Thermal dissociation rate of ethane at the high pressure limit from 250

Thermal dissociation rate of ethane at the high pressure limit from 250 to 2500 K ... Analytical Rate Expression for Association Reactions with Classi...
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The Journal of Physical Chemistty, Vol. 83, No. 8, 1979

Acknowledgment. Support of the National Aeronautics and Space Administration under Grant No. NSG 7105 is gratefully acknowledged. References and Notes (1) H. Schor, S. Chapman, S.Green, and R. N. Zare, J . Chem. Phys., 69, 3790 (1978). (2) J. G. Pruett and R. N. Zare, J . Chem. Phys., 64, 1774 (1976).

D. B. Olson and W . C. Gardiner (3) For references and a review, see J. C. Polanyi, Acc. Chem. Res., 5. 161 (19731. (4) 2. Kariy and'R. N. Zare, J . Chem. Phys., 68, 3360 (1978). (5) Recent reviews include (a) R. N. Porter and L. M. Raff in "Dynamics of Molecular Collisions", Part B, W.H. Miller, Ed., Plenum Press, New York, 1976, p 1; (b) P. J. Kuntz, ibid., p 53; (c) R. N. Porter, Annu. Rev. Phys. Chem., 25, 317 (1974). (6) For a discussion, see ref 5b. (7) S. Chapman and D. L. Bunker, J . Chem. Phys., 62, 2890 (1975).

Thermal Dissociation Rate of Ethane at the High Pressure Limit from 250 to 2500 K D. B. Olson and W. C. Gardiner, Jr." Department of Chemistry, University of Texas, Austin, Texas 78712 (Received August 9, 1978) Publication costs assisted by The Robert A. Welch Foundation and the Petroleum Research Fund

Experimental measurements of the thermal decomposition rate of ethane from 1330 to 2500 K, extrapolated to high pressure limit rate constants using RRK theory, are found to be in accord with previous work. Combining low temperature methyl radical recombination rate constants with ethane decomposition rate constants results in a coherent set of rate measurements for this process at the high pressure limit from 250 to 2500 K. RRKM calculations using several models for the critical configuration were performed and compared with this data base. A critical configuration model using a minimum density-of-states criterion for defining the critical configuration and a hindered rotor description €or the four degrees of freedom that are converted from vibrations in the molecule to free rotations of the methyls was found to give a substantially better description of the data than any vibrator or free rotor model. Since it was not possible to fit the experimental temperature dependence of the high pressure limit recombination rate constant with any critical configuration model, one must conclude either that the minimum-density-of-states version of the RRKM model is incorrect, or that the strong-collision assumption inherent in extrapolating the high temperature decomposition rate data leads to a substantial underestimate of the high pressure limit rate constant.

Introduction The decomposition of ethane and recombination of methyl radicals form the most thoroughly studied unimolecular reaction. As such it has been frequently used as a test case for theoretical descriptions of the unimolecular decomposition process.lJ We present here an extension of the high pressure limit rate constant data to 2500 K, approximately doubling the temperature range previously covered. Our data show that it is possible to display the high pressure limiting rate constant at temperatures up to 2500 K as a virtually linear extrapolation of Arrhenius expressions found previously in low temperature dissociation experiments, using as activation energy the C-C bond dissociation energy of 87.76 kcal/ mol.3 In addition we report calculations of high pressure limit rate constants using two forms of RRKM theory, and investigations of various assumptions about the description of the critical configuration used in the theory. None of these rate constant calculations give a satisfactory fit to the temperature dependence of the data from 250 to 2500 K, although ACM calculations do provide a reasonable fit a t least up to 1500 K.2 Experimental High Pressure Limit Data We reported4 an experimental measurement of the rate of ethane decomposition behind incident shock waves with 1330 < T < 2500 K and 1.1< p < 4.4 X lo4 mol/cm3. In that report the data was extrapolated to the low pressure limit, and a discussion of the available data for the limiting behavior of this reaction a t low pressures was presented. We now consider the extrapolation of our data to high pressure limiting values and compare our results with those from previous investigations. The extrapolation to P = 0022-3654/79/2083-0922$0 1 .OO/O

