) and measuring the e.m.f. at different temperatures.All four consist-ently gave the same readings.When the reference junction was interchanged with one of them,it too gave i d e n t i c a l readings. In the case of the one- l i t r e reactor;the two uppermost thermocouples usually read l°C.,(or less),higher ,and the next-to-bottom one read 2°C.,(or less),higher than the bottom one. For the f i v e - l i t r e reactor;the uppermost thermocouple consist-ently read 1°C. higher,and the two middle ones read 3°C.higher than the bottom one.The temperature of the gas i n the vessel was taken to be the average of the four.When the temperature c changed during a run the average temperature was taken. The low pressure runs were carried out at about 4 4 9 ° C , as this was the temperature used by previous workers.At this 10 temperature a suitable decomposition of about 30% could be obtained i n t h i r t y minutes to two hours. The reactors were seasoned before use by leaving a few cm. pressure of ethylene i n them for several days at 449°C.,or higher temperatures. The order in which the experiments were performed was as follows : decompositions at pressures between about 40 and 10 mm. were carried out f i r s t i n the 100 ml. reactor at various temper-atures between 398°C.and 450°C.,so that the energy of activation and the pre-exponential factor could be calculated.Then the one-l i t r e reactor was i n s t a l l e d and decompositions at about 449°C. -3 and i n i t i a l pressures from 1 mm. down to 10 mm. were studied. Afew runs were done using ethylene at low pressures to see if> any decomposition occurred.When the one-litre reactor cracked i t was replaced by a 100 ml. one and a second series of low pressure cyclobutane pyrolyses were carried out.A third series was carried out i n the f i v e - l i t r e reactor,to see i f a decrease i n the surface-to-volume ratio made any fif f e r e n c e to the shape of the f a l l o ff curve. 3.Pressure measurement. Pressure measurements down to 0.6 mm. were made using a wide-bore,mercury manometer.The two arms of the manometer were made of 18 mm. glass tubing and were joined at the base by c a p i l l a r y tubing,to regulate the flow of mercury.Measurements 11 of lower pressures were made on a McLeod gauge.The l e v e l of the mercury meniscus i n both cases was measured using a cathetometer. The t o t a l volume of the bulbs of the McLeod gauge was measured by f i l l i n g them with water from a burette.The volumes of the smaller bulbs were calibrated by comparison with the manometer,in the pressure region where the two overlapped.The diameters of the two c a p i l l a r y tubes used i n the McLeod gauge were measured with the cathetometer. 4.Sampling The glass tubing connecting the reactor to the vacuumline was out of the furnace and therefore the gas i n i t was not at the reaction temperature.This was corrected for at the end of a run by expanding the gas i n the reactor into a dead space of about 30 ml.The reactor tap was then shut and the dead space evacuated.A sample was taken by expanding the gas i n the reactor into a 250 ml. glass sample bulb.The sample was analysed by gas chromatography. The reactor tap was usually held open for about 15 to 20 seconds while sampling the gas at low pressures.At pressures of about a micron,diffusion effects become important.As the molecular weight of ethylene i s half that of cyclobutane i t w i l l diffuse -JIT times faster than cyclobutane.Therefore unless equilibrium i s established i n the time taken to sample the gas, the gas sampled w i l l not be representative of the gas i n the 12 reactor.To check this,several runs were sampled using sampling times of up to ten minutes and larger sampling bulbs of one and two l i t r e s . S e v e r a l samples were also taken by d i l u t i n g the gas i n the reactor with up to 10 mm. of prepurified nitrogen,just p r i o r to sampling.The rate constant was found to be the same for a l l the sampling methods t r i e d . 5.Analysis. Analyses were made on a Perkin Elmer model 154-0410 Flame Ionization Accessory K i t to the model 154-C Vapor Fractometer. The Golay U column,which i s a 150 foot,squalane coated,stainless s t e e l , c a p i l l a r y column of int e r n a l diameter 0.010 inches,was used.The column temperature was maintained at 0°C. by using an ice-bath. The c a r r i e r gas was prepurified nitrogen and was supplied by the Matheson Company of Canada Ltd. The rate of gas flow through a long c a p i l l a r y column i s very low and very small samples must be used to avoid capacitance effects and a large vapour spread at the head of the column.This was effected by s p l i t t i n g the stream of c a r r i e r gas and sample M upstream of the column.The gas flowed past a "0 r e s t r i c t i o n at a c a r r i e r gas pressure of 12 p.s.i.,and only one five-hundredth of the sample passed into the column for analysis. A flame ionization detector was used.Hydrogen at 10 p . s . i . and a i r at 30 p . s . i . were diluted with the c a r r i e r gas from the 13 column and ignited to give a flame about 2 mm. high.The flame jet served as the positive electrode and a platinum wire,set 1 mm. away,as the negative electrode.A potential of two hundred volts was applied between the electrodes.The sample molecules i n the flame underwent thermally induced ionization and produced a current,proportional to the concentration of sample i n the ca r r i e r gas stream.This current was amplified e l e c t r o n i c a l l y and the signal from the amplifier was recorded on a Leeds and Northrup model G Speedomax recorder,adapted for use on a one or a f i v e m i l l i v o l t range.The detector was found to be sensitive to atmospheric conditions;if placed i n a draught i t produced a l o t of background noise,but i f the lab. windows were shut a steady baseline was usually obtained. The usual procedure followed for an analysis was to expand the gas i n the sample bulb into a Toepler pump and then compress i t into a c a p i l l a r y loop.The stream s p l i t t i n g tap was opened and a few seconds l a t e r the c a r r i e r gas was diverted through the loop.After about fo r t y seconds the c a r r i e r gas was rediverted to i t s o r i g i n a l path and after a minute the stream s p l i t t i n g tap was shut,to conserve gas. The low pressure samples were diluted with nitrogen before analysis. Preliminary calibrations were performed with mixtures of cyclobutane and ethylene i n knowm ratios,and at various pressures. The peak heights recorded were found to be i n direct ratio to the 14 p a r t i a l pressures,within experimental error.Calibrations could b.e reproduced to within - 4 $ at higher pressures,but at lower pressures of the order of a micron,the error was about 15%. About six analyses were made on the higher pressure runs, but only two or three were possible for the lower pressure runs. The analyses of the higher pressure samples d i f f e r e d by about 4% and the analyses of the lower pressure samples by about 6%. Few analyses d i f f e r e d by more than 10%.The average value was used m the calculation of the rate constant.The differences i n the analyses were probably due to d i f f i c u l t i e s i n mixing the sample. The system was flushed with nitrogen before each analysis, and a blank analysis was carried out to see i f there were any residual products from a previous analysis remaining i n the system. 