KINETICS OF DIENE REACTIONS AT HIGH TEMPERATURES BY D. ROWLEY AND H. STEINER Received 5th February, 1951 The rates of the dimerization of butadiene t o form vinylcyclohexene and of the reaction of butadiene with ethylene to form cyclohexene have been measured in the temperature range of 400°-6000C, and a t low converions. The reactions were found to be homogeneous bimolecular associations, leading essentially to the products indicated. Combination of the rate data for the dimerization reaction with data obtained by other workers at lower tem- peratures shows that the activation energy is temperature dependent. This fact is correlated with statistical rate calculations. Such calculations are also carried out for the cyclohexene reaction, the reverse reaction of decomposition of cyclohexene into butadiene and ethylene and the resulting equilibrium. I t is shown that a cyclic tran-ition complex accounts best for all available rate data, provided adjustments are made for the vibrational frequencies assocated mith bonds to be formed or to be broken.It is assumed that these frequencies are lowered because of the extension of these bonds in the transition configurations. The reason for the study of diene reactions at high temperatures was their importance in certain cracking reactions, which, starting from paraffins and naphthenes, lead to aromatic products. Wheeler znd Woods l were the first to point out the correct key reaction for the forma- tion of cyclic bodies under these conditions by demonstrating the reaction of ethylene and butadiene to give cyclohexene.A similar reaction, namely the dimerization of butadiene to give vinylcyclohexene had been investigated previously, and the kinetics studied in a lower temperature range. We have studied both the kinetics and rate of the dimerization reaction oi butadiene, and that of ethylene and butadiene in a temperature range of 400-600° C. These experiments, and the general conclusions derived from these rate measurements, are rcported hcre. The Dimerization of Butadiene. The dimerization of butadiene has been studied by several authors under various conditions. The general conclusion derived from a number of investigations is that i t is a homogeneous bimolecular reaction, not catalyzed by oxygen, and unaffected by anti-oxidants. The primaq' product was identified as vinylcyclohexene.This compound can react with a further molecule of butadiene to give a trimer which was identified as octahydrodiphenyL2 At low temperatures in the liquid phase and under the influence of peroxides or of oxygen, butadiene forms long chain polymers, but this reaction proceeds parallel to and independent of the dimerization and can be suppressed by adding antioxidants. The rate of the dimerization reaction was studied first by Vaughan at temper- atures frcm 330" C to 400' C. It was later reinvestigated by Kistiakowsky and Ransom in the range frcm r70-3g0° C in an extended and very accurate study. , In the liquid state, the rate of the reaction was measured by Lebedew Wheeler and Woods, J . Chem. Soc., 1930, 1819. and by Robey and collaborators.6 'Wheeler, J .Chew.. SOC., 1929, 378. 3Vaughan, J . Amer. Chem. SOL, 1932, 54, 3863. 6 Robey, Wiese and Morrell, Ind. Eng. Chem., 1944, 36, 3. Alder and Richert, Ber., 1938, 71, 373. Kistiakowsky and Ransom, J . Chem. Physics, 1939, 7, 725. Lebedew and Sergienko, Compt. rend., U.S.S.R., 1935, 3, 79. T 98D. ROWLEY AND H. STEINER I99 Finally at high temperatures from 400' C to 600' C, i.e. in the cracking range, the rate of the reaction was measured by Moore, Strigaleva and Shjljaeva.' This investigation, however, can only be classed as semi- quantitative, since both temperature and reaction time were ill defined in the flow system used by these authors. Moreover, their experiments were carried out at large conversions, when extensive secondary reactions takc place, especially at the higher temperatures.In the present investigation we have tried to use well-defined con- ditions of contact time and temperature, and have restricted the reaction to only small conversions t o avoid secondary reactions. Experiment a1 Materials .-BUTAD1ENE.-crude butadiene was prepared according to the method of Kuhoff * by cracking cyclohexene vapour. It was purified further through the cuprous chloride addition compound. The final product contained not more than z yo impurities ; this small contamination being mainly ethylene. NITRoGEN.-Special oxygen-free nitrogen purified over hydroquinone was used. Apparatus.