Calculated R.R.K.M. unimolecular dissociation rate constants for hydrazinel

Transcription

1 Calculated R.R.K.M. unimolecular dissociation rate constants for hydrazinel D. W. SETSER' AND W. C. RICHARDSON Department of Chemistry, Kansas State University, Manhattan, Kansas 66502, Received November 26, 1968 Unimolecular rate constants for hydrazine dissociation by thermal and chemical activation have been calculated according to the R.R.K.M. theory. The two activated complex models used in the calculations represent plausible upper and lower bounds to the rate constants. The calculations are mainly directed toward establishing expected decomposition to stablilization ratios of N,H4 produced by combination of NH, radicals; however, a general comparison to available experimental data for hydrazine dissociation is made. Canadian Journal of Chemistry, 47, 2593 (1969) Introduction N2H4 decomposition was assumed to belong to During the course of an experimental the class of dissociation reactions having loose,tion of NH and NH2 radical reactions in our transition states and positive entropies of activalaboratory, thestabilization (S) to decomposition tion, such as the dissociation of ethane (4). Or in (D) ratio at various pressures and temperatures of terms of the reverse reaction, NH, combination, hydrazine formed by reaction was needed. the assumption is that the combination rate constant is typical for radical combination. R.R.K.M. (2j calculations were performed for two models which are believed to give upper and lower bounds to the rate constants. Only a very general outline of the equations (3, 5) and procedures (1) used in the calculations are presented because they are relatively standard. We also have done R.R.K.M. calculations for the dissociation of methylamine. The rate constants have values similar to those for acetaldehyde (5). Since CH,NH, is of less general interest than hydrazine, these rate constants are not included here, but they are available upon request (1). Since experimental information was not available, a Rice Ramsperger Kassel Marcus (R.R.K.M.) (2) theoretical estimate of the S/D ratio (3) was made. The NH, radical combination reaction has been suggested to be of importance in many photolysis and pyrolysis systems involving nitrogen-hydrogen compounds, and our calculated results are summarized and compared to the existing experimental data. The calculations suggest that most experiments were done at much too low a pressure to obtain the true rate constant for NH, combination due to the occurrence of reverse dissociation. For the models chosen for the activated complex, the calculated results also indicate that the shock tube investigations of N2H4 dissociation have been conducted in the fall-off region rather than in the high pressure region. Reliable experimental information, e.g., entropy of activation, is not available for the formulation of a good model for the activated complex for hydrazine dissociation. Therefore, 'Abstracted from the thesis of W. C. Richardson, which was submitted in partial fulfillment of the requirements of the Master's Degree, Kansas State University, 1969.,Alfred P. Sloan Foundation Fellow. Calculated Results In order to obtain R.R.K.M. values of the specific rate constants, kc, for hydrazine, a model of the molecule, models of the activated complex for reaction[l 1, and the critical energy for rupture of the H,N-NH, bond are needed. The thermochemistry (8), vibrational frequencies (9a), and moments of inertia of N2H4 (9b) are relatively well known. However, despite several shock tube investigations (6, 7) of N2H4 dissociation, a reliable value for the high pressure pre-exponential factor is not available and other information was used to obtainanestimate of this pre-exponential factor. We combined calculated values of the equilibrium constant (NH,, N2H4) with values of the NH, bimolecular combination rate constant to obtain the pre-exponential factors for the