15 RESULTS 1.Calculation of the results. The p r i n c i p a l reaction taking place i n the decomposition of cyclobutane i s :-cyclo-C 4H 8 > 2 C 2H 4 (1) Since this i s f i r s t order,the rate of decomposition i s :-4 - 8 - . k [ C J i J (2) dt 4 8 On integrating :-In [ C . H j = - k t + C (3) 4 o If [C.H 0] i s the concentration of cyclobutane when t = 0,then :• 4 8 o ta . . k t (4) C 0 4 H 8 ] o The material balance :• C C 4 V o " [ C 4 H 8 3 + l [ C 2 H 4 ] ( 5 ) w i l l hold at any time. 16 Combining (4) and (5) gives :-1 C C 2 H 4 ] k - t l n ( 1 + ) ( 6 ) The rate constant for reaction (1) was calculated by finding the [C^H^] to [C^Hg] ratio from the recorded peak heights of the analysis,and substituting this and the duration of the run,in seconds,into equation (6). 17 2.High pressure r e s u l t s . The high pressure data i s given i n Table I on page 18, and i s plotted i n Figure II on page 19. The decomposition of cyclobutane i n the pressure range 10 to 40 mm. and temperature range 398° to 450°C.,was found to obey the rate law :-k = l O 1 5 ' 5 ± °'Q e" ( 6 1 ' 7 ° ° ± " 0 0 ) / E T B e c > - 1 This was calculated from the data i n Table I using a least squares method.The l i m i t s of error are given at the 95$ confidence l e v e l . The value i s lower than that reported By Genaux,Kern and 3 Walters , of :-k = l O 1 5 ' 6 0 e" 62>500/R T sec-l This i s probably due to the fact that i n the pressure range 10 to 40 mm.,the rate i s beginning to f a l l below the high pressure l i m i t i n g rate, The concentrations of the impurities i n the s t a r t i n g material did not a l t e r appreciably during a run,and no new compounds were observed i n the products.The 0.7$ ethylene present i n the star t i n g material was corrected for i n the calculation of the rate constant. The rate constant was measured over a range of conversions from 3$ to 81$ and was found to oe independent of conversion, thus establishing that the reaction was t r u l y f i r s t order,(see Table l O . TABLE I. HIGH PRESSURE DATA OBTAINED IN THE 100ml.REACTOR TEMPERATURE TIME $ k x 10 0 „ i n C. i n minutes. conversion i n sec.-450.2 41.5 66 43«0 449.2 33.9 60 45.5 449.0 10.0 22 40.7 448.9 56.2 81 48.5 448.8 29.8 47 35.9 448.8 8.5 24 53.9 438.5 33.6 34 20.6 425.8 190.0 33 9.58 425.2 67.0 33 9.94 422.5 18.0 11 10.1 419.8 30.0 13 7.52 418.8 114.8 33 5.94 416,7 54.4 15 5.00 411.2 60.1 13 3.76 404.0 17.0 3 2.50 401.2 35.0 4 1.87 398.6 758.0 54 1.69 398.6 336.0' 27 1.58 398.6 70.0 8 1.96 398.6 52.0 6 1.99 1 19 FIG.II TEMPERATURE DEPENDENCE OF THE HICH PRESSURE RATE CONSTANT 5.Lower pressure results. The runs at lower pressures were carried out at temperatures within 10° of 449°C. The rate constants were corrected to 449°C using the temperature dependence of the high pressure rate constant. In many of the low pressure pyrolyses in a l l three reactors a and a compound were detected i n the products. Their retention times were compared with the retention times of known C.^  and compounds on the same column,and i t was concluded that they were probably propylene and 1-butene. D o w n _2 to about 10 mm. pressure the amount of these compounds formed was small and the correction to the rate constant on the assumption that they were formed from cyclobutane or from ethylene was negligible.At pressures below this,however,their concentration increased and in some cases the concentration of propylene exceeded that of ethylene. The cyclobutane samples of purity 99.1$ and 99 .7$, contained a compound,probably 2-pentene,as the main impurity.The 99.9$ pure sample contained a compound, probably cis- or trans-2-buteneXJt was a different compound from that formed in the pyrolyses.)The concentration of these impurities decreased during a run,but there was no correlation between their decrease and the amount of propylene or 1-butene that was formed. Several ethylene pyrolyses were carried out under the same conditions as a cyclobutane pyrolysis.The ethylene sample was 97$ pure.The main impurity was about 3$ of benzene,and this did not decompose during a run.It contained no C,,C, or C,-3 4 P compounds.The results are shown i n Table V on page 29-.The and compounds formed had i d e n t i c a l retention times with those formed, i n the cyclobutane pyrolyses,but t h e i r concentration was less than that obtained from cyclobutane under the same conditions.In the f i r s t two pyrolyses several other , and compounds were observed.These were not detected i n cyclobutane pyrolyses. The rate constants for the runs at pressures above about _2 10 mm. were uncorrected for the formation of propylene and 1-butene.Those at lower pressures were corrected on the assump-tion that these compounds were formed by a wall reaction of cyclobutane only.(The formation of propylene and 1-butene i s discussed i n section 3 of the Discus s i on.) I t was assumed thatthe stoichiometry of these reactions was :-3 cyclo-C 4H 8 > 4 C-Rg and cyclo-C^Hg f 1-C^ Hg When the rate constants for these runs were calculated, the f i n a l concentration of cyclobutane was corrected to the value i t would have had i f there had been no wall reaction, 22 i.e.( [cyclo-C 4H 8] + | [C^Hg] + [1-^Hg] ). This lead to the following expression for the rate constant :-[C 2H 4] k = } In ( 1 + ) 2 C[cyclo-C 4H 8] + J[C 3H 6] + [1-C 4H 8]) The low pressure data i s given i n Tables II to V on pages 23 to 26.lt i s plotted i n Figures IV,V and VI, TABLE I I . L0\¥ PRESSURE DATA OBTAINED IN THE ONE-LITRE EE AC TOR PRESSURE TIME TMCPERATURE o % C 2 H 4 C3 H6 G 4 H 8 5 k x 10 5 k xlO 449° x i n sec Z ' i n cm. i n sec i n C. conversion ( D ^ G 3 H 6 + C 4 H 8 )(0+\C H+C H ) (n*%C H+C H ) ' 3 6 4 8 3 6 4 8 i n secT1 -1 1.86x10 i 777 462.2 45 1.65 77.6 35.2 1.26x10 1996 446.4 40 1.31 25.2 29.5 — j . 0.79x10 -2 8.79x10 1060 444.4 24 0.639 26.8 34.5 1430 446.0 23 0.609 18.6 22.3 _g 2.70x10 o 1414 446.2 22 0,.'576 17.9 21.2 8.35x10 1467 446.2 23 0.606 0.002 18.0 21.4 _g 1.48x10 1098 447.5 13 0.306 12.9 14.1 1.37x10 8187 442.7 34 1.04 19.5 28.1 _g 1.17x10 2461 444.2 31 0.905 15.2 20.4 1.00x10 787 447.5 13 0.300 17.8 19.5 —o 9.66x10 964 447.2 11 0.257 12.6 14.1 *~3 6.67x10 1023 446.4 11 0.236 - 10.9 12.8 ~3 5.