m was done initially using Emanuel's5 tabulated Kassel integrals with S = 12, E, = 87.76 kcal/mo13, an energy transfer efficiency of 0.07 for Ar relative to C2Hs,and a strong-collision deactivation cross section (from viscosity data) of 0.30 nm2. This value of S was used following Lin and Back,6 who found that S = 12 gave the best RRK fit to their experimental ethane decomposition falloff curves a t 910 < T < 1000 K. Temperature-dependent S expressions such as S = E,+,/RT did not give as good results as S = 12. Figure 1 shows a line describing our experimental rate data and the RRK-extrapolated high pressure limit, which is given by the expression log (k,/s-l) = 16.85-19700/T. In view of the fact that S and the deactivating collision rate are expected to be temperature dependent, but in a presently still uncertain way, meaningful error limits cannot be assigned to this expression. Also shown in Figure 1 are the h , results of earlier experiments on ethane d i s s ~ c i a t i o n and ~ - ~the ~ results of two high temperature investigations of methyl recombination.I5J6 It would appear that all studies of the CzH6 dissociation rate are in satisfactory agreement with one another and show, collectively, a dependence upon temperature in accord with simple theoretical expectations. One should note, however, that the RRK extrapolation is quite large in our temperature range, exceeding three orders of magnitudes at 2500 K, even though the pressures were about half atmospheric. For comparison with the many reported studies of CH3 recombination near room t e m p e r a t ~ r e l ~it- *is~ expedient to convert dissociation rate constants to recombination rate constants, using standard thermochemical proper tie^.^^*^^ High pressure limit recombination rate constants from 250

0 1979 American Chemical Society

The Journal of Physical Chemistry, Vol. 83, No. 8, 1979

Thermal Dissociation Rate of Ethane

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Figure 1. High pressure limit rate constants for C2H, dissociation. The heavy solid line is a reference line whose slope corresponds to an activation energy of 87 76 kcal/mol: (0) this work,4 measured second-order decomposition rate constant converted to a first-order rate constant through muitiplication by [MI; (0)this work, high pressure limit rate constant extrapolated using RRK method; (0)ref 7; (H) ref 8; (A) ref 9; (A)ref 6; (V) ref IO; (V)ref 11; (e)ref 12; (0) ref 13; (A)ref 14. Also included are the high temperature methyl recombination rate constants of ref 15 (+), and ref 16 (X) converted to dissociation rate constants using equilibrium constants from standard thermochemical properties. The recombination rate constant from ref 15 was extrapolated to P =: m just as for the dissociation data. The procedures for extrapolating to the high pressure limit are discussed in the text. The ref 16 point refers to their extrapolation to P = a.

to 2500 K are shown in Figure 2, together with a number of theoretical curves to be discussed later. The consensus value of the recombination rate constant near 1000 K is seen to be ablout a factor of 3 lower than the room temperature consensus value. We see from Figures 1 and 2 that there is very good coherence of the experimental high pressure limit data based on CzH6dissociation and CH, recombination. The coherence extends from 250 to 2500 K and over five orders of magnitude in pressure. The theory used to extrapolate to the limits and interconvert forward and reverse rate constants is venerable. As far as the thermochemical parameters are concerned, one must regard them as secure; the parameters of tlhe RRK extrapolations cannot be considered unreasonable. The satisfaction one can have about the experiments, however, will be shown below not to extend to their match with theoretical expectations. Figure 2 does not show any theoretical rate constant expressions that are in accord with the observed temperature dependence over the entire range. Since one is now expected to have confidence in the ability of suitably parameterized RRKM t h e ~ r y ~ 'to "~ describe thermal unimolecular reactions, this discord is disturbing. In the following section we discuss whether it may be due to misapplication or misparameterization of RRKM theory, or whether the theory itself must be a t fault. In the latter case, we would have to consider whether the extrapolation methods used to generate the bimolecular and unimolecular limiting rate constants have secure foundation. Similar doubts about the applicability of RRKM theory to this reaction have been expressed previously.'I2 We note here that our results apparently do not confirm a suggestion from single-pulse shock tube dissociation experiments ol Bradley and Frend3, that the dissociation

