J. Phys. Chem. 1988, 92, 2442-2448
2442
complexes studied here, although interaction with the C-N triple-bond P electron density cannot be ruled out. The extrapolation from a perturbed potential function to binding energy is risky and yet commonly done on a qualitative basis. Within the limitation, the shifts here suggest a stronger interaction between C1F and (CH3)3Nthan between ClF and NH,. This is contrary to the ab initio calculations of SchaeferZSand of Morokuma,26 who predict distinctly greater binding for the NH3 complex. The current results, on the other hand, are in good agreement with the solution binding energies of I, complexes of a number of amine^.^*^^ The discrepancy may lie in the relatively small basis set used for the T M A system (although a relatively large basis set was used for the NH3/C1F system). The difficulty may, of course, lie with the extrapolation of shift in frequency to binding energy. In any event, it is noteworthy that the shift in the C I F S ( C H ~ ) ~complex N was roughly 50% greater than the shift in the CIF-NH, complex. An interesting result from the present study is the magnitude of the matrix shift between argon and nitrogen matrices. For nonpolar or somewhat polar molecules, this shift is typically quite ~ m a 1 1(approximately ~ ~ ~ * ~ ~ 4 cm-' for parent ClF, with a dipole moment47of 0.88 D). For very polar molecules and for ion pairs, this shift can be much larger,28a,48-50 on the order of 50-100 cm-I. The shifts observed here for the N H 3 and TMA complexes were on the order of 30-50 cm-I, which suggests considerable charge redistribution in the complex. The limiting configuration of [NH3Cl]+.F is undoubtedly not correct, but these large matrix shifts do indicate a formulation with some partial charge dis(45) Nagakura, S.J. Am. Chem. SOC.1958,80, 520. (46) Craddcck, S.;Hinchliffe, A. J. Matrix Isolation; Cambridge University Press: New York, 1975. (47) Gilbert, D. A,; Roberts, A,; Griswold, P. A. Phys. Reu. 1949, 76,
1723.
(48) Ault, B. S.; Andrews, L. J . Chem. Phys. 1915, 62, 2320. (49) Pimentel, G. C.; Charles, S. W. Pure Appl. Chem. 1963, 7, 11 1. (50) Barnes, A. J.; Hallam, H. E. Q.Rev., Chem. SOC.1969, 23, 392.
tribution of this type. This is consistent with the considerable intensification of the Cl-F stretching mode and the lowering of the stretching frequency. The results for the CIF/HCN system are, at first glance, puzzling in that no reaction was detected. However, H C N is clearly the weakest base of the set and should perturb C1F the least. With proton affinities4I as a guide (which from Figure 2 appears appropriate within a family), this mode should come between 720 and 740 cm-I. However, this region is obscured by the intense bending mode of monomeric and dimeric HCN. Consequently, it is very likely that a weak complex is formed but the most distinctive feature, the Cl-F stretch, is hidden by intense parent modes.
Summary Stable complexes of CIF with several nitrogen-containing bases have been characterized through matrix isolation infrared spectroscopy. All complexes were characterized by a red-shifted C1-F stretching mode, as well as certain perturbed base modes. Assignments were confirmed by using deuteriated counterparts of the bases. The focus of the characterization was on the red-shifted C1-F stretching mode, where the magnitude of the shift correlated well with the intrinsic basicity of the base subunit, as measured by either proton affinity or ionization potential. However, while the correlation was effective within the series of nitrogen-containing bases, the trend did not hold when comparing bases with different donor atoms. Qualitatively, HSAB provides a better predictor of magnitude of interaction than does proton affinity or ionization potential over a wide range of bases. Acknowledgment. The authors gratefully acknowledge support of this research by the National Science Foundation through Grant C H E 84-00450. N.P.M. also thanks the University Research Council of the University of Cincinnati for a summer fellowship and the Department of Chemistry for a Lowenstein-SchubertTwitchell fellowship.