-19x10 2028 448.8 19 0.482 0.019 0.013 10.6 10.7 4.01x10 2806 445.3 20 0.515 0.009 0.007 8.18 10.3 —3 3.11x10 2305 442.4 18 0.440 0.025 0.014 8.64 12.9 IV) TABLE I I . (continued) PRESSURE TIME TEMPERATURE % C H 2 4 C,H 3 6 4 8 5 k x 10 5 k xlO 449° i n cm. i n sec. i n C. conversion (04%C,H t+C»H«) (0+%G,H*+ 0U i n sec7 H«)(MC*H*C aIL ) in s e c ' -3 1.74x10 -4 1000 448.0 7 0.139 0.045 0.016 6.76 7.26 9.63x10 -4 1052 446.8 6 0.122 5.63 6.45 5.34x10 -4 1041 444.0 6 0.123 0.114 5.69 7.73 1.22x10 -4 3607 445.5 8 0.169 0.105 0.037 2.25 2.78 1.02x10 1894 444.2 4 0.085 0.265 0.066 2.19 2.94 TABLE I I I . LOW PRESSURE DATA OBTAINED IN THE 100 ml. REACTOR PRESSURE TIME TEMPERATURE . i n °C. G 2 H 4 C 4 H 8 5 k x 10 k x : 449° i n cm. in sec conversion i n sec.' ) in sec 4.314 510 448.8 24 0.642 53.9 54.6 3.115 n 600 449.0 22 0.552 40; 7 40.7 — X 9.64x1© 2490 450.2 66 3.83 43.0 40.0 0.75x10 -2 4i12x10 4400 447.3 67 4.07 25.0 27.7 3540 448.5 54 2.38 22.1 22.8 _g 3.06x10 2316 447.2 31 0.910 16.2 18.1 _2 2.30x10 3062 447.7 35 1.09 14.2 15.4 _2 4.71x10 3923 449.2 33 0.983 0.011 0.006 10.2 10.3 - o 2.10x10 2257 447.8 17 0.418 0.054 0,031 8.40 9.04 - 0 1.89x10 —3 4102 441.4 18 0.428 0.035 4.73 7.55 1.64x10 5540 '446.8 35 1.09 7.85 8.98 —3 1.40x10 3520 448.7 21 0.540 0.012 6.79 6.92 _ g 1.2x10 —3 2522 447.0 14 0.319 0.027 0.015 5.87 6.63 1.10x10 _A 5000 448.5 28 0.789 0.016 0.006 6.64 6.89 5.00x10 7217 441.0 23 0.591 0.071 0.030 3.59 5.81 TABLE I I I . (continued) PRESSURE TIME TEMPERATURE fo 2 4 C EL C H 3 6 4 8 kxlO k XlO 449° i n cm. i n sec. in ° C . conversion (D+^C 3H 6 + C ^ ) ( a t J / ^ H ^ I L j ( l H ^ C , H ^ H j ) i n sec i n se^ -4 3.08x10 7244 —4 446.7 30 0.874 0.320 5.00- 5.76 3.03x10 6000 -4 2.2 xlO 6678 / 447.0 23 0.591" 0.199 4.32 S.88 447.0 25 0.664 0.235 4.29 4.85 1.2 XlO 7402 -4. 447.1 21 0.574 - 0.416 3.20 3.59 1.0 x 10 4945 440.5 12 0.278 0.278 2.63 4.44 o 6.5 xlO 6306 _ K 446.8 28 0.553 0.428 3.87 4.43 - U 5.4 xlO 4456 447.2 17 0.402 0.348 4.11 4.59 -I IV) TABLE IV. LOW PRESSURE DATA OBTAINED IN THE FIVE-LITRE REACTOR PRESSURE TIME TEMPERATURE 1o °2 H4 3 6 °4 H8 5 k x 10 k i l i 449° i n cm. i n sec. i n °C. conversion in sec i n se< -1 .1.05x10 c 2434 448.1 51 2.08 29.3 30.9 4.30x10 3600 450.1 62 3.00 25.5 23.9 •~2 1.06x10 4200 449.5 41 1.40 12.6 12.2 —o 7.24x10 4000 449.9 34 1.01 10.2 9.71 —O 2.89x10 4626 448.7 23 0.588 5.57 , 5.68 —C 2.22x10 8455 447.1 38 1.22 0.011 0.003 5.63 6.32 -3 1.43x10 4600 450.2 20 0.491 4.85 4.51 1.41x10 A 3758 448.4 16 0.391 0.087 0.096 0.76 4.97 — i± 6.12x10 —A 4370 442,1 11 0.247 0.010 0.003 2, .'6 5 4.03 3.93x10 5053 449.0 18 0.435 0.080 0.018 3.89 3.89 —*t 3,87x10 -4 2.05x10 8850 449.2 30 0.836 0.024 0.012 3.95 3.89 4974 449.3 14 0.304 2.84 2.79 1.90x10 6300 448.2 15 0.344 0.118 2.56 2.69 TABLE IY. (continued) 5 5 PRESSURE TIME TEMPERATURE % C 2H 4 CgHg C4Hg k x 10 k x 10 i n cm. i n sec. i n °C. conversion i n sec. i n secT -4 1.75x10 A 4973 448.5 14 0.334 0.015 0.007 3.11 3.22 — Hi 1.63x10 8692 449.4 26 0.698 0.153 0 3.45 3.36 — 0 8.99x10 6914 448.2 6 0.122 0,976 0.073 0.858 0.901 —0 8.78x10 4157 449.0 10 0.222 0.048 2.53 2.53 8.38x10 c 6660 448.2 19 9.478 0.133 0.008 3.22 3.38 — D 8.14x10 9880 446.0 21 0.519 0.199 0.046 2.34 2.81 —o 6.5 xlO 4400 449.0 12 0.266 0.266 0.029 2.83 2.83 — 0 5.42x10 3664 450.7 19 0.458 0.167 5.62 5.07 5.07x10 c; 5918 448.2 14 0.322 0.031 2.52 2.65 - D 4.57x10 5650 448.8 22 •0.558 0.279 4.36 4.41 — 0 2.46x10 9650 450.3 27 0.724 0.284 3.20 2.96 — O 1.68x10 5540 449.4 $2 0.267 0.978 2.89 2.92 IV) 00 .29 TABLE V. DATA FROM ETHYLENE PYROLYSES IN THE ONE-LITRE REACTOR PRESSURE i n cm. TIME in sec. TEMPERATURE in°C. $ C 3H 6 5 $ C 4H Q r e l a t i v e to the i n i t i a l concentration of ethylene 4.7 x l O " 2 13,570 449.2 0.059 0.354 4.2 x l O " 2 9,639 444.7 0.048 0.054 1.2 x l O " 2 1,707 446.6 0.095 0.260 1.8 x i o - 5 102,419 449.3 2.54 1.5 x l O " 5 2,831 450.1 0.92 0.44 3-7 x 1 0 - 4 2,403 446.6 1.50 0.81 5.4 x l O " 5 58,810 447.2 0.51 In the 2nd run, i n the above table, Q.019 5 i trans-2-butene, 0.016$ cis-2-butene and 0.14$ of a C^  compound were also observed.In the 3 r d run,0.20$ trans-2-butene and 0.21$ cis- 2 -butene were observed.The f i r s t 3 runs may be compared to a)the 6th run i n Table II.The 4th and 5 t h runs may be compared tob)the 16 th run i n Table II.The 6th run may be compared toc)the 18th run i n Table II.The 7th run may be compared to d)the 21st run i n Table IV. PRESSURE TIME TEMPERATURE $ C H,. $ C H 3 6 4 8 re l a t i v e to the i n i t i a l i n cm. i n sec. i n C. concentration of cyclo-C^a a<) 2.4 x 10*"2 1467 b) 1.7 x 10~ 5 1000 c) 5 . 3 x l O - 4 1041 d) 5 . 4 x 10' ,-5 3664 446.2 448.0 444.0 450.7 0.20 4.2 11.4 16.7 1.5 30 DISCUSSION 1.Unimolecular reaction theories. a.THe Lindemann-Hinshelwood Mechanism. The Lindemann-Hinshelwood mechanism i s the basis of a l l the successful theories of unimolecular reactions. The molecules are assumed to be activated by c o l l i s i o n . I f a molecule were to dissociate the moment i t became activated the rate of the reaction would depend on the c o l l i s i o n rate and hence on the concentration.No f i r s t order kinetics would be observed. Lindemann postulated a time-lag between the activation of a molecule and i t s decomposition.lt i s not assumed that the time-lag w i l l be the same for a l l molecules of the same species under the same conditions.The extent of the time-lag w i l l depend on the vibrations of the molecule.A simple molecule with few vibrations w i l l have a time-lag less than i t s c o l l i s i o n frequency,at normal pressures,and therefore w i l l undergo second order reactions. I f an activated molecule i s polyatomic i t may either be deactivated by a second c o l l i s i o n or i t may dissociate.Both courses are independent and occur at random.If the i?ate of reaction i s k^,then the p r o b a b i l i t y of an activated molecule dissociating i n a short time A t , i s k^t.The pr o b a b i l i t y that i t 31 w i l l suffer a second c o l l i s i o n i s tot,where wis the c o l l i s i o n 8 a frequency .Slater has shown that the absolute p r o b a b i l i t y that an activated molecule w i l l dissociate rather than be deactivated,is given by :-The rate of deactivation at high pressures where an equilibrium exists between the activated molecules and the rest of the molecules, i s c f ,where c i s the concentrationaahd f i s the s t a t i s t i c a l equilibrium p r o b a b i l i t y of the activated state.At high pressures the rate of deactivation i s very much greater than the rate of reaction and hence i t can be equated with the rate of activation.Therefore the number of molecules dissociating i n unit time i s (1) CO + k. c f w k (2) co + k Therefore the rate constant k -ldC C at (3) i s given by :-k (4) to + k 32 At high concentrations, ^ -^>oo,and k approaches the value f k^.Therefore the high pressure rate w i l l he f i r s t order. At low concentrations,^ —} 0,and k tends to the form Therefore the reaction w i l l become second order as the pressure decreases. The assumption that a l l activated molecules react at the same rate k^ leads to a simpler pressure dependence of the rate constant than i s observed experimentally.If it? i s assumed that the higher the energy an activated molecule possesses above the c r i t i c a l value necessary for dissociation,the faster i t w i l l react, then better agreement i s observed with experiment. The general formula (4),can be extended.If k £ At i s the prob a b i l i t y of dissociation of a molecule with energy E i n the short time At,and f„ i s the s t a t i a t i c a l equilibrium probability of the molecules with energy E,then the expression becomes :-k & f uJ k ( 5 ) . U) + k E 33 b . T h e K a s s e l T h e o r y . 