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Figure 2. High pressure limit rate constants for CH, recombination. Measured dissociation rate constants (symbols as in Figure 1) were extrapolated to P = a as described in the text and then converted into recombination rate constants using equilibrium constants from standard thermochemical properties.2gs30 The other symbols refer to recombination rate constants: (0)ref 17; (0)ref 18; (e)ref 19; (Q) ref 20; (0)ref 21; (a)ref 22; (El) ref 23; (m) ref 24; (H) ref 25; (E) ref 26; (D) ref 27; (a) ref 28. The theoretical lines are labeled with the acronyms used to identify the different models in the text. The RRK extrapolation of the results for ref 11 is lower than Figure 2 of ref 11 would indicate to be correct.

rate of C6H6reaches a limiting value near 1300 K. Since our mechanism studies4did not offer any suggestions about chemical reasons for their ,obsservations, we are led to assume that systematic errors in their experiments must have existed.

Theoretical While there are many theories of unimolecular reactions, the only ones which have been cast in forms with which actual rate constant calculations are readily possible are variations upon the now-standard RRKM t h e ~ r y Both .~~~~~ the high pressure and the low pressure limiting rate constants are described, although important reservations must be made concerning the validity of its strong-collision assumption at the high temperatures considered here.34v35 Let us first assume that the RRK procedures used as described above to find high pressure limiting rate constants are accurate, and consider whether RRKM theory can correctly predict the temperature dependence of the unimolecular decomposition rate with a reasonable model for the critical configuration of C2H6. Of the several published RRKM calculations on CZH, we select for consideration that of Waage and Rabinovitch,' which inspection of the literature cited by them and below will show to be typical of all of them. They assumed the moment of inertia of the critical configuration to be 2.45 times the CzHG value, the torsional vibration of C2H6 to become a free rotor, let the two doubly-degenerate CH3 rocking frequencies of CzHs be reduced to 66 and 95 c r d , and let the other CZH6 vibrations be essentially unchanged in the critical configuration. This choice of parameters leads to h, values for CH3recombination that increase by an order of magnitude between room temperature and 2500 K, in contradiction to experiment. Is this failure a consequence of the Waage and Rabinovitch parameterization, or is it inherent in the structure of RRKM theory itself? To seek an answer to this question we carried out a series of k , calculations for a wide variety of assumptions about the critical configuration.

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Figure 3. Sum of states calculated using different models for the criiical configuration of C2H8as function of energy above threshold: (-) direct count of states for 16 vibrations and one hindered rotation; (---) semiclassical (Whitten-Rabinovitch) treatment of sum of states for 16 vibrations and direct count of one hindered internal rotation; (- -- -) direct count of sum of states for 12 vibrations and 5 free rotations: ( 0 - 0 ) direct count for 12 vibrations and 5 hindered rotations; ( 0 0 ) extrapolated sums of states for the free rotor and hindered rotor models, obtained using method discussed in the text; (- -) direct count sum of states for the 12 vibrational degrees of freedom only.

We first modified a standard RRKM program36in order to model the dissociation process more accurately. A direct count over vibrational states was made for energies up to 1 2 kcal above threshold, and the semiclassical formula used for higher energies. The validity of this dual procedure can be seen in Figure 3. The semiclassical technique overestimates the sum of states by about an order of magnitude at the lowest energies, but the two methods merge at energies somewhat above 10 kcal. The second change involved a more accurate treatment of the contribution to the sum of states from the hindered torsional internal rotation of ethane. The standard semiclassical method31 treats an internal rotation as a half-vibration and uses (kT)1/2/Q,for its contribution to the product of vibrational frequencies, where Q, is a free rotor partition function. We used for this degree of freedom instead a direct counting procedure similar to that used to count vibrational states. In this procedure we first computed the energy levels of the hindered rotor, E?, using the method given by Wilson37for a molecule with a cosine restricting potential of depth Vo. Then in order to calculate the total number of vibration-rotation states a t energy E+, the number of vibrational states up to E+ was first counted for the internal rotation in its ground state E?; the number of vibrational states up to energy E+ - Elh‘was calculated and added to the first sum of states; and the process was repeated for E+ - EZb and so on, taking explicit account of the level degeneracies, until an energy level of the hindered rotor was reached that was equal to or greater than the available energy E+. Figure 3 shows the sum of states calculated by this method. We find that this exact (to the accuracy of Wilson’s energy levels) count over the internal rotation levels gives a sum of states that is about the same as that resulting from the semiclassical method at low energies, but about a factor of 3 lower a t higher energies. Densities of states for the excited ethane molecule were calculated using the semiclassical (Whitten-Rabinovitch)