2 2594 CANADIAN JOURNAL OF CHEMISTRY. VOL. 47, 1969 TABLE I Models for N,H, molecule and activated complex Molec~le"~~ Complexasb Vibrational Vibrational I (g cm2 x 1040) frequenciesc I (g cm2 x 1040) frequencies" (cm - ') Adiabatic (cm-') Active Adiabatic Model I Model I1 3220(2) 275(2) (2) 200(2) (2) The measured torsional frequency of 377 cm-' was used for computation of density of states for NIH, molecule. For the complex the torsional motion was treated as a free internal rotor with a symmetry number of 2. &For both molecule and complex the three overall rotations were treated as adiabatic. The moments of inertia ofthe complex were obtained hv extending the rcn-nj of hvdrazine - from 1.47 to 3.0.& and assuming the comolex to be olanar. <The N2H4 frequencies are from ref. 9. *The three hlgh sets of frequencies for the complexes are the same as for NH2 (12). The two low sets were assigned to obtain the steric factors specified in the text. unimolecular rate constant which served to define the model of the activated complex. The thermochemistry of reaction [l] seems well established, and if a 1 kcal mole-' barrier is taken as the activation energy for association of NH, radicals, the critical energy for N2H4 decomposition becomes 56.8 kcal mole-'. The overall rotational degrees of freedom of N,H4 were considered to be adiabatic, and all internal degrees of freedom were taken to be active. The torsional motion was treated as a vibration for the computation of the density of states for N2H4, although the barrier to internal rotation is only 2.5 kcal mole-' (9b). Representing the torsion as a vibration gives a lower limit to the density while using an internal rotor gives an upper limit. The latter would have increased the density of states by about a factor of 3; and hence, the rate constants would be lowered by this amount. For our purpose of estimating a range of rate constants, there is no point in considering anharmonicity (10) or centrifugal stretching (11) effects. The model for N,H4 is summarized in Table I. The N2H4, NH, equilibrium constant was calculated from the model of N2H4, D(H,N- NH,) and the molecular parameters of NH, (12). The combination reaction of NH, radicals has not been thoroughly studied but the available data (13, 14) indicate that it is a "typical" radical combination reaction with a rate constant between 0.1 and 0.01 of the collision number. The pre-exponential factors from these two assumed steric factors correspond to the models of activated complex which are listed in Table I. In terms of partition function ratios and critical energies, the unimolecular high pressure thermal activation rate constants are k, = 3.35 x 1016 exp (-56.8 kcal mole-'/rt) and 2.52 x 1015 exp ( kcal mole-'/rt) at 720 OK. The torsional degree of freedom of the complex was treated as a free rotation; the three overall rotations were taken to be adiabatic as in the molecule. The vibrational frequencies of the activated complex are those of 2 NH, radicals (12) with 4 additional low bending frequencies. The latter were arbitrarily adjusted to obtain the two pre-exponential factors defined by the values of the NH, combination rate constants. It could be argued that one of the overall rotational degrees of freedom should be active for both the complex and the molecule; this would merely lower the specific rate constants by about a factor of 2 (5). The specific rate constants and distribution functions, f(~), of activated N2H4 molecules formed by NH, association were computed from standard equations (5) and are shown in Figs. 1 and 2. These rate constants must be matched against a collisional deactivation model and then averaged over the distribution function to obtain quantities (SID, k,) which can be compared to