9 T h e m o l e c u l e , i n t h e c l a s s i c a l K a s s e l t h e o r y , i s t h o u g h t o f a s a s e t o f o s c i l l a t o r s w h i c h a r e c o u p l e d b y s m a l l f o r c e s , s u c h t h a t e n e r g y c a n f l o w b e t w e e n t h e m . T h e a c t i v a t e d m o l e c u l e w i l l d i s s o c i a t e w h e n s u f f i c i e n t e n e r g y f l o w s i n t o t h e c r i t i c a l o s c i l l a t o r a f f e c t i n g t h e b a n d w h i c h i s t o b r e a k . T h e L i n d e m a n n t i m e - l a g i s i n t e r p r e t e d a s t h e t i m e t a k e n f o r s u f f i c i e n t e n e r g y t o f l o w i n t o t h e c r i t i c a l o s c i l l a t o r . The c h a n c e t h a t a n a c t i v a t e d m o l e c u l e h a s a n e n e r g y E , whic f t i s g r e a t e r t h a n o r e q u a l t o t h e c r i t i c a l e n e r g y E Q , i n a p a r t i c u l a r o s c i l l a t o r , i s t h e c h a n c e t h a t i t w i l l h a v e l e s s t h a n E - E Q i n t h e o t h e r o s c i l l a t o r s . T h i s i s g i v e n b y : -L ( E - E ^ / E ] 8 " 1 (6) w h e r e s i s t h e n u m b e r o f o s c i l l a t o r s a f f e c t i n g t h e d i s s o c i a t i o n , I . e . ( s - 1 ) i s t h e n u m b e r o f o s c i l l a t o r s f r o m w h i c h e n e r g y f l o w s t o t h e c r i t i c a l o s c i l l a t o r . T h e s p e c i f i c r a t e , t h e p r o p o r t i o n o f m o l e c u l e s w i t h e n e r g y E ( g r e a t e r t h a n E Q) t h a t d i s s o c i a t e p e r s e c o n d , i s k E = A (CE - E 0 ] / E ) S - 1 ( 7 ) w h e r e A i s a p r o p o r t i o n a l i t y c o n s t a n t w h i c h c a n b e t h o u g h t o f a s t h e r a t e o f e n e r g y f l o w i n t o t h e c r i t i c a l o s c i l l a t o r . I n p r a c t i c e t h e e x p e r i m e n t a l p r e - e x p o n e n t i a l f a c t o r i s s u b s t i t u t e d . T h e p r o p o r t i o n o f m o l e c u l e s w i t h e n e r g y i n t h e r a n g e E t o 34 E + dE,is given by :-f(E) dE = 1 I^Y'1 e " E / k T dE (8) (s-1) I I kT/ kT Substitution of (7) and (8) i n the general formula (5), and l e t t i n g ^ — ^ 0 0 ,leads to the,high pressure rate constant :-k^ = A / ( E - E 0 ) S _ 1 e - E / k T dE (s-1): (kT) S J to = A e" V k T (9) which i s of the Arrhenius form. The rate at any pressure i s given by :-k = A e- V k T J e"X x 5 - 1 dx (10) (s - 1)1 / 1 + C x/(b+x)] S" 1 A/u where b = E /kT. o' The f a l l o ff of the rate constant with decreasing pressure can be found from (9) and (10) :-• CO k = 1 I X S" 1 e" X dx (11) k ^ (s-1): I 1 + [ x / ( b + x ) ] s _ 1 A/ Although the rate constant cannot be calculated a p r i o r i from Kassel's theory, the theory i s valuable i n that i t enables the parameter s ,to be found from a comparison of the theoretical and experimental f a l l o f f curves.If the number of o s c i l l a t o r s , s , 35 that contribute to dissociation i s known,a reasonable dissociation mechanism,compatible with the structure of the molecule,can generally be found.If there are several possible mechanisms for a reaction,it may help to decide between them. 8 c.The Slater Theory. The molecule,in Slater's theory,is thought of as a set of harmonic o s c i l l a t o r s which are uncoupled so that there can be no transfer of energy between them.This i s the antithesis of Kassel's postulate. The molecular vibrations are described by a suitable series of int e r n a l coordinates,q r,which may be distances or angles i n the molecule,or a combination of the two.The vibrations of the molecule are analysed into normal coordinates Q^,which are related to the int e r n a l coordinates by the l i n e a r t rans f o rmat i on: 1=1 n . , = 2 <* • J £ cos.2TT(^.t +f.) (13) " Y n I V I ' l where £ ^ i s the energy, 14 the frequency of vibration and jf^ the phase of the i th. normal mode.The 06^ a r e termed amplitude factors.Each internal coordinate can therefore he regarded as a superposition of m normal modes.The amplitude factors determine the contribution of each normal mode to a p a r t i c u l a r internal coordinate. Reaction occurs when the reaction coordinate,which may be one of the internal coordinates or a combination of several of them,is extended beyond a c r i t i c a l value,q Q.The reaction coordinate w i l l be affected by a l l the normal modes of vibration of the molecule,but some may make a neg l i g i b l e contribution as the corresponding amplitude factors may be very small.The Slater parameter,n,is the ef f e c t i v e number of normal modes that contribute to extension of the reaction coordinate. The energies of the normal modes are constant between collisions.Reaction occurs when the n normal modes come s u f f i c i e n t l y into phase to cause extension of the reaction coordinate to the c r i t i c a l value q .The Lindemann time-lag i s o the time taken for this to come about. The high pressure rate constant derived from the general formula (5), i s ^oo = 2 J E k E (14) The proportion of molecules with energy i n the range E^ to E^ +dEi i s the i th. mode of vibratio n i s given by :-e - E/kT dE/(kT)* : (15) 1 itx 37 "TV where E = £. i The s p e c i f i c dissociation rate k ( C , . . . . of a molecule with these internal energies,is the chance per second that the reaction coordinate reaches the c r i t i c a l value,q Q.It i s given by: k =1/2 lim [G ( T ) / T ] . (16) where G^ i s the number of zeros of q - q Q i n the time (0,r),q being the reaction coordinate.The factor of 1/2 i s necessary as q can only approach q Q from a value less than q Q. Substituting (15) and (16) i n the general formula (15) gives :-f OO k = 00 (1/2 lim [G ( T ) / T ] ) e " E / k T d ^ (17) (kT) Tl This can be integrated to give a high pressure rate constant of the form:--E /kT k = V e o' (18) where the pre-exponential factor , ^ , i s a weighted mean value of the vibrational frequencies of the molecule.lt can be expressed: I 2 , V. 2 oi l S. cv2 oi (19) where the subscript 0 denotes the reaction coordinate-38 Substitution of (15) and (16) i n the formula for the general rate constant (5),leads to the expression for the rate constant at any pressure :-k = y e - V k I /">-x>/2 e"x dx (20) [(n - l ) / 2 ] ! 1 + x ( ° - l > / 2 e " 1 Jo where © i s a function of the concentration. The pressure dependence of the rate constant can be expressed :-k = 1 [ x ( n - D / 2 e - x d x ( 2 1 ) k ^ ([n-l]/2)I 1 + x ( n - 1 ) / 2 9 ' 1 I f the experimental.activation energy i s known,and i f a detailed spectroscopic study of the molecule has been carried out to enable a vibrational analysis to be made,then i n Slater's theory i t i s possible ±© calculate the rate of reaction at any pressure and the number of normal modes of vibration that contribute to extension of the reaction coordinate. d.Comparison of the Kassel and Slater f a l l off parameters. Schlag,Rabinovitch and Schneider"1"^ have compared the Kassel and Slater f a l l o ff parameters,s and n. The two equations describing the f a l l off behaviour can be written :-Kassel : I ( 9 » ) = k = [ P ( S ) ] T 1 ( - B ~ 1 -~ X -oO dx i+[x/(b+x)] f a _ x e s-1 .,-1 Slater : I ( 9 ) = k = [itn+lJ/gT 1 ( x ( n - 1 ) / 2 e " x dx k - 1 + x ( n - l ) / 2 e - l These are of the same form i f (b+x) i n the Kassel s—1 equation i s replaced by the approximation b,and i f b i s then formally incorporated i n 9 . From calculations i n the upper region k / k o 0 ) 0 . 