D. B. Olson and W. C. Gardiner

treatment for the vibrations and a direct counting procedure for the restricted torsional rotation analogous to that described above for the sum of states calculation for the critical configuration. The results of a k, calculation done with the above procedure are shown as RRKM in Figure 2 to illustrate the large disagreement between theory and experiment. For the critical configuration model the molecular frequencies and moments of inertia were taken from ref 30, the I + / I ratio was taken to be 2.6, the retained vibrational frequencies of the critical configuration were taken as CH3 frequencie~,~’ and the four C-C-H rocking frequencies which are converted into CH3 rotations upon dissociation were assumed to have decreased to 100 cm-l at the critical configuration. The hindered internal rotation was treated as described above for a molecule with Vo = 2960 cal/molm and for a critical configuration with Vo = 1000 cal/mol. In repetitions of this type of calculation for different critical configuration models, we found that neither I + / I nor the choice of rocking frequencies affected the shape of the log h, vs. 1/T curve appreciably; only vertical shifts of the k, curve could be made. The essence of the disagreement between experimental and theoretical values of the intramolecular dissociation rate is that the observed effect of temperature is far less than predicted by this type of RRKM model; whatever set of critical configuration parameters is adopted, increased thermal populations of the higher molecular and critical configuration states invariably predict too much increase of decomposition rate with temperature. One can however question the implicit assumption of these forms of RRKM theory that the statistically populated critical configuration states are the same states at all temperatures. This question was raised in particular by Bunker and Pattengill,3s who suggest instead that the best assumption to make in order to specify the critical configuration may be that the critical configuration corresponds to that extension of the dissociating bond for which the density of states of the critical configuration is a minimum. We carried out a series of such RRKMBP calculations similar to those reported by H a ~ e . ~ ~ To perform these calculations a potential energy curve for the dissociating bond and the variation of the CH3 rocking frequencies with increasing C-C bond distance must be specified. A Morse function with a force constant corresponding to 995 cm-l, the v3 vibration frequency of CzH6,and a bond dissociation energy of 87.76 kcal/mol was used to describe the classical potential energy curve. The value of De was calculated from De = Moo + E,, - E,t.2 The degenerate moments of inertia were assumed to increase as the square of the reaction coordinate, while the third moment was assumed to be a constant. To describe the loosening of the C-C-H frequencies we used the function v(r) = vo exp[-a(r - roll where a is taken to be a single adjustable parameter for all frequencies and r ro is the displacement of the C-C bond length. The zero point energy of the critical configuration was calculated using these C-C-H frequencies. The barrier to internal rotation was calculated assuming that the same exponential decay constant a describes its corresponding fundamental frequency. Figure 4 shows as functions of inverse temperature the critical configuration C-C bond length and the two doubly-degenerate C-C-H frequencies calculated for a = 0.75 k1using the RRKMBP criterion. At the higher temperatures the critical configuration is indeed seen to have a substantially shorter C-C bond and higher C-C-H frequencies than at room temperature.

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Thermal Dissociation Rate of Ethane

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Figure 4. C-C bond length, rf, and the two C-C-H rocking frequencies for the critical configuration of ethane, calculated using the RRKMBP method with a = 0.75 A-‘, as functions of temperature. At the higher temperatures the C-C bond length corresponding to the minimum density of states is seen1 to be smaller, resulting in higher rocking frequencies.