-Because of the short reaction times required for small con- versions at the elevated temperatures of the present experiments we chose a flow system.All experiments were carried out a t approximately atmospheric pressure, the partial pressure of butadiene being varied by dilution with nitrogen. The apparatus consisted of the necessary combination of flowmeters, purifying train, preheater, reactor tube, etc. Traces of oxygen were removed by passing the gases over reduced copper turnings a t 300°C. They were then dried over calcium chloride and Ascarite and led to the reactor system. In order to achieve well-defined conditions of temperature, metal reactor tubes with thick walls were used ; some were fabricated from mild steel, others from phosphor bronze. The results were identical in both types of reactor, neither was the rate affected by an increase in surface.It was possible to reduce the temperature gradient in the reaction vessel to 1.5" a t low gas flows and to 3-2' under the most unfavourable conditions of the highest gas flows. The average temperature was taken as that of the experiment. The average duration of a run was from 60-90 min. During this period the temperature could be kept constant to within IO C. The gases leaving the furnace were cooled to - 80" C to recover the products of the reaction and most of the butadiene. The uncondensed gases passed out of the system through a gas meter. The essential parts of the apparatus could be evacuated by a mercury pump backed by an oil pump to I O - ~ mm. Hg. At the end of a run, the gases condensed a t - 80' C were separated from the dimer by fractionation through a small column fitted to the product trap and provided with a reflux head cooled with solid CO,.In a trial experiment, 0.10 ml. of benzene was separated from 30 ml. of liquid butene with a loss of less than I yo of the benzene and its purity unchanged. The amount of liquid product was found by weighing. In nearly all experiments, the refractive index, the density and the bromine number were determined also, Results Products of Reaction.-The analytical results on the liquid products from the various runs are given in Table I. The last line of Table I gives the literature values for the density and refractive index, and the calculated bromine number for vinylcyclohexene. It is seen generally that the analytical data of the products approximate closely to those of pure vinylcyclohexene.There are indications from Kistiakowsky and Ransom's work that the rate of formation of trimer from butadiene and vinylcyclohexene increases rapidly with temperature. However, from an inspection of bromine numbers and refractive indices, and from a micro-fractionation of the product of the ethylene- butadiene reaction (see Fig. 3), one can conclude that trimer, if formed a t all, must be present in quantities well below 10 yo. The product gases were analyzed in Expt. 12 and IG on a Podbielniak and Bone and Wheeler apparatus. Apart from a small amount of ethylene due to contamination of the feed gas, only Moore, Strigaleva and Shiljaeva, J . Gen. Chem. U.S.S.R., 1938, 5 , 518. * Ruhoff, Orqanic Syntheses, 17, 25. 9 Podbielniak, Ind. Eng. Chem.(And.), 1931, 3, 177 ; 1933, 5, 119.2 00 DIENE REACTIONS z5 butadiene was found. A weight balance for all ingoing and outgoing products tallied very well in both experiments. We conclude from all this evidence that within the range of conversions of the present experiments the product of the dimerization reaction is vinyl- cyclohexene. Thus the reaction even at these elevated temperatures leads to the same products as were obtained previously in lower temperature ranges. Cracking reactions of butadiene are absent. "44 TABLE I.-ANALYSIS OF LIQUID PRODUCTS Expt. No. I7 16* I5 I4 8 I2* I9 I 1 22 ^^ Temp. C 445 492 544 544 588 592 593 600 650 c % Conversion 2.90 6.95 3-80 5'35 2'42 2-90 4'92 4'73 4-03 3-06 0 0.830 0.830 0.830 0.832 0.828 0.829 0.833 0.839 - - 0.8304 1.4640 1.4640 1-4640 1.4640 1.46450 - 1'4650 1-4650 1.4660 1.4626 - Bromine Number k.Brlroo g.) 2 90 290 288 2 90 2 80 28.5 290* 283 288 286 296 * Podbielniak fractionation carried out on gas. Rate Measurements .-The rate constant of the dimerization reaction was calculated according to the following formula : * where a stands for the concentration of butadiene (mole~/cm.~), Aa is the drop in concentration during the time of contact At (sec.). The results of all rate measurements are given in Table I1 : Comparison of Expt. 14 and 15, and of 11 and 12, where the partial pressure of butadiene was varied considerably, show that the reaction is of the second order. Within the range studied, the rate constants are independent of con- version as shown by a comparison of Expt.14 and 15, and 4, 10, 11 and 12. In Expt. 21, a reactor (No. 111) packed with a roll of thin iron sheeting was used, which increased the surface to volume ratio about 10 times over that of reactor 11. Comparison of Expt. 21 with 16, where reactor I1 was used, shows that the packing does not affect the rate. The reaction therefore can be con- sidered to be homogeneous. This is also borne out by the consistency of the results obtained in a number of reactors of varying volume and material (see list of reactors, Table 11). Discussion Within experimental error the rate