0 8 , taking b to be 40 ,Schlag,Rabinovitch and Schneider found that to about s = 4 ,the relationship s =(n+l)/2 was valid.Above this s increases more rapidly than n,so that at about s = 18 , n and s are equal. 40 2.The pre-exponential factor. The pre-exponential factor of the Arrhenius equation :-12 14 -1 l i e s i n the range 10 to 10 sec. for most reactions.The pre-exponential factors for the decomposition of cyclobutane and A 15 -1 i t s derivatives are of the order of 10 sec. .(See Table V i i ) According to Slater's theory the pre-exponential factor i s a weighted mean value of a l l the vibrat i o n a l frequencies of the molecule,and hence i t should l i e i n the normal range of vibration 12 14 -1 frequencies of 10 to 10 sec. .If the molecule has certain symmetry properties the theoretical value of the pre-exponential 14 factor may be greater than 10 .For example i n the case of 8b cyclopropane,Slater took as the reaction coordinate a diminution of the distance of a hydrogen from a non-adjacent carbon,and calculated the mean frequency for a single coordinate 1 3 - 1 to be 3.33 x 10 sec. .Because of i t s symmetry,cyclopropane has twelve equivalent reaction coordinates.The pre-exponential factor i s therefore twelve times the mean frequency for a single linate:4 -1 (11) coord ed.0 x l O 1 ^ sec. ''".The experimental value i s 15 x l O 1 ^ sec. I f the same reaction coordinate were taken for cyclobutane the pre-exponential factor would be sixteen times the mean frequency for a single coordinate ,and a value of the pre-exponent-i a l factor which would be i n reasonable agreement with experiment 41 12 could be calculated.But Srinivasan and Kellner have shown that no hydrogen migration occurs i n the decomposition of cyclobutane,so that a reaction coordinate involving a hydrogen i s improbable.Other feasible reaction coordinates,such as the extension of a C—C bond or the increase i n a C-C-H angle,can only lead to pre-exponential factors four or eight times the mean frequency for a single coordinate.The calculated value w i l l therefore be lower than the experimental one. 13 Thiele and Wilson ' have extended Slater's unimolecular • irate expression for high pressures to include the case where reaction occurs when two reaction coordinates exceed a c r i t i c a l value simultaneously.They calculate the gre-exponential factor to be given by an energy-weighted average of the two Slater frequencies for the individual reaction coordinates.This does not lead,however,to any increase i n the value of the theoretical pre-exponential factor,which i s s t i l l considerably less than experimental value. S t e e l 1 ^ has proposed a formula for the rate of a reaction at high pressure where the c r i t i c a l enrgy needed for reaction i s present i n z of the s o s c i l l a t o r s . l t can be based on the Kassel or the Slater viewpoint as i t i s immaterial whether the o s c i l l a t o r s are coupled or uncoupled.If z i s 2,as i s possible for cyclobutane,the expression reduces to :-K>= X- C ( V k T) + 1] e - E 0 A T 42 Where,A i s the frequency of reaction of molecules which contain the c r i t i c a l energy l o c a l i z e d within the z c r i t i c a l o s c i l l a t o r s . I t i s of the order of 1 0 1 2 to 1 0 1 4 . For cyclobutane the factor ([E /kT]+ 1}' i s 45.However for the two c r i t i c a l coordinates to rupture simultaneously they must be i n phase.Steel estimates the prob a b i l i t y of t h i s to be about 25$.Therefore the factor for cyclobutane w i l l reduce to about 11. This could lead to a value for the pre-exponential factor i n \ 14 agreement with experiment i f A were of the order of 10 The pre-exponential factor i n the t r a n s i t i o n state theory can be expressed :-A = K e k T e A S * / R h where K i s a transmission coefficient and A s i s the entropy of activation.An abnormally high pre-exponential factor can thus be interpreted as resulting from an increase i n the entropy of the molecule on going to the tr a n s i t i o n state.For cyclobutane th i s would lead to an entropy of activation of about 9 e.u.at 449°C. (assuming a transmission coefficient of un i t y ) . Walters et a l . have calculated the entropy • change i n the reaction at 700°K to be 45 e.u.Therefore the t r a n s i t i o n state W i l l be much closer to cyclobutane i n structure than to ethylene. A reasonable structure for the t r a n s i t i o n state i s one i n which two opposite C—C bonds are lengthened s l i g h t l y and the other 4 3 two are shortened and have a p a r t i a l double bond character. CH- •CH, <?2 CH, CH. CH, CH, -CH, CH- CH^ CH. CH, 3.Minor Products. In many of the lower pressure pyrolyses of cyclobutane a 0^ and a compound were detected i n the reaction products. Their retention times corresponded with those of propylene and 1- butene.Their rate of formation compared to that of ethylene increased as the pressure was lowered. These compounds could have been formed by a second unimolecular reaction of cyclobutane,or by a wall reaction of either cyclobutane or ethylene,or from a reaction of the impuri-t i e s i n the s t a r t i n g material. The l a s t p o s s i b i l i t y can be rejected,The main impurities were less than 0.1$ of a compound,probably cis© or trans-2- butene,in the 99.9$ pure sample and about 0.7$ and 0.3$ of a C^ compound,probably 2-pentene,in the 99.1$ and 99.7$ pure samples,respectively.Butenes and pentenes decompose by a radical mechanism and therefore more than two products would be expected i f the decomposition of the impurities were important.In addition,different compounds would be expected 44 from the reactions of different impurities.The concentrations of the impurities did decrease s l i g h t l y during a rum but there was no correlation between the i r decrease and the amount of propylene or 1-butene formed.Certainly the reactions of the impurities could not explain the greater formation of these compounds with decreasing pressure. One of the objects of this work was to fi n d evidence for or against the occurrence of a second unimolecular reaction of cyclobutane.If this second reaction had a value of n ,the Slater f a l l o f f parameter,less than that for the main reaction,then the greater r e l a t i v e concentrations of propylene and 1-butene at lower'pressures cannot be accounted f o r . I f i t had a value of n greater than that for the main reaction i t s high pressure l i m i t i n g rate would start to f a l l o f f at lower pressures than that of the main reaction.If the reactions were occurring concurrently the second reaction could become more important as the pressure was lowered.This situation can^-be pictured :-I 7 loj p 45 The formation of propylene and 1-butene became important at _2 about 10 mm.pressure.If they were formed by a second unimolecular reaction of cyclobutane then the point i n the diagram at which the two curves cross would occur at about 10 mm.pressure.The experimental rate constants at this pressure are i n the region —5 —1 5 to 9 x 10 sec. (depending on the size of the reactor). Therefore a minimum value for the l i m i t i n g high pressure rate -5 -1 constant of the second reaction i s 5 x 10 sec. This value i s only ten times less than the l i m i t i n g high pressure rate constant f o r the main reaction.Therefore about 10$ of propylene and 1-butene would be expected at high pressures.Actually 4 l e s s than f i v e parts i n 10 of these compounds were observed at pressures greater than a millimetre.A second unimolecular reaction i s therefore very improbable. Thus the formation of propylene and 1-butene must be due to a wall reaction of cyclobutane or ethylene.Both propylene and 1-butene were formed i n the p^yrolysis of ethylene, but the amount formed was less than that formed from cyclobutane under the same conditions.For example 1 . 