3 SETSER AND RICHARDSON: UNIMOLECULAR DISSOCIATION RATE CONSTANTS 2595 FIG 1. Hydrazine R.R.K.M. specific rateconstants for models I and I1 as a function of the energy in the molecule; E~ = 56.8 kcal mole-' XCOl t$s 7.15 kcal (0 = 7.80 kc01 IS 20 d5 ENERGY ABOVE Emin ( kcal/mole ) FIG. 2. Distribution functions of activated NZH, molecules in chemical (reaction[l]) and thermal activation. The average energies are specified for each distribution function. -.-, thermal activation at 1200 OK; - - -, chemical activation model I (300, 720, 1200 OK); ---, chemical activation model II (300, 720, 1200 OK). experiment. We have used a strong collision formulation with the appropriate equations (3, 5) ; the S/D results are listed in Table 11, and the k, = o(d/s) values are plotted in Fig. 3. The klk, curves often used in thermal activation studies may be constructed (3) from the S/D values of Table 11, i.e., klk, = S/(S + D). lo", -/ 1, & I I I I I I I I I I I log PRESSURE (cm) FIG. 3. Values of the chemical activation rate constants at various temperatures (OK) for model I (dotted lines) and model I1 (solid lines). The k, values match the S/D values at the indicated pressures of Table 11. Since some shock tube investigations employ a Kassel s parameter, these values were also extracted from the calculations. Kassel s values were obtained from the average energy of the reacting molecules at high pressure in thermal activation (sf = <s),f/rt), which were s' = 5.4 and 5.0 at 720 OK and s' = 6.3 and 6.0 at 1200 OK for models I and 11, respectively. These Kassel parameters were compared to those obtained by matching the shape of the Kassel and R.R.K.M. fall-off curves, and the values were quite similar, as would be expected (1 5). Since the distribution functions of N2H4 in chemical activation depend upon the model of the association complex (3), the f(s) of Fig. 2 are slightly different for models I and 11. The exact shape of chemical activation distribution functions is usually not very important. However, it is of interest for hydrazine because the average 1

4 TABLE 11 Calculated S/D values for hydrazine Temper- Pressure (cm Hg) 0 ature ("K) Cal~ulation".~.' Model lo6 lo5 lo4 lo3 lo s/ D I 1.89x F 3.15~10-~ 2: II 3.38 x lo4 3.38x a <~)r? I C (kcal/mole) I SID I ~ 3.06~ E II 2.13 x lo3 2.18x % <&)*I I C) (kcal/mole) II , s/d I x lo-z 7.24~ 9.72~ I ~ 1.16~10-~ <&)r? I (kcal/mole) I < S/D I ~ 5.51 x lo4 7.22~ lo ~10-'? I x lo-z 9.38 x lo4 1.26~10-~ 2 <&),I I w (kcal/mole) w.a temperature independent collision cross section of 3.5 A was used for the calculation of the collision frequency. b<~> t is the average in~ernal energy of the reacting molecules above E, (56.8 kcal mole-'). c~hdaveragenergy of the formed molecules for complex models (I) and (11) is 2.68 and 2.16 kcal mole-' at 300 "K, 5.61 and 5.02 kcal mole-' at 550 OK, 7.80 and 7.15 kcal mole-' at 720 "K, and 15.0 and 14.3 kcal mole-' at 1200 OK. - - I 3

5 SETSER AND RICHARDSON: UNIMOLECULAR DISSOCIATION RATE CONSTANTS 2597 TABLE 111 Reported and calculated Arrhenius rate constants for hydrazine dissociation Reference Arrhenius rate constant (s-l) Conditions (7) 101"0 exp (-54 kcal mole-l/rt) ( OK, atm)" ( exp (-60 kcal mole-l/rt) ( OK, atm)b (6b) exp (-48 kcal mole-l/rt) ( OK, atm)' (6b) exp (- 52 kcal mole-l/rt) ( OK, atm)' Model I 6.72~ lo1' exp (-61.2 kcal mole-l/rt) 1200 OK, co pressure Model I x 1016 exp ( kcal molecl/rt) 1200 OK, co pressure - - The rate under these conditions depended upon [N2H4] and the [pressurellll. The results were "corrected" to the high pressure limit and combined with data from ref. 60 to obtain the Arrhenius parameters. bthese results were not sufficiently complete for experimental determinations of Arrhenius parameters so the authors used 60 kcal as the activation energy in order to assign a pre-exponential factor. The experiments were done at constant density which corresponds to the two pressure ranges quoted. The Arrhenius parameters were obtained under conditions where chain reactions were believed to be negligible. energies of formed molecules differ by about 0.5 kcal mole-' which enhances