constants if plotted in the customary way as log k against the reciprocal of the absolute temperature lie on a straight line. This is shown in Fig. I where both the present and Kistiakowsky and Ransom's 4 results are plotted.The upper part of the graph (crosses) representing the present experiments leads t o the following equation : log,, K = 11-14 - - 26800 2'30RT' * (1) 1°Lebedew and Sergienko, Zhur. Obshech. Khim, 1935, 5, 1839. Aschan, * This formula neglects diffusion against the gas stream (see Bodenstein However, a t the very low con- Bere, '9'4, 57, '959. and Wolgast, Z . physik. Cheulz., 1908, 61, 422). versions used, the error introduced by this factor is very small.D. ROWLEY AND H. STEINER 20 I in the lower temperature range Whilst Kistiakowsky and Ransom obtained 23690 2-30 RT' log,, K = 9'95 - ~ TABLE II.-RATE MEASUREMENTS-BUTADIENE DIMERIZATION ~ Expt. No. 24 I7 I6t 21 15 I4 8 9 I 0 I1 I 2 t I9 23 22 Reactor V 11 I1 III* I1 I1 I I I I I I1 IV IV Temp.("C) 418 445 492 494 544 544 592 592 592 593 600 644 650 588 Contact Time (sec.) 9.00 1-96 1-68 2-48 0.98 0.98 0.374 0.276 0.540 0.730 0.633 0.630 0.295 0.387 Initial Partial Pressure Butadiene (-. Hg) yo Conversion 6-17 2-87 7.00 3-80 5.26 2.42 1-28 2-90 4-92 4'73 3-06 3'96 I 1-3 2'12 k x 10-2 (moles-1 cm.8 sec.-1) 4-13 9-05 28-3 31.0 83.0 78.5 3 40 236 20 I 208 232 235 563 520 Reactors I Mild steel 7-46 ~ r n . ~ I1 ), 12-6 ) ) I11 ,) 18.2 ,, -packed tube 10 times surface of reactor 11. IVPhosphor 14-0 ,, VRronze 61.0 ,, * Packed tube. t Podbielniak analysis carried out. It is seen from Fig. I that the experiments of Kistiakowsky and Ransom in the lower part of the temperature range which they investigated x Rowley and Steiner 0 Kistiakowsky and Ransom. FIG.1.-Butadiene dimerization. can well be represented by eqn. (z), b u t deviations are noticeable at higher temperatures. It seems significant, however, that their points lead smoothly into the straight line relation obtained from the present experi- ments. These facts suggest that the activation energy increases over202 DIENE REACTIONS the combined temperature range of the two investigations. Such a tendency was noted already by Kistiakowsky and Ransom,' but partly attributed to intrusion of the trimerization reaction. The present results do not support this last conclusion. In order to establish with greater certainty that the deviations from the Arrhenius equation are outside the experimental error, we calculated the deviations of all experimental points from eqn.(I), i.e., A log K (expt.) - log k (eqn. ( I ) ) . The results are plotted in Fig. 2. It is seen clearly that whilst the present results, if taken by themselves, can be represented by an Arrhenius type equation, if taken together with Kistiakowsky and Ransom's points the deviations are outside the experimental error. This is brought out further by the measurements of Robey, Wiese and Morel1 * at still lower temperatures in the liquid phase, which is included in this graph, though comparison of rate data obtained in the gaseous and liquid phase respectively may not be fully significant. x Rowley and Steiner. 0 Kistiakowsky and Ranscm. m Robey, Weise and Morell. FIG. 2.-Butadiene dimerization, deviations from Arrhenius equation.Calculations applying the transition state theory to the dimerization reaction of butadiene were carried out first by Kistiakowsky and Ransom.4 Their main purpose was to account for the low temperature-independent factor, but at the same time they showed that the transition state theory might account for the deviations from a simple Arrhenius type temper- ature dependence. It is therefore of interest to extend these calculations and apply them to the present results. Kistiakowsky assumed for his calculations the average hydrocarbon vibration frequencies proposed by These authors give their results in yo butadiene dimerized per hour ; from their values the rate constants for dimerization in moles-' ~ m . ~ sec.-l were calculated using the following formula : * Data from Robey.Wiese and Morell, Ind. Eng. Chem., 1944, 3, 36. s 1 54 h i , = - I00 * 3600 - d' where S stands for the percentage dimerized per hour and d for the density of liquid butadiene at the temperature of the experiment. These data were taken from Scott et al., J . Bur. Nat. Res. Stand., 1945, 35, 39.T'K Open Chain O0 22,800 500' 23,770 600°* 24,770 900° 25,900 * Reference temperature. The experj- mental data given for comparison were interpolated for the temperatures stated from our and Kistiakowsky and Ransom's data. It is seen that the rates calculated under the assumption of a cyclic complex are too high by a factor of 4, whereas those based on a straight chain complex are too high by a factor of 10. Both these discrepancies must be considered within the errors of the method because of the un- certainties in the molecular constants.In order t o compare further to what extent