5 $ of propylene,relative to the i n i t i a l concentration of ethylene,was formed i n the _3 one l i t r e reactor at 3.7 x 10 mm. pressure and a temperature of 446.6°C.,in 2403 seconds.Whereas 11.4$,relative to the i n i t i a l concentration of cyclobutane,was formed i n the same reactor at — 3 o 5.3 x 10 nam. pressure and 444.0 C. i n 1041 seconds.In addition several other compounds were observed i n a few of the ethylene 46 pyrolyses that were not detected, i n cyclobutane pyrolyses. It was concluded that the propylene and 1-butene were formed mainly from a wall reaction of cyclobutane,but possibly with a minor contribution from a wall reaction of ethylene. When the rate constants were corrected on the assumption that propylene and 1-butene were formed from cyclobutane only the f a l l off curve was found to l e v e l out at about 10 "mm.pressure and the points lay reasonably on the curve.If they were corrected on the basis of a wall reaction of ethylene the curve started to r i s e again at pressures below about 10 mm. and there was considerable scatter of the points. 4.The low pressure l i m i t i n g rate,k Q. The low pressure data i s plotted i n Figs.17,V and VI. The three curves f a l l below the high pressure l i m i t i n g l e v e l as the pressure i s decreased and then start to l e v e l out again —1 2 at about 10 to 10 mm. pressure.The curves plotted from the data obtained i n the 100 ml. and f i v e - l i t r e reactors l e v e l out completely at about 10-^mm. to give low pressure l i m i t i n g rate constants,k , of 4.6 x l O ^ s e c . - 1 and 2.9 (-)0 .3) x l O ^ s e c . - 1 o respectively .No data below 10 mm.pressure was obtained for the one-l i t r e reactor,so no value of k Q was obtained.lt could be estimated from the way i n which the curve started to l e v e l out iff that the value of k would he between the values obtained o for the other two reactors. It seems reasonable that the f a l l o f f curve w i l l start to l e v e l out when the mean free path of a cyclobutane molecule approaches the same order of magnitude as the dimensions of the reactor.When the molecules are being activated by c o l l i s i o n with the'-walls of the reactor rather than with each other the rate of reaction w i l l be independent of pressure and the curve w i l l l e v e l out completely.The mean free path of a cyclobutane molecule w i l l be about the diameter of the 100 ml. reactor at 10 mm. pressure.At this pressure a cyclobutane i n an i n f i n i t e reactor would undergo about a hundred c o l l i s i o n s per second.The experimental curve for the 100 ml. reactor l e v e l l e d out at a pressure corresponding to a c o l l i s i o n rate 4 -1 of about 10 sec. I f the size of the reactor i s increased the value of k o should decrease.The decrease might be expected to be i n the ratio of the surface-to-volume ratios of the reactors.The r e l a t i v e surface-to-volume ratios of the 100 ml.,the on e - l i t r e and the f i v e - l i t r e reactors were about 1.00 : 0.47 : 0.28 (to within 15$).The ratio .of k Q for the 100 ml. and f i v e - l i t r e reactors was 1.0 : 0.61 ,or a minimum value of 1.0 : 0.54,which i s half that expected. 48 5.Comparison of the theoretical and experimental f a l l o f f curves. In the Kassel theory the parameter affect i n g the shape of the f a l l off curve i s s,the number of o s c i l l a t o r s that contribute to dissociation.In the Slater theory the parameter i s n,the number of normal vibration modes that contribute to extension of the reaction coordinate. Schlag,Rabinovitch and Schneider 1 0 have evaluated Kassel's integral for a range of values of n and ©. An attempt was made to f i t the Kassel curves for s = 3,7,11, 15,21 and 26, and the Slater curves for n = 3 up to 16,to the experimental f a l l o f f curves.The value of b,(EQ/RT),was taken to be 44,which corresponds to 442°C.Ihe values of k^/k^obtained from the experimental f a l l off curves were added to the values of Ig(©') and In(®:) to correct for the activation of the molecules b y coll-ision with the walls of the reactor.Plots of log[I n(9)+kyk a o] versus log (0),and log[I s(&') + k^/k^] versus log were drawn' s - l -x , x e • dx 1 + [x /Cb+x)] 8 -^©')" 1 for a range of values of s,©' and b. 8c Slater has evaluated his i n t e g r a l 49 for the values of n and s given above,on the same scale as the experimental plots of log k/k^ versus log p.The theoretical curves were superposed on the experimental ones and the values of n and s that gave best agreement were found.The results are shown i n Table VI. The f i t of the theoretical curve i s very sensitive to the value of k^.The best method of obtaining k ^ i s by extrapolation of the curve k""^ " versus p - " ^ 2 ^ . U n f o r t u n a t e l y not many points i n the pressure region of 1 to 3.0 mm. were taken and this made accurate extrapolation d i f f i c u l t .The plots of k _ 1 versus p - 1 / / ^ are shown i n Fig.III.By extrapolation of these plots to i n f i n i t e pressure and comparison with the data of Genaux,Kern and Walters, and of Pritchard,Sowden and Trotman-Dickenson a value of 4.6 x 1 0 - 4 s e e . - 1 was taken for k M f o r the experiments i n the -4 -1 100 ml. and one-litre reactors.A value of k^, = 4 .9 x 10 sec. was chosen for the runs i n the f i v e ^ l i t r e reactor,because the temperature may have been closer to 450°C. Genaux,Kern and Walters obtained a value for koo of 4.86 x 10~" 4sec. _ 1 and Pritchard,Sowden and Trotman-Dickenson -4 -1 obtained a value of 3 . 