We have now reduced the model to one characterized by only one adjustable parameter, namely C Y . A number of RRKMBP trials were made for a range of a. The result of the optimum one is shown in Figure 2 as BPV for comparison with the experimental results. Also shown are calculations of and Quack and Troe,2 denoted in the figure as curves H and ACM. It is not possible to obtain agreement with the data as shown for any value of CY.

The four degrees of freedom associated with the C-C-H deformations which change upon dissociation into rotations of the methyl fragments have been described in these models of critical configurations as “loosened” vibrations. The temperahre dependence of the resulting k, values is too strong. These degrees of freedom would perhaps be more correctly described in the critical configuration as hindered rotations, which would be expected to result in a smaller temperature dependence of the rate constant. To see whether such a change in model would be worthwhile, we first investigated the results of describing them as independent, completely free rotations. Using the same direct counting routine as described above, we computed free rotor energy levels and calculated sums of states for a critical configuration with 12 vibrations and 5 free rotations. The moments of inertia were taken to be those of‘ CH3.29 The resulting sums of states were indeed found to be much larger than those computed for a critical configuration with loosened vibrations, as shown in Figure 3. The computer time demands of these calculations were such that the direct count could only be made at low energies. We therefore used an empirical extrapolation procedure based on the observation that a plot of log(sum of states) vs. (E+)1/4 was nearly linear over the range of energies where the direct counts could be made. Some uncertainty exists in the sums of states estimated by this method at high energies, but the rapidly decreasing Boltzmann factor reduces the importance of the sums of states at high energies for rate constant calculations. Methyl recombination rate constant calculations were done using this five-free-rotor model for the critical configuration. The results show, as expected, less increase of k, with temperature than for the vibrator model, approximately a5 P4 from 300 to 2400 K. However, the rate constants increase (by the much larger sums of states) to values much larger than the experimental data indicate,

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e.g., 1.2 X 1014cm3 mo1-ls-l a t 300 K and 4.8 X 1014cm3 mol-l s-l at 2400 K. These values may be compared with 0.76 X 1014cm3 mol-’ s-l at 300 K and 1.1 X 1014cm3 mol-’ s-l at 1400 K calculated using a Gorin-type free rotor model.16 In order to calculate sums of states for a critical configuration model with five independent hindered rotational degrees of freedom we used the direct counting method described above for treating the hindered torsional rotation of ethane. Hindered rotor energy levels were computed (again using Wilson’s method)37and a direct count of states made. Restricting barriers were chosen so that at the equilibrium C-C bond position the fundamental vibrational frequencies were obtained. These barriers were reduced exponentially with increasing C-C bond length as in the BPV vibrator model. Again the computer time demands were such that an extrapolation procedure was necessary to obtain the sums at high energies, although direct counts were possible for higher energies than for the five-free-rotor model. For routine calculations the direct count was made up to 8 kcal, although tests were made up to energies of 15 kcal. At room temperature there was no difference in the k, calculated by the full direct count or by the extrapolation procedure. The calculated sum of states for the hindered rotor model is seen in Figure 3 to lie, as expected, between the vibrator and the free rotor results. Rate constant calculations were performed similar to BPV, assuming as before a = 0.75 A-l. These results are shown as BPHR in Figure 2. The correct magnitude of the rate constant is computed by this model. In addition, it predicts a smaller temperature dependence than either the free-rotor or the lossened-vibrator critical configuration models. The calculations, however, still do not give a satisfactory fit to the experimental data. Calculations performed using other values of CY indicated that it would not be possible to fit the temperature dependence of the data with any hindered rotor model using the minimum density-of-states criterion to locate the critical configuration. Figure 2 does not contain all of the available experimental information about the intramolecular (high pressure limit) part of this reaction, since we have thus far ignored chemical activation experiments on We chose for comparison with the predictions of our models the recent data of Growcock, Hase, and Simons.40 In these experiments vibrationally excited singlet methylene was produced in the photolysis of diazomethane at 435.8 nm and allowed to react with CH4 to produce CzH6 in the ground electronic state but with excess vibrational energy. Based upon a fairly long but well-documented line of reasoning, the average energy of the excited C2H6 was suggested to be 114.9 f 2 kcal/mol, with the rotational energy distribution expected to be thermal. An average decomposition rate constant of (4.6 f 1.2) X lo9 s-l was measured for this chemically excited C2&. We calculated rate constants for decomposition of ethane molecules containing 114.9 kcal/mol of vibrational energy using the one-parameter BPV model (four loose vibrations and one hindered internal rotation, 01 = 0.75 A-l) and the BPHR model (five hindered rotations, CY = 0.75 A-1). The results were substantially larger than the experimental rate constant: log (kls-’) = 10.3 and 10.9 for the two models, respectively. The discrepancies, a factor of 15 in the case of BPHR, would appear to be greater than the experimental error in the rate constant determination. It is possible that at this energy (27 kcal above threshold) the empirical extrapolation of the sum of states introduces