the calculations can repre- sent the temperature dependence of the reaction rate we adopted the l1 Pitzer, J. Chem. Physics, 1937, 5, 469, 473. l2 Wassermann, J. Chem. SOC., 1942, 612. l3 See, for instance, Eyring, Glasstone, Laidler, The Theory of Rute ~'rocesses. The calculated rate constants are listed in Table IV. Cyclic Complex Obs. - 2 I ,400 23,070 2 1,500 24s770 24,700 26.500 26,800204 DIENE REACTIONS following method. By adjustment both of the activation energy and the temperature independent factor we made the calculation agree with the rate determined experimentally at 600' K. The adjusted equations are given below, (3) and (4) : hcyclic = 2-23 X I d 3 X T-5'2.fvib exp (- 22380/RT) . (3) (4) hstzafghtchain = 0.85 x IO" x T-s'2. flvib eXp (- Z 4 I O O / R T ) . where f and f' stand for the vibrational contribution to the partition function. We then calculated the deviations of these equations from the standard Arrhenius equation (I) drawn through the points of the present experiments (Fig. I). TABLE IV.-COMPARISON OF CALCULATED AND EXPERIMENTAL RATE CONSTANTS Temp. O K 500 600 700 800 900 Complex Cyclic open chain Cyclic open chain Cyclic open chain Cyclic open chain Cyclic open chain k calc. 1 k expt. (mole+ cm.8 sec.-1) 0.885 4'64 49'0 274 9-11 x 102 5-03 x 103 9-14 x 103 5-45 x 104 5-58 x 104 33-3 x 104 0*446* 22-4* 5-12 x 102 5.63 x 103 4.0 x 104 k adjust 0.337 0.303 22'2 22.4 4.58 x I O ~ 4-82 x 102 5-36 x 103 5-91 x 103 3-96 x IO* 3-27 x 104 * From Kistiakowsy and Ransom's data.A plot of the curve representing these deviations can be found in Fig. z where both the values for the straight chain and the cyclic complex are plotted. Marked deviations from the Arrhenius straight line are notice- able, and we note that both equations follow, though not quantitatively, the trend of the experimental points. The calculations assuming the cyclic complex agree somewhat better than those for the straight chain one, but no matter what complex is assumed, it is clear that the transition state calculations lead to the right type of deviation from the Arrhenius straight line. The Reaction of Ethylene and Butadiene It has been pointed out already that the occurrence of a reaction between ethylene and butadiene was first demonstrated by Wheeler and W0od.l In what follows, we shall describe the determination of the rate of this reaction, which was carried out in a manner very similar to that of the dimerization of butadiene described above. The reverse reaction of dissociation of cyclohexene into ethylene and butadiene has been studied by KU~h1er.l~ Thus the rate of formation and decomposition of cyclohexene, and the resulting equilibrium, which can also be calculated from thermal data, can all be compared.More- over, these reactions are so similar to the dimerization of butadiene that the transition state models used in the previous case can, with slight modifications, be applied here. l4 Kuchler, Nach.Ges. Wiss. Gottingen, 1939, I, 231.D. ROWLEY AND H. STEINER 205 Experimental Ethylene was obtained from the British Oxygen Company as " pure ethylene for medical purposes ". It was subjected to no further purification except to remove traces of oxygen as described before, Butadiene was obtained as de- scribed above. The same apparatus was used for the rate measurements and with a few modifications the method of operation remained unaltered. Method of Analysis.-The liquid product was analyzed in the manner described above, and by determination of the bromine number and of the re- fractive index. In the present experiments, the liquid product was anticipated to be a mixture of cyclohexene and vinylcyclohexene, the latter arising from the simultaneous dimerization of butadiene.The bromine number of this mixture was relied upon to give the exact amount of cyclohexene formed, the values for the two pure compounds being sufficiently different from each other. This was shown to be accurate by fractionating the combined products from several experiments (about I ml.) on a micro-column of the rotating band type. Results Products of Reaction.-A graph reproducing the distillation of the com- bined products from several runs on the micro-column is shown in Fig. 3 where the volume distilled is plotted against the distillation temperature and the Fraction I . Fraction I1 . Cyclohexene) . (Vinylcyclohexene) . FIG. 3.-Fractionation of liquid products. refractive index of the distillate. It is seen clearly that two products only are present corresponding to the two plateaux of the curve, the amount boiling below the first plateau being negligible.The characteristics of the two fractions are given in Table V. TABLE V.