9 x 10 sec. The best f i t with the Kassel curves was obtained with values of s of 7,7 or 3,and 3 for the o.ne-litre,the 100ml. and the f i v e - l i t r e reactors respectively. Kern and Walters used a c y l i n d r i c a l reactor of volume 50 TABLE VI. EXPERIMENTAL VALUES OF n AND a. REFERENCE REACTOR s 0'/pmm n e/P, This work 100 ml. 7 or 3 5 x 10 8 200 or 5 x 10~ 5 o n e - l i t r e 7 4 x 10" 6 8 250 f i v e - l i t r e 3 5 x 10"" 5 5 10 Kern amid 490 ml. 7 1 x 10~ 5 9 1000 2 Walters Pritchard, two-litre 7 or 3 1 x 1 0 _ o 9 1400 _3 Sowden and or 8 x 10 Trotman -4 Dickenson 52 490 ml.Their f a l l off curve was closest i n shape to the one obtained i n the 100 ml.reactor and gave the best f i t with s = 7. Pritchard,Sowden and Trotman-Dickenson used a two-litre reactor.Their f a l l off curve l a y i n between that obtained i n the o n e - l i t r e reactor and that obtained i n the f i v e - l i t r e reactor. I t corresponded with s = 7 and s = 3. Powell states states that the data of Pritchard,Sowden and Trotman-Dickenson and that of Walters and co-workers matches the curve for s = 5,which i s consistent with the above. It seems therefore that the value of s l i e s between 3 and7; .a larger value being u n l i k e l y . With the Slater curves,the best f i t was obtained using values of n of 8 for the 100 ml. and the one-litre reactors and 5 for the f i v e - l i t r e reactor. The data of Pritchard,Sowden and Trotman-Dickenson ,and that of Walters and co-workers agree with n = 9. F I G . I V FALL O F F PLOT, I o<j k / k « , v s . 109 p mm., a t 4 4 q ° C . i n t h e ofie-litr* T h e p o i n t s a r e f i t - r e d f o r T h e Kasfcel c u r v e S » 7, (1 rvcl ud i r\g k 0 / k o c ) . vn v>) o I -3 -Z -I 0<^ p tf\m. FIG. VI FALL OfF PLOT, |o<j |</k«, vs. I03 p mwi., at 4 6 0 °C in t-h£ X ) ve-11 '*-•»"«. rea.cfr>T. T h e p o i ^ s are. fil~) - « .o l -fof »-Ke S l a ^ r corve U- 6", cl odi noj k a / K o J • VJ l 56 6.Related reactions. Cyclopropane undergoes a thermal,unimolecular isomerization to form propylene.The reaction therefore involves the migration of a hydrogen.Slater took as the reaction coordinate the diminution i n the distance between a hydrogen and a non-adjacent carbon,and otained good agreement between his calculations and the experimental data of Pritchard,Sowden and Trotman-Dickenson. 1 1 I f cyclobutane decomposed by a similar mecnanism to cyclopropane the product of the reaction might be expected to be a butene,probably 1-butene,rather than ethylene.Only traces of 1-butene are formed i n the high pressure decomposition and these can be attributed to a wall reaction of cyclobutane. 12 Srinivasan and Kellner have shown that hydrogen migration does not occur i n the decomposition of cyclobutane.They studied the decomposition of cyclobutane-l,l,2,2-d 4 and found the products to be C 2H 4,C 2H 2D 2 and C2D^ i n the rat i o 1 : 2 : 1 . I f hydrogen migration occurred C2H^D and C^ED^ should be formed also.The fact that the rat i o of C 2H 4 to C2H,-,D2 to C^B^ i s 1 : 2 : 1 shows that cyclobutane-l,l,2,2-d 4 decomposes at' an equal rate by two methods,both involving the rupture of two r 2 CH 1 CH 57 opposite C — C bonds. The derivatives of cyclobutane,whose thermal decompositions have been studied,give products which are consistent with the s p l i t t i n g of the ring across two opposite C — C bonds.This i s shown i n Table V I I . The bond dissociation energy for a C—G bond i n the cyclobutane ring has been estimated by several methods.Most of them give values i n agreement with the experimental activation activation energy,but they involve many assumptions and generali zations. P£itchard,Sowden and Trotman-Dickenson^" have calculated values of 60 Kcal. and 59 Kcal. by the following methods, a). The heat of formation of a tetramethylene b i r a d i c a l can be calculated, from the heat of formation of n-butane,the C — H bond dissociation energy and the heat of combination of hydrogen atoms: A H „ n-butane = - 29.8 Kcal./mole. 2 x D( C — H ) = + 200 Kcal./mole. AH H + H —-» Ho = - lQ4 Kcal./mole. A.H f C H 2 C H 2 C H 2 C H 2 = + 66 Kcal./mole. The C — C bond dissociation energy of cyclobutane i s the difference i n the heats of formation of cyclobutane and tetramethylene: D(C—G) = +66 - 6.3 Kcal/mole = 60 Kcal./mole. 58 TABLE VII. THE THERMAL DECOMPOSITION OF CYCLOBUTANE DERIVATIVES COMPOUND PRODUCTS A E Refer--1 . ,r ~\ ence. m sec. mKcal. • C2 H4 4.0 x 1 0 1 5 62.5 3 C 2H 4 +C 2H 2D 2 +C 2D 4 i n the ratio 1:2:1 12 C H . c 2 % C 2H 4 + CH3CH=CH2 C 2H 4 + CH5CH2CH=CH2 2.4 x 1 0 1 5 61.2 18 3.6 x 1 0 1 5 62.0 19 C 2H 4 + CH2=C=CH2 C 2H 4 * CH2=C0 1.2 x 10 15 3.6 x 10 14 61.5 20 52.0 21 C.H, c M 3 as-C3 H6 C0H, + CH_CH=CH CH„ ^ 4 3 3 (ci s and trans) 3.0 x 1 0 1 5 60.4 22 3.7 x 1 0 1 5 63.0 C = O c f C0H. H- CH,CH=CHCH, 2 4 3 3 (ci s and trans) C 2H 4 + CH2=CHCOCH3 r C2 F4 C 3F 6 2® x 10 15 2.9 x 10 15 3.4 x 10 14 1.0 x 10 16 17 61.6 23 63.4 54.5 24 74.3 25 1.6 x 10 ' 87.0 59 b). The heat of formation of a str a i n l e s s cyclobutane molecule would be four times that of a methylene group.The s t r a i n energy i n the cyclobutane ring i s given by the difference between the actual heat of formation o f cyclobutane and that i i of s t r a i n l e s s cyclobutane. Strain energy = 6.3 - (-4.9 x 4 ) Kcal./mole. = 26 Kcal./mole. I f the normal value for a C—C bond dissociation energy i s taken to be 85 Kcal./mole.Then the bond dissociation energy of cyclobutane w i l l be: 85 - 26 = 59 Kcal./mole. 15 It has been postulated by Burwell that the thermal isomerization o f o t - and |?-pinene involves the s p l i t t i n g of the four membered ring as the i n i t i a l step.The activation energy of the isomerizations can be equated with the bond dissociation energies involved i n the s p l i t t i n g of the four membered ring to form a b i r a d i c a l . The experimental activation energies are 44 and 49 Kcal./molte.for oi- and p-pinene respectively.Pritchard, 16 and Trotman-Dickenson postulate that cyclobutane bears the same relationship to tt- and p-pinene as propane does to 4,4-dimethylpentene. $ . 6 • ~i I o'-pinene (3-pinene cyclobutane propane 4,4-dimethyl-pentene 60 The d i f f e r e n c e i n the bond d i s s o c i a t i o n e n e r g i e s o f the l a t t e r p a i r i s 28 K c a l . / m o l e . I f the d i f f e r e n c e i n the bond d i s s o c i a -t i o n e n e r g i e s o f the pi n e n e s and o f c y c l o b u t a n e i s a l s o 28 K c a l . / mole,then the bond d i s s o c i a t i o n energy mf c y c l o b u t a n e w i l l be 46 + 28 = 74 K c a l . / m o l e . T h i s i s c o n s i d e r a b l y h i g h e r than the e x p e r i m e n t a l a c t i v a t i o n energy. 17 I n r e p l y , s e u b o l d s t a t e s t h a t the f o u r membered r i n g r i n the pinenes s h o u l d be more s t a b l e than c y c l o b u t a n e as i t i s a s u b s t i t u t e d ring.He c a l c u l a t e s the s t r a i n energy f o r the f o u r membered r i n g i n the pinenes to be 11 Kcal./mole.,compared to 26 K c a l . / m o l e , f o r cyclobutane.Hence the bond d i s s o c i a t i o n energy f o r c y c l o b u t a n e s h o u l d be : 46 + 26 - 11 = 61 K c a l . / mole.,which agrees w i t h the a c t i v a t i o n energy. 