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Flgure 5. Falloff graph for experimental bulb dissociation data from Lin and Back’ at T = 958 K. The dashed line represents the extrapolated high pressure limit rate from Lin and Back. The solid line represents the strong-collision falloff curve calculated using the BPHR model with cy = 0.75 A?’. The calculations are seen to predict somewhat too rapid falloff with decreasing pressure.

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LOG (P/torr) Flgure 6. Falloff graph for the experimental shock tube methyl recombination data of Glanzer, Quack, and Troe’’ at T = 1350 K, using the BPHR, cy = 0.75 A-’ model. The dashed line represents their estimate of k,. A collisional efficiency of 0.10 was assumed for Ar relative to CpH, for the calculations.

significant error into the h (E+)calculation. We note that ACM calculations2 have been successful in computing chemical activation rate constants, and that thermochemical uncertainties may render the interpretation of the data invalid.41 For further details, see ref 42.

Discussion We return at this point to consider the logical inconsistency we incurred in using RRK extrapolations to high pressure limiting rate constants but RRKM calculations to compare theory with the extrapolated h , values. To determine the effect upon h , of different RRKM models, falloff corrections using the strong-collision assumption were computed as applicable to the conditions of our experiment^.^ Using in particular the falloff corrections for BPHR, a = 0.75 k l , our data would extrapolate to high pressure limiting rate constants described by the expression log (h,/s-l) = 16.31 - 19200/T, differing from the expression obtained from the S = 12 RRK falloff corrections by at most a factor 2, at 2500 K. Figure 2 shows this rate constant in recombination form. Either h , expression would be considered to be in satisfactory agreement with the rest of the data set. The difference between the two results is considerably less than the uncertainty one has about the collisional inefficiency. Our assumption of 0.07 of gas-kinetic cross sections may be a reasonable estimate, but it is more likely to be a function of temperature giving rather different efficiencies at 1200 and 2500 K. Since the accessible pressure range is nearer the low pressure limit than the high, errors in estimating the collisional efficiency will be propagated essentially linearly to the derived high pressure limit rate constants. In order to investigate further the validity of the shape of the calculated falloff curves, we compared the BPHR model’s predictions to the experimental pressure dependence data of Lin and Back (LB)6and Glanzer, Quack, and Troe (GQT).16 The results of these calculations are shown in Figures 5 and 6. The slope of the calculated falloff curve is somewhat larger than that of the LB data but fits the GQT data closely. These experimental results thus support the general validity of the falloff corrections calculated for our data and the resulting high pressure limit rate constants. An overview of the situation one faces in obtaining experimental estimates of the high and low pressure