-ANALYSIS OF FRACTIONS FROM MICRO-DISTILLATION 84 1-4440 (83) (1'4440) 130 1'4645 (130) (1 -4650)206 DIENE REACTIONS The distillation also confirms the method of analysis based on the deter- mination of the bromine number. The bromine number of the mixture before distillation was found to be 230 g. Br/Ioo g. which, assuming only vinylcyclo- hexene and cyclohexene to be present, corresponds to a cyclohexene content of 66 yo, whereas from the distillation graph we find 66.5 yo. A full analysis of all product gases was carried out for Expt. V and XI. This showed that only ethylene and butadiene were present.A weight balance for all icgoing and outgoing materials tallied well. Rate Measurements.-The rate constant was calculated according to the equation : A (cyclohexene) At = k , (ethylene) (butadiene), where the expressions in brackets stand for the respective concentrations, and At for the contact time. TABLE VI.-RATES OF ETHYLENE-BUTADIENE REACTION Expt. No. XIV IX XI * VIII XI1 VI I1 Etr V* IV XI11 VII teactor I11 I11 I11 I11 I11 I1 IIB I11 I1 I1 I1 I I1 Reactors : Temp. (" C ) 487 507 530 559 549 5 50 553 5 90 593 594 603 62 I 648 Contact Time (sec.) 5.02 3-16 3.16 2'35 2-40 0-97 0.94 1-62 0-72 0.77 0.76 0.834 0.436 Partial Pressure (-. Hg) 3 t h ylene Buta- diene 69 69 69 69 69 69 109 79 109 69 69 69 69 - I 14-0 cm.3 phosphor bronze.[I 12-6 cm.3 mild steel. Total :onversion % 5.68 8-40 10.25 9'5 4'33 7'25 7-10 7'52 I 1-87 8.86 5-60 3-48 8'44 yo Cyclo- hexene in Liquid Product # 73 67 71 71 73 68 66 40 63 68 70 70 70 ka (mole-1 m.3 sec-1) 384 560 938 I565 1340 1230 1590 3120 4050 3470 3740 5620 8200 IIB 13.0 ~ m . ~ mild steel packed (surface of reactor II x 11). I11 61 ~ r n . ~ phosphor bronze. * Podbielnak analysis carried out on product gases. 3 % Vinylcyclohexene = IOO yo - cyclohexene. Diluted with nitrogen joo mm. Hg. The results from all experiments are collected in Table VI. In Expt. VIII, XII, VI and I1 the contact time was varied keeping the temperature as con- stant as possible ; i t is seen that the variations of rate which occur are compara- tively small and are not systematic.In Expt. X, I11 and V, the partial pressure of ethylene was varied by a factor of three with no systematic effect on the mag- nitude of the bimolecular rate constant. To obtain a variation of the partial pressure of butadiene was more difficult, because of the small rates of flow of butadiene which i t would have been necessary to use. In Expt. I11 acd V, the partial pressure of butadiene was varied from 69 to 109 mm. Hg, this repre- sents a variation of 45 yo while the two rate constants differ by 15 yo. W'hilst this is admittedly not as conclusive as would be desirable to show that the rate is proportional to the partial pressure of butadiene, nevertheless in conjunction with the rest of the experimental evidence there is no reason to doubt that the reaction proceeds according to this simple bimolecular mechanism.In Expt. I1 a reaction vessel packed with a roll of mild steel sheet was used to test for surface effects, but as comparison with VIII, XII, VI shows, no such effects are noticeable. The amount of butadiene dimer found in the liquid product corresponded quantitatively to that to be expected from the rate data obtained above.TI. ROWLEY AND 13. STEINER 207 The experimental accivation energy was obtained from a plot of log R against I / T (reproduced in Fig. 4) where the points lie reasonably well along a straight line. The activation energy calculated from this graph is 27,500 cal. and the rate as a function of temperature can be expressed by k, = 3-0 x 101Oexp (- 27,500 T ) moles-' ~ r n .~ sec.-l/ . - (5) Eqn. ( 5 ) shows the present reactio k to be a typical diene association, as demonstrated by the low temperature-independent factor, which is 103-104 times smaller than that of " normal " bimolecular reactions, and also by the low activation energy of 27,500 cal./mole. In both these features, the reaction resembles clo ;ely th2 butsdiene dimerization dealt with above. FIG. +-Temperature dependence of rate of cyclohexene formatioi, Discussion Comparison of Experimental and Calculated Activation Energies.- Evans and Warhurst l6 calculated the activation energy of the reaction of butadiene and ethylene from potential energy diagrams constructed from spectroscopic data, and from an estimation of the resonance energy of the cyclic transition complex.The calculated value for the activation energy of this reaction was 17 kcal./mole. The experimental value for the activation energy found here at 800' K was 27.5 kcal., and if reduced to the absolute zero using standard formulae 13 and the data listed in Table X one obtains E , = 25.1 kcal. This value substantially confirms the calculations of Evans and Warhurst. The Equilibrium C,H4 + C4H, C,H,,.-The monomolecular rate constant of the cyclohexeiie decomposition according to Kuchler l4 can be represented by Combining eqn. (5) and (6), we obtain eqn. (7) for the equilibrium constant of the reaction C2H4 + C4H, 2 C,H,, k d = 9.0 x 1o12exp (- 57,5oo/RT) (sec.