the difference in k, since the broader f(e) goes with the higher k, values for the calculation of S/D ratios. The distribution functions also give the average energies of reacting molecules at the low and high pressure limits. The distribution function of reacting N,H4 molecules at the high pressure limit in the thermal activation system is the same as the distribution function of formed chemically activated molecules, reaction [I.], at the same temperature. The difference in average energies of reacting molecules at the low and high pressure limits in thermal activation is 11.6 and 10.9 kcal mole-' for models I and 11, respectively. This energy difference at 1200 OK for the chemical activation is similar, 11.3 and 11.1 kcal mole- l. These large values arise from the steep energy dependence of the rate constants and the broad 1200 OK distributions. These are the same factors which cause the large change in the values of the chemical activation rate constants with pressure shown in Fig. 3. Since the difference between the average energies for the two limiting pressures, ( E ), ~ - (E):, decline with decreasing temperature (4.7 and 2.3 kcal mole-' at 550 and 300" for model I), the ratio of kam to kao also diminishes with temperature. However, even at room temperature the ratio is quite large, more than a factor of 10, due to the very steep dependence of k, upon energy in the energy range just above e0. rate constants was more reliable than the existing unimolecular decomposition data for N,H4. It is now interesting to compare the results from shock tube studies (6, 7) with the calculated predictions. Table I11 gives the Arrhenius parameters and shows serious disagreement between the calculated and experimental Arrhenius A factor. Diesen (14) seems to have directly. shown that the primary process is reaction [I ]and not the less endothermic formation of NH and NH,, and even at the lower temperatures (1400 OK) the reaction was essentially second order at 0.15 atm pressure. The rate constant at 1400 OK and 0.15 atm was reported (14) as 3 x lo3 s- ' but the accuracy of these values has been questioned (7). McHale studied the reaction at low temperatures and found that at atm the rate depended upon the square root of the total pressure (mostly argon). A correction factor was applied to the measured rate constants to give rate constants at P = a, and these rate constants were combined with other high temperature data (6a) to obtain the first set of Arrhenius parameters listed in Table 111. The recently reported rate constants of Michel and Wagner (6b) show a slight dependence upon gas density but the data are not of great accuracy. The Arrhenius parameters from their first study (6a) were merely assigned (see Table 111) and are probably not reliable. It should be noted that the experimental rate constants of Table I11 are numerically about the same at 1200 OK but differ in their temperature coefficients. Comparison of Calculated Results to The measured pressure dependence of the Experimental Data reaction and the low activation energies from The point of view adopted for these calculations most shock tube investigations to the was that our knowledge of radical combination hydrazine decomposition reaction being in the

6 2598 CANADIAN JOURNAL OF ( 2HEMISTRY. VOL. 47, 1969 fall-off region even at 2-8 atmospheres of pressure. The calculated k/km = S(S + D) values are in agreement with this. At 1200 OK and for 5 atm pressure of a unit eficiency gas, k/km is and 0.12 for models I and 11. Since argon was the actual experimental gas which has a collisional efficiency of -0.1 (16), the experimental rates should be only 10- and lo-' of the high pressure values of model I and 11, respectively. Thus if the degree of fall-off is as great as outlined above, this explains the apparent discrepancy in the preexponential factors of Table 111. It is worth noting that the calculated limiting low pressure activation energy at 