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Figure 7. Recession of unimolecuhr decomposition rate constants from their asymptotic values at temperatures characteristic of experimental studies of CpH, dissociation and CH3 recombination. The limiting rate constant k,,,, the lesser of the high and low pressure limiting rate constants, and the unimolecular rate constant k were calculated as described in the text for the BPHR model. The arrows denote the pressure ranges used in bulb dissociation (BD) studies with 700 < T < 1000 K, bulb recombination (BR) studies with 300 < T < 450 K, shock tube dissociation (STD) studies with 1200 < T < 2500 K, and a shock tube recombination(STR) study near 1400 K. The curves are drawn on the assumption that the strong-collision assumption pertains, as indicated by the SC subscript on klk,,,; its anticipated breakdown particularly at higher temperatures would shift the curves to the right.

limiting rate constants for this reaction at various temperatures is given in Figure 7. We see that the actual rate constants recede from the limiting ones in a manner that broadens dramatically with increasing temperature. Further, the comparison with experimentally accessible pressure ranges shows that while it is hardly possible to get below the high pressure limit near room temperature, at 2500 K one cannot hope to approach it at all. The breadth and shift of the recession curves essentially forces one to get low pressure limit shock tube dissociation data, high pressure limit recombination data, and falloff curves from bulb dissociation experiments.

Conclusions Using either RRK or RRKM methods, extrapolated high pressure limiting rate constants h , were obtained from experimental C2H6thermal decomposition data4from 1330 to 2500 K. These h , values are in excellent agreement with previous work. The data base of rate constants for the ethane dissociation-methyl recombination system at high pressures extends from 250 to 2500 K and shows a high degree of coherence. Over this temperature range the high

Thermal Dissociation Rate of Ethane

pressure limiit recornbination rate constant appears to decrease by about a factor of 3. We showed that in RRKMBP k , calculations the vibrator model fails to predict the temperature dependence of the experimental rate data, while the free-rotor model fails to predict their magnitude. A hindered rotor model successfully predicts the magnitude of k,, but it also fails to account for the experimentally observed temperature dependence, although it is closer than the vibrator model. It is difficult a t this time to assess whether this failure is due to inaccuracies m our methods of calculation, limitations in the critical configuration model, the strongcollision assumption, or to fundamental failure of the statistical theory itself.43 Further work using better computationad techniques4*to calculate sums of states for restricted internal rotors should be valuable in clarifying this situation. Detailed theoretical investigations of the potential surface for dissociating ethane could provide insight into the decay of internal motions we have modeled as a single exponential. The best description of CzH6 decomposition a t present appears to be that of the adiabatic channel model,2 which shows virtually no dependence of the recombination rate constant upon temperature.

Acknowledgment. We express our appreciation to D. M. Golden, R. A. Marcus, M. Quack, and J. Troe for helpful discussions and correspondence. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. This research was also supported by The Robert A. Welch Foundation and the U.S. Army Research Office. References and Notes E. V. Waage and B. S.Rabinovitch, Int. J . Chem. Kinet., 3, 105 (1971). (2) M. Quack and J. Troe, Ber. Bunsenges. Phys. Chem., 78, 240 (1974). (3) W. A. Chupka, J . Chem. Phys., 48, 2337 (1968). (4) D. B. Olson, T. Tanzawa, and W. C. Gardiner, Jr., Int. J. Chem. Kinet., in press. (5) G. Emanuel, Int. J . Chem. Kinet., 4, 591 (1972). (6) M. C. Lin and M. H. iBack, Can. J . Chem., 44, 2357 (1966). (7) A. Burcat, (3. B. Skinner, R. W. Crossley, and K. Scheller, Int. J . Chem. Kinet., 5, 345 (1973). (8) G. B. Skinner and W. E. Ball, J . Phys. Chem., 64, 1025 (1960). (9) P. D. Pacey and J. H. Purnell, J. Chem. SOC.,Faraday Trans. 1 , 68, 1462 (11972). (10) C. P. Quinn, Proc. R . SOC. London, Ser. A , 275, 190 (1963). (1)