-l). . - (6) where k, stands for the rate of the association reaction. also be calculated from thermal and spectroscopic data.The equilibrium between cyclohexene, butadiene and ethylene can To obtain the Evans and Warhurst, Trans. Faraday SOC., 1938, 34, 614.208 DIENE REACTIONS 3 3 41 47 l - -- I heat of reaction, the heats of formation of benzene, l7 ethane Is and butane were combined with the heat of hydrogenation of benzene l9 and cyclo- hexene l9 respectively to cyclohexane, and ethylene to ethane and buta- diene to butane. This allowed us to calculate the heats of formation of 294 163 136 2-56 X I the reactants involved at 355" K.* 290 I45 I45 2-47 x 10-57 I2 Cyclohexene (g) . . -2820 cal./mole Ethylene (g) * 11,614 ,, Butadiene (g) . * 25,490 3 , The heat of reaction at 800° K was calculatea using these heats of formation corrected for the increase in vibrational heat content.This correction was calculated from the following sources : ethylene from Guggenheim, 2 o butadiene from Wassermann, l2 cyclohexene from Table X, using Pitzer's rules.'l In this way one arrives at a value of AH,",, of 37,860 cal./mole, and of AEioo = 36,280 cal./mole. The latter value can be compared directly with the one derived from our and Kiichler's activation energies, AEio0 expt. = 30,000 cal. /mole. The disagreement is cowiderable, but it is unlikely that the thermal value is in error by more than a few hundred calories. The value obtained by us for the activation energy of the association reaction is as expected of the order of that of the butadiene dimerization. This fact suggests that Kuchler's activation energy for the dissociation may be in error.The absolute value of the equilibrium constant was calculated from the calculated heat of reaction and partition functions, using spectro- scopic data. The data for cyclohexene are summarized in Table VII-X, and those for butadiene and ethylene were taken from the sources men- tioned.12, 2 O TABLE VIL-DIVISION OF DEGREES OF FREEDOM Translation . Rotation . Int. rotation Vibration . C y clohexene Cyclic Complex Str. Chain Complex 3 3 3 38 - 47 - TABLE VIII.-MOMENTS OF INERTIA AND SYMMETRY NUMBERS Benzene (g. cm.3 x 1040) Cyclohexene and Cyclic Complex (g. cm.2 x 1040) Str. Chain Complex (g. cm.a x 1040) 629 629 2-20 x I O - ~ ~ 12'2 1 17 Prosser, Gilmont and Rossini, J . Res. Nut. Bur. Stand., 1945, 34, 65. 18 Rossini, J. Res. Nut. Buy. Stand., 1934, 21, 13.l9 Kistiakowsky, Ruhoff, Smith and Vaughan, J . Amer. Chem. Soc., 1936, 146. * The data used were adjusted from 298" K to 355" K by using specific heat data listed by Parks and Huffmann, Free Energy of Organic Substances (The Chemical Catalogue Co., New York, 1932), pp. 68, 93. 2O Guggenheim, Trans. Farnday Soc., 1941, 37, 101.D. ROWLEY AND H. STEINER 209 Rotation around Torsional Vibration Bond around Bond 1-2 5-6 4-5 - 1, 1 2 2-3 I 3 3-4 TABLE IX.-MOMENTS OF INERTIA OF INTERNAL ROTATIONS AND TORSIONAL VIBRATIONS (STR. CHAIN COMPLEX) I (g. cm.2) 3.0 x I O - ~ O 28 x I O - ~ O 50 x I O - ~ O Mode of Vibration I. C-H stretching . 2' ">C bending . H 3. H-4-C H--C---C ">,-C bending . 13 H JC-C 4. C-C stretching . 5. k C stretching . 6. C-C stretching .7. c-c--c c-c-c C-C-C bending . C--c-c 8. C-C-C bending . c-c-c 9. C---C torsion * 10. C - - - C torsiont . Frequency (cm-1) - 3000 I440 950 1000 I 600 I335 320 190 407 190 * Between atoms 5-6 of stra t Between atoms 4-5 of stra No. of Modes in : yclohexene I0 4 16 5 I - 6 - - - Cyclic Complex I 0 4 16 3 I - - 7 - - 3pen Chain Complex I 0 4 I4 2 2 4 - I I h t chain complex. ht chain complex. This calculation leads t o a value of K, = 6-65 x 104 mole-1 ~ m . ~ at SooOC, compared with the experimental value of 5-9 x 105. This cal- culated value was arrived at using Pitzer's frequencies (320 cm.-1) l1 for the bending vibration of cyclohexene ; according to Wassermann much lower bending frequencies occur in cyclic molecules. Using a value of 190 cm.-l for the latter frequencies, and making the necessary adjust- ments, we obtain for K, (low frequencies) = 1-55 x I O ~ .Comparison2 I 0 DIENE REACTIONS with the experimental equilibrium constant shows that the normal fre- quency value is about g times too low, and the low frequency value 3 times too high. These deviations, though large, probably fall within the error introduced by the rather crude molecular constants uscd. Statistical Rate Calculations.-The present reaction of butadiene and ethylene is very similar to the butadiene dimerization, and calculation of its rate according to thz transition state mcthod can be carried out using suitably modified complexes of the cyclic or straight chain free radical type (cf. Fig. 5 ) . Moreover, using the molecular models and par- tition functions for cyclohexeiie derived in the last paragraph, the rate of Free radical complex I 2 3 4 5 6 I 1 I I I 1 CHZ-CH -CH,-CH=-- CET---CH, I Cyclic complex FIG.5.