61 7.Mechanism of the decomposition of cyclobutane. Most unimolecular reactions that have been studied in the region where the rate constant decreases with decreasing pressure, have experimental values of n f a i r l y close to the total number of normal vibrational modes of the molecule; JN - 6 for a non-linear molecule containing N atoms.Experimental values of n and s for a number of compounds are given in Table VIII. Cyclopropane was found to have a value of n = 13.The total number of vibrational modes in cyclopropane is 21,compared to 30 for cyclobutane.As cyclobutane has more vibrational modes than cyclopropane i t might be expected to have a greater value of n. The results of this experiment show that the value of n for cyclobutane is of the order of 5 to^8. The decomposition of cyclobutane involves no hydrogen migration ,whereas the isomerization of cyclopropane does.Therefore i t i s possible that the C—H vibrations are relatively unimportant in the decomposition of cyclobutane.If the vibrations of the carbons alone is considered,the number of normal vibrational modes i s 6,which agrees with the experimental value of n.It seems probable,therefore,that i t i s the ring vibrations that are important in the dissociation,and that the C—H vibrations are relatively unimportant. The structure of cyclobutane is s t i l l uncertain.The two possible structures are one in which the ring is planar,D 4n 62 TABLE ¥ 1 1 1 . EXPERIMENTAL VALUES OF n AND s FOR A NUMBER OF COMPOUNDS. COMPOUND TOTAL NUMBER OF VIBRATION MODES n , s , Reference expt. expt. N02C1 26 trans-C 2R" 2D 2 12 10 27 cyclopropane N2°5 21 15 13 14 - 15 6 5 11 28 cis-C^Hg 30 28 trioxymethylene 30 20 29 octafluorocyclobutane 30 20 25 The experimental values of n ,except for octafluorocyclo-5 butane,are those given by Rabinovitch and Michel , The experimental values of s ,are those given by Powell. symmetry,and. one i n which the ring i s puckered and there i s minimum repulsion between the hydrogen atoms,symmetry.The planar structure may have an out of plane bending vibration and the puckered structure may undergo inversion through the planar structure. Electron d i f f r a c t i o n measurements favour the puckered str u c t u r e ^ 0 ' and I.R. measurements tend to favour 32 33 34 34 the planar structure »^»-^\ Pitz e r and co-workers have suggested that although the puckered structure should be more stable, the potential b a r r i e r for inversion i s probably low so that atroom temperature a considerable proportion of the molecules w i l l have a planar equilibrium structure. At 449°C., therefore, cyclobutane w i l l probably have a planar equilibrium structure. 35 Schafer, Monter and Wolff-Mitscherlich have worked out a normal vibration analysis of cyclobutane, assuming symmetry. The six normal modes of vibration of the ring are shown i n F i g . VII. There are several possible ways i n which the reaction may occur : one C—C bond may be broken forming a tetramethylene b i r a d i c a l which l a t e r s p l i t s to form two molecules of ethylene; or two opposite C—C bonds may be broken simultaneously; or a mechanism intermediate between the two may occur. 65 I f a tetramethylene b i r a d i c a l i s an intermediate i n the reaction i t may either have a normal l i f e t i m e and r e a c t i v i t y ( l i k e an a l k y l radical) or i t may have a very short l i f e t i m e . The f i r s t p o s s i b i l i t y i s unlikely.Many of the standard tests for the presence offree radicals have been applied to theddecomposition of cyclobutane and i t s derivatives and none have proved positive.Walters and his co-workers have added radica l scavengers such as propylene,toluene and n i t r i c oxide and observed no difference i n the rate of the reaction.They have also t r i e d adding cyclobutane to reactions which are known to be accelerated by free radicals,such as the polymer-i z a t i o n of ethylene and the decomposition of formaldehyde, without success.More conclusive evidence for the absence of a normal free radical i s provided by the fact that no other products besides ethylene are observed ,except for those which can be attributed to a wall reaction(,see section 3 of the discussion).A normal free rad i c a l would be expected to add to ethylene and also abstract hydrogen from cyclobutane,to form a whole gamut of products by reactions such as :-2 C,Hfi CH 0CH-CH„CH 0 + C 0H.-» CH 0CH 0CH 0CH 0CH 0CH 0^ 0 ° 2 * 2 2 ^ 4 ^ c y c l o - C 6 H 1 2 CH2CH2CH^CH2CH2CH2 + C ^ - * ^(CH 2)g > 2 C^Hg ^ °3 H6 + C5 H10 c y c l o - C 8 H l 6 X • (CH ) * + Y C H -» polymers 2 n m 2m 66 Tetrametylene has been postulated as an intermediate i n the photolysis of cyclopentanone,to account for the formation of polymeric compounds and higher o l e f i n s and cyclohexane.lt i s likely,though,that this mechanism i s incorrect and that these products are due to the secondary photolytic decomposition of 4-penfcenal^. No polymeric compounds were detected i n the decomposition of cyclobutane and the walls of the reactors looked perfectly clean after many decompositions. Several estimates of the activation energy of the reaction mole.,using a value of 73 Kcal./mole for the a l i p h a t i c C—C T O bond dissociation energy.Benson has estimated i t to be 4 Kcal./ mole.He calculated the bond dissociation energy at 450°C. to be 58.5 Kcal./mole.,which i s 4 Kcal./mole less than the experimental activation energy. The activation energy for the addition of an a l k y l r a d i c a l to ethylene i s about 7 Kcal. and for hydrogen abstract-39 ion from cyclobutane i s about 9 Kcal.-'-' Therefore i f the activa-tion energy for the decomposition of tetramethylene were 15 Kcal many products would be expected.Even i f the activation energy were 4 Kcal. the rate constant for the addition of tetrameth-have been made.Bawn and Milsted 37 calculated a value of 15Kqal/ 67 ylene would be about ten times less than the rate constant for the dissociation of tetramethylene (assuming a si m i l a r pre-exponential factor for the two reactions),at 449°C.Appreciable amounts of products other than ethylene would be expected. The values that have been calculated for the bond dissociation energy of cyclobutane are i n agreement with the experimental activation energy,(see section 6 of the Discussion).It i s possible that the f i s s i o n of tetramethylene requires no activation energy.Its l i f e t i m e would then be 3 extremely short.V/alters and his co-workers have estimated the entropy change for the formation of tetramethylene to be about 15 e.u.fhis i s greater than the experimental entropy of activation of 9 e.u.Therefore i f tetramethylene i s formed i n the reaction i t should be an intermediate and not the activated complex.They suggest that the activated complex may undergo a transformation into the b i r a d i c a l which would then have only a momentary existence. The period of time for which an intermediate must exist before i t can be c l a s s i f i e d as a separate species i s a philoso-phical question.The c o l l i s i o n frequency of a eyclobutane q o molecule i s about l ( r per second at 449 C. and 126mm.pressure. Walters and his co-workers have analysed products from a decomposition at this pressure and 438°C. on a mass spectro-meter and found no s i g n i f i c a n t products besides ethylene. Therefore i f the b i r a d i c a l exists i t s l i f e t i m e must be less -9 than 10 sec.If the l i f e t i m e of the radic a l i s very short i t can be regarded as being merely a bump on the potential energy surface, and.not as a separate entity.This mechanism i s then e s s e n t i a l l y the same as that i n which two bonds rupyure simultaneously. 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