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(11) J. A. Clark and C. P. Quinn, J . Chem. Soc., Faraday Trans. I,72, 706 (1976). (12) A. S.Gordon, "Symposium on the Kinetics of Pyrolytic Reaction", Chemical Institute of Canada, Ottawa, 1964. (13) A. 8. Trenwith, Trans. Faraday Soc., 62, 1536 (1966). (14) A. S.Gordon and D. C. Tardy, 174th National Meeting of the American Society, Chicago, Ill., Aug 1977, Division of physical Chemistry, Paper 91. (15) T. C. Clark, T. P. Izcd,M. A. Divalentin, and J. E. Dove, J. Chem. Phys., 53, 2982,(1970); T. C. Clark, T. P. Izod, and G. B. Kistiakowsky, ibid., 54, 1295 (1971). (16) K. Ghnzer, M. Quack, and J. Troe, Chem. Phys. Lett., 39, 304 (1976); Symp. (Int.) Combust., [Proc.], 7976, 949 (1977). (17) D. A. Parkes, D. M. Paul, and C. P. Quinn, J. Chem. Soc., Faraday Trans. I , 72, 1935 (1976). (18) R. Gomer and G. B. Kistiakowsky, J . Chem. Phys., 19, 85 (1951); G. B. Kistiakowsky and E. K. Roberts, ibid., 21, 1637 (1953). Recalculated by A. Shepp, ibid., 24, 939 (1956). (19) R. E. March and J. C. Polanyi, Proc. R. Soc. London, Ser. A , 273, 360 (1963). (20) J. C. Biordi, Mellon Institute Radiation Research Laboratory Quarteriy Report, 47, 12 (1969). (21) F. K. Truby and J. K. Rice, Inf. J . Chem. Kinef., 5, 721 (1973). (22) A. B. Callear and M. P. Metcalfe, Chem. Phys., 14, 275 (1976). (23) N. Basco, D. G. L. James, and R. D. Suart, Int. J . Chem. Kinet., 2, 215 (1970). (24) H. E. van den Bergh, A. B. Callear, and R. J. Norstrom, Chem. Phys. Lett., 4, 101 (1969). (25) F. C. James and J. P. Simons, Int. J . Chem. Kinet., 6, 687 (1974). (26) F. Moseley and J. C. Robb, Proc. R . Soc. London, Ser. A , 243, 130 (1957). (27) A. M. Bass and A. H. Laufer, Int. J . Chem. Kinet., 5, 1053 (1973). (28) W. Braun, A. M. Bass, and M. J. Pilling, J . Chem. Phys., 52, 5131 119701. (29) D. R. Stull and H. Prophet, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 37 (1971). (30) . , J. Chao, R. C. Wilhoit, and B. J. Zwolinski. J. Phvs. Chem. Ref. Data, 2, 427 (1973). (31) P. J. Robinson and K. A. Holbrook, "Unimolecular Reactions", Wiley-Interscience, New York, 1972. (32) W. Forst, "Theory of Unirnolecular Reactions", Academic Press, New York, 1973. (33) J. N. Bradley and M. A. Frend, J . Phys. Chem., 75, 1492 (1971). (34) J. Troe, Ber. Bunsenges. Phys. Chem., 78, 478 (1974). (35) B. S.Rabinovitch, Proceedings of the 10th Shock Tube Symposium, Kyoto, 1975. (36) These calculations were done using the general RRKM program of W. L. Hase and D. L. Bunker, Quantum Chemistry ProgramExchange No. 234, 1975. (37) E. B. Wilson, Jr., Chem. Rev., 27, 17 (1940). (38) D. L. Bunker and M. Pattengill, J. Chem. Phys., 48, 722 (1968). (39) W. L. Hase, J. Chem. Phys., 64, 2442 (1976). (40) F. B. Gowcock, W. L. Hase, and J. W. Simons, Int. J. Chem. Kinet., 5, 77 (1973). (41) G. P.Smith, M. Lev-On, and D. M. Golden, J. Chem. Phys., submitted for publication. (42) M. Quack and J. Troe, Gas Kinet. Energy Transfer, 2, 175 (1977). (43) E. R. Grant and D. L. Bunker. J . Chem. Phvs.. 68. 628 (1978). (44) S.E. Stein and B. S. Rabinovitch, J. Chem. Phys., 58, 2438 (1973); 60, 908 (1974).