-Configuration of transition state complexes. decomposition of cyclohexene can be calculated and com- pared with Kiichler’s values. The molecular constants used for the two complexes are given in Tables VII-X. They were calculated strictly analogous to the method de- scribed in detail by Wasser- mann for the butadiene dimerization.ll For the cyclic complex, Wassermann’s as- sumption of the bending frequencies (190 cm.-1) was adopted, but calculations were also carried out using Pitzer’s value of 320 cm.-l. The torsional vibrations of the straight chain complex were calculated according t o Ki~tiakowskv.~ The rate of the dissociation reaction of cyclohexene was calculated for the same alter- natives of straight chain and cyclic complex, the latter with high and low bending frequencies respectively.In Table XI are listed the rate constants calculated under the three alternative assumptions. Inspection of Table XI reveals clearly that the rates based on the assumption of a straight chain complex, both for the association and dissociation reaction, are too high by factors ranging from 102 t o 104. Since there is no doubt that such discrepancies exceed even the consider- able error of the present calculations, these results show that in the present reaction the straight chain complex cannot be the correct one. A model stiffer than the present one would agree better with experi- ment, but it is difficult to see how this could be visualized without intro- ducing quite arbitrary assumptions.On the other hand the rate constants assuming a cyclic model all agree within a factor of m with the experi- mental values (see Table XI). In the present case it is even unnecessary to use the low bending frequencies proposed by Wassermann, since quite good agreement can be obtained with Pitzer’s frequencies, as was also the case for the equilibrium between cyclohexene, ethylene and butadiene discussed previously. On the other hand it will be recalled that in the butadiene dimerization the cyclic complex led t o satisfactory values for the rate constant only if the low bending frequencies were used. One can hardly assume that these bending frequencies occur in the butadiene dimer complex but not in the very similar cyclohexene complex and in the fully formed cyclo- hexene molecule, and one is led therefore to the following alternatives.Either the cyclic complex with low bending frequencies is the correct transition state in both reactions, and such low frequencies occur also in the fully formed cyclohexene molecule, or a cyclic complex with normal bending frequencies is operative in the cyclohexene formation, and aD. ROWLEY AND IH. STEINER 21 I straight chain one in the butadiene dimerization. The second alternative implies a considerable change in mechanism in going from the one to the other reaction which, while it cannot be excluded, seems unlikely. If the first alternative is preferred, it is necessary to examine the evidence for low bending frequencies in cyclic structures.The Raman spectrum of cyclohexene has been examined by a number of authors,21 amongst tht m Weiler, who observed lines corresponding to frequencies of 176 and 273 cm.-'. These are frequencies of the magnitude required by Wassermann. However, the intensity of the lines is given as very weak and by analogy to similar lines found in the benzene spectrum i t is most probable that they have to be assigned to combination frequencizs and not to fundamentals. The line of lowest frequency having an appreciable intensity is that at 396 cm.-l, which corresponds more nearly with Pjtzer's estimation of 320 crn.-l for C-C-C bending vibrations. The evidence therefore from spectroscopic data is doubtful ; one cannot say that it clearly supports the assumption of low bending frequencies.TABLE XI.-CALCULATED RATE CONSTANTS AT 800' K Association reaction. k (mole-l ~ r n . ~ sec.-l) Cyclic Complex I Str. Chain Complex Expt. 1-45 x 10' (v = 190 crn.-l) (v = 320 cm.-l) 5-8 x 102 15'3 8.7 x I 0 2 Dissociation reaction. k (sec.-l) 1-33 X I O a 1-66 x I O - ~ (U = 190 cm.-l) 2-25 x I O - ~ (U = 320 cm.-l) 1-30 x I O - ~ Apart from spectroscopic data, an accurate determination of the entropy of cyclohexene is available. 4 2 From this, using standard formulae and the molecular data of Tables VII-X, the vibrational entropy of cyclo- hexene was calculated. This " calorimetric " value is compared in Table XI1 with the calculated value using (a) Pitzer's frequencies for all vibrations, and (b) Wassermann's frequencies for the bending vibrations of C-C-C and C-C=C bonds (190 cm.-l) and Pitzer's values for all other vibrations.It is obvious that Pitzer's values agree much bettef than Wassermann's value with the experimental thermal determination. Since the evidence from the thermal determination of the vibrational entropy of cyclohexene strongly supports Pitzer's frequencies, it does not appear possible to account for the reaction rates by the adoption of a uniformly low frequency of the order of 190 cm.