1200 OK would be about 49 kcal/mole. The arguments of this paragraph indicate that the shock tube data do not provide compelling reasons for considering the N2H4 dissociation to be different from C2H6 (3) or C2F6 (16) dissociation3 reactions. If future data are obtained which show that activated complex models with a tighter structure (smaller preexponential factor and smaller steric factor) are appropriate, then those models would not require the experimental data of Table I11 to be as far into the fall-off region as they presently appear. Calculated R.R.K.M. unimolecular rate constants have been shown to satisfactorily describe a large variety of unimolecular reaction rate data (18, and recent papers by Rabinovitch) if proper models for the reaction are chosen. The arguments already presented indicate that our calculations for N2H4 should encompass the correct description of its unimolecular dissociation. Therefore, it should be possible to use the calculated results with some confidence. The calculations show (for either model) that at temperatures of 300 OK or more, pressures of 100 cm are needed to stabilize a large fraction of N2H4* formed by radical association. Most experiments have been done at considerably lower pressures, and reverse dissociation of N2H4* should have been important. From a practical point of view, stabilization 'CZF6 dissociation (17) has recently been treated by using a Gorin model for the activated complex to obtain a frequency factor of -5 x 10". The C-C distance was extended by nearly a factor of 4 relative to C,F6 which introduced a large centrifugal correction factor. Such a correction is not necessary, if the C-C distance is not extended so much and the high frequency factor is obtained from the large entropy contributions of low frequency bending vibrations, as was done in the N2H4* models of Table I. of N,H,* produced by higher energy chemical activation reactions, such as H + N2H3, would be a slow and strictly pressure dependent reaction (19). The combination reaction of NH, has been suggested in a variety (20) of photolysis and photosensitization studies of NH3 and N2H4 but only a few attempts have been made to extract rate constants. In one such effort Hanes and Bair (13a) used a pulsed radio frequency discharge in ammonia and followed the NH, concentration by ultraviolet absorption spectroscopy. The data were originally discussed in terms of a simple bimolecular association process. The error of ignoring the NH, disproportionation reaction in this treatment was pointed out by Diesen (14) In Diesen's (14) shock tube study the rate constant for disproportionation was given as 2.5 x 1013 cc mole-' s-' (2000 OK) and kd/kc was estimated as 0.4. A reinvestigation by Salzman and Bair (13b) using room temperature NH, flash photolysis revealed that the rate of NH, disappearance was dependent on total pressure in the pressure range of 5-10 Torr. Extrapolation to low pressure gave the disproportionation rate constant as 0.46 x 10" cc mole-' s-', and extrapolation to high pressure gave 2.5 x 10" cc mole-' s- ' as the combination rate constant (kc). These data give kd/kc = 0.18, which is a reasonable value by comparison with ethyl radical kinetics. However, some caution should be maintained because the high pressure extrapolation was made from data in the 1-10 Torr region which, according to Table 11, are 2 orders of magnitude away from the high pressure limit. A recent investigation (21) of NH, kinetics used an ammonia glow discharge flow system as the NH, source. The reported kd/kc ratio was 1.O, but the absolute values of the rate constants seem impossibly low. The pressure dependence of the rate of NH, combination found by Bair is in qualitative agreement with the calculated results. Further data are required before any discrimination can be made in favor of model I or 11. The decomposition of N2H4 was assumed to be a reaction similar to the decomposition of C2H6 or CH3CH0 for which R.R.K.M. calcula-