-l for aZZ bending fre- quencies in the transition complexes. However, it seems to us that the following compromise solution not only has the merit of agreeing well with all experimental data, as will be seen below, but seems in itself logically more consistent than the previous assumption of uniformly low bending frequencies.We propose to retain Pitzer's frequencies for all C-C-C and C-C=C bending vibrations of the stable molecules cyclo- hexene and vinylcyclohexene respectively, and equally for all bending modes of the reaction complexes, which are not directly involved in the formation or in the breaking of new bonds. On the other hand, for all 21 For references see Hibben, The Raman Effect and its Application (Reinhold, New York, 1g3g), p. 218. 22 Parks and Huffman, J. Anrev. Chem. Sot., 1930, 52, 4381.212 DIENE REACTIONS bending frequencies involving bonds to be formed or to be broken we shall assume Wassermann’s value of xgo cm.-l. These assumptions seem to us justified because in the transition complex the atoms linked by bonds to be formed or to be broken are displaced from their equilibrium positions.Consequently the binding forces must be weakened considerably, which should lead to a reduction of the frequencies of all vibrational modes affected. TABLE XII.-COMPARISON OF VIBRATIONAL ENTROPY OF CYCLOHEXENE (Units : cal. deg. -1 mole -l) Calculated Value I Calorimetric Value Pitzer’s Frequencies I ~~~~~~ I I 10’2 1 9’7 1 15‘4 In Table XI11 we indicate the splitting of the vibrational bending frequencies in the cyclic complexes into those which are stable and thus will be assumed to have Pitzer’s frequency of 320 cm.-l, and those which are associated with new bonds to be formed or to be broken, and therefore will be assumed to have a reduced frequency of 190 cm.-l.TABLE XIII.-BENDING FREQUENCIES IN MODIFIED CYCLIC COMPLEXES Butadiene I I Cyclohexene Frequency (cm.-l) Number of bending modes 4 2 5 4 Assuming a cyclic complex, and basing it on this new splitting of bending frequencies, the rates of the association and dissociation reaction of cyclohexene and the rate of dimerization of butadiene were recalculated. The results are tabulated in Table XIV, where they are compared with the experimental values both for the cyclohexene and butadiene dimer- ization reaction already given in earlier tables. The results given in Table XIV show that the rate constants calculated under these last assumptions, with the exception of the dissociation re- action agree within a factor of 10 with the experimental values.The rate constant of the dissociation reaction is 60 times greater than the experimental value. However, i t may be significant that very good agreement is obtained when Kiichler’s value for the activation energy (57,500 cal.) which, as mentioned previously, may be in error, is adjusted to agree with the calculated heat of reaction and the activation energy of the association reaction (adjusted activation energy 63,800 cal.). We note too that under the present assumptions, i.e., bending fre- quencies of 320 cm.-l for all vibrations of “ stable ” bonds, these last frequencies have to be used for the calculation of the vibrational par- tition function of the stable cyclohexene molecule. We recall that the equilibrium constant of the cyclohexene equilibrium calculated in this way also agreed within a factor of 9 with the experimental value. We can conclude, therefore, that these last assumptions regarding the fre- quencies of the transition complex, namely “ normal ” frequencies for all vibrations not affected by the reaction and “ low ” frequencies for all vibrations loosened due to the reaction, leads to quite reasonable agreement with the available data.D. ROWLEY AND H. STEINER 213 The present results confirm that the assumption of a similarity of transition state and final reaction product in diene association reaction is in the main correct. However, because of its greater looseness, the transition complex does not correspond in all its characteristics to the final rnolccule. Significant deviations occur, of which the lowering of the frequencies of all bending vibrations associated with bonds to be formed or to be broken seem to be the most important. TABLE XIV.-CALCULATED RATE CONSTANTS ASSUMING MODIFIED CYCLIC COMPLEXES Association reaction k, calc. (mole-1 ~ r n . ~ sec.-l) k , expt. (mole -1 ~ r n . ~ sec. -l) 1-66 x 103 Dissociation reaction I 8-70 x I O ~ kd calc. (sec. -l) 1-66 x I O - ~ I 1-02 x 10'1 k, expt. (sec. -l) But adiene di merization kCF& (mole -1 ~ m . ~ sec. -l) kexpt (mole -l ~ m . ~ sec. -l) 104.0 One of us (D. R.) wishes to thank the Central Research Committee of the University of London for a grant in support of the work recorded in this paper. We are also very grateful to Prof. M. G. Evans, F.R.S., and to Dr. A. Wassermann for several helpful discussions. 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