7 SETSER AND RICHARDSON: UNIMOLECt JLAR DISSOCIATION RATE CONSTANTS 2599 tions have been done. It is instructive to compare the results from chemically activated C2H6 and CH3CH0 to those of Table 11. Similar models should be used for the comparison, and we will compare models that most nearly resemble model I for N2H4. The easiest comparison is the half quenching pressures (SID = 1) which are 1, 7, and 1400 Torr, at 300 OK for C2H6*, CH3CH0 :" and N,H4" respectively. In this series the critical energies are 85.3, 79.0, and 56.8 kcal, and the number of active degrees of freedom successively decline by 3 for each member. Detailed examinations of the relative values of sums and densities of states for these three reactions show that the increase in rate constant for N2H4 relative to CH,CHO is due to both the lower critical energy (about a factor of 15) and to the smaller number ofvibrational degrees of freedom. Thevibrational frequencies for N2H4 are higher than those for CH,CHO which also enhances the difference in rate constants for N2H4 relative to CH3CH0. Although the models for C2H6, CH3CH0, and N,H4 dissociation reactions are not strictly comparable, it is worth noting that CH3CH0 is the anomalous member of the series due to the fact that replacing 2 hydrogen atoms by 1 oxygen atom introduces sufficiently low frequencies in the CH3CH0 molecule, so that the density of states for CH,CHO is nearly the same as for C2H6. Acknowledgments This work was supported by the U.S. National Air Pollution Control Administration, Consumer Protection and Environmental Health Service, Public Health Service under contract AP W. C. RICHARDSON. Master's Thesis, Kansas State University, Manhattan, Kansas (a) R. A. MARCUS and 0. K. RICE. J. Phys. Colloid Chem. 55, 894 (1951). (6) R. A. MARCUS. J. Chem. Phys. 20, 352 (1952); 43, 2658 (1965). 3. B. S. RABINOVITCH and D. W. SETSER. Advan. Photochem. 3, 1 (1964). 4. (a) D. W. SETSER and B. S. RABINOVITCH. J. Chem. Phys. 40, 2427 (1964). (6) M. C. LIN and K. J. LAIDLER. Trans. Faradav Soc (1968). 5. D. W. SETSER. J. Phys. dhern. 70,'826 ( (a) K. W. MICHEL and H. GG. WAGNER. Technical Summary Report No. 3, Contract No. AF61 (514) (1962). (6) K. W. MICHEL and H. GG. WAGNER. 10th Intern. Symp. Comb. Cambridge p E. T. MCHALE, B. E. KNOX, and H. B. PALMER. 10th Intern. Symp. Comb. Cambridge p. 341, and Project Squid Technical Report PSU-12-D (1964). 8. JANAF Therrnochernical Tables. The Dow Chemical Company, Midland, Michigan. August, 1965; Addendum 1, August, 1966; Addendum 2, August, (a) J. S. ZIOMEK and M. D. ZEIDLER. J. Mol. Spectry. 11, 163 (1963). (6) A. YAMAGUCHI, I. ICHISHIMA, T. SHIMANOUCHI, and S. MIZUSHIMA. Spectrochim. Acta, 16, 1471 (1960). 10. (a) K. A. WILDE. J. Chem. Phys. 41, 448 (1964). (6) Z. PRASIL and W. FORST. J. Phys. Chem (1967). 11. (a) W. FORST. J. Chem. Phys. 48, 3665 (1968). (6) E. TSCHUIKOW-ROUX. J. Chem. Phys. 49, 3115 (1968). \- ~ ~,- 12. D. E. MILLIGAN and M. E. J~cox. J. Chem. Phys. 43,4487 (1965). 13. (a) M. H. HANES and E. J. BAIR. J. Chem. Phys. 38, 672 (1963). (6) J. D. SALZMAN and E. J. BAIR. J. Chem. Phys. 41,3654 (19641, and private communications. 14. R. W. DIESEN. J. Chem. Phys. 39, 2121 (1963). 15. D. W. PLACZEK, B. S. RABINOVITCH, G. Z. WHITTEN, and E. TSCHUIKOW-Roux. J. Chem. Phys. 43,4071 (1965). 16. F. FLETCHER, B. RABINOVITCH, K. WATKINS, and D. LOCKER. J. Am. Chem. Soc. 70,2823 (1966). 17. E. TSCHUIKOW-Roux. J. Chem. Phys. 43, 2251 (1965); 49, 3115 (1968). 18. (a) C. W. LARSON, B. S. RABINOVITCH, and D. C. TARDY. 47, 4570 (1967). (6) K. DEES and D. W. SETSER. J. Chem. Phys. 49, 1193 (1968). 19. P. K. GHOSH and E. J. BAIR. J. Chern. Phys. 45, 4738 (1966). 20. (a) C. C. MCDONALD and H. E. GUNNING. J. Chem. Phys. 23, 532 (1955). (6) D. HUSAIN and R. G. W. NORRISH. Proc. Roy. Soc. London, Ser. A, 273, 145 (1963). 21. D. C. CARBAUGH, F. J. MUNNO, and J. M. MAR- CHELLO. J. Chem. Phys. 47, 5211 (1967).