Formation of H and D Atoms in Pyrolysis of Benzene-ds, Chlorobenzene, Bromobenzene, and Iodobenzene behind Shock Waves V. Subba Rao and Gordon B. Skinner* Department of Chemistry, Wright State University, Dayton, Ohio 45435 (Received: February 17, 1987; In Final Form: July 20, 1987)
Highly dilute mixtures of benzene-d6, chlorobenzene, bromobenzene (including the 4-d and 2,4,6-d3isotopic compounds), and iodobenzene in argon were pyrolyzed behind incident shock waves with a total pressure of 0.4 atm and temperatures between 1450 and 1900 K. H and D atom concentrations were measured, both of them for the partially deuteriated bromobenzenes. Rate constants for dissociation of benzene and of the phenyl radical were determined, but attempts to deduce the specific mechanism or mechanisms of phenyl radical dissociation from the product distributions from partially deuteriated bromobenzenes were unsuccessful. RRKM calculations were made to evaluate unimolecular falloff and to evaluate the rate constant for dissociation of C6H6 from that of C$6.
Introduction The main goal of this work has been to investigate the first elementary steps in the pyrolysis of benzene under shock-tube conditions. One expected first step is loss of H by the reaction C6H.5 C6H5 + H -+
which could be followed by steps such as
H
-t C,H6
-+
C&5
+ H2
and decomposition of the phenyl radical by reactions such as 0022-3654/88/2092-2442%01.50/0
C6H5
+
C4H3
+ C4H3 C4H2 + H
C2H2
+
All of the above reactions were suggested by Bauer and Aten,' who made the first shock-tube study of benzene pyrolysis. Formation of C2H2and C4H2as major products of benzene pyrolysis has been reported by Smith and Johnson2 on the basis of Knudsen (1) Bauer, S. H.; Aten, C. F. J . Chem. Phys. 1963, 39, 1253. D.; Johnson, A. L. Combust. Flume 1983, 51, 1.
(2) Smith, R.
0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988 2443
Pyrolysis of Benzene cell/mass spectrometer studies, and by Kern et aL3 by the shock-tube/mass spectrometer method. W e recently4 reported results on the pyrolysis of benzene-d6 behind reflected shock waves, a t an average total pressure of 2.7 atm and in the temperature range 1630-1940 K, using very dilute mixtures containing 3-20 ppm of C6D6 in argon. Use of these low concentrations avoided the consecutive chain reactions that would be expected to occur in earlier work referred to in that paper, only unimolecular reactions being of major importance. In the same paper we reported on the formation of H atoms from the phenyl radical, produced by dissociation of chlorobenzene. Since phenyl radical was found to dissociate much faster than benzene, the overall process can be written (in terms of ordinary benzene) as C&j
-+
C2H2 + C4H2 + 2H
where the molecular products are known from the mass spectrometric studies. These studies suggest that other minor reaction channels exist, and of course if the benzene concentration is increased the product distribution will change substantially due to bimolecular reactions. One of the concerns in our earlier work4 was the extent of unimolecular falloff in the dissociation of benzene and phenyl. Since then, we have modified our shock tube so that measurements can be made behind incident waves, at pressures of 0.3-0.6 atm, a factor of 5-10 below the earlier studies. We have studied not only benzene and chlorobenzene, as before, but also bromobenzene and iodobenzene, which decompose faster than chlorobenzene and would be expected to give better data on phenyl dissociation. Finally, we have measured H and D concentrations in pyrolysis of partially deuteriated bromobenzenes, with the goal of learning more about the mechanism of phenyl dissociation. Since the publication of that paper, Frenklach, Clary, Gardiner, and SteinS suggested that phenyl radicals could be formed by addition of vinyl to diacetylene or of acetylene to C4H, to produce a "linear" C6H5of formal structure H e C - C H = C H - C H = CH, which then cyclizes to give phenyl radical with a low activation energy as there is no need for rearrangement of H atoms. Colket6 has recognized the reverse of this process as a likely channel for phenyl radical dissociation, based on his single-pulse shock-tube findings of C2H2and C4H2as the main products of benzene pyrolysis at low concentrations (not much higher than those used by Smith andd Johnson in their Knudsen cell/mass spectrometer work). His studies showed that these species can be produced directly by dissociation of benzene and phenyl radical, whereas in earlier shock-tube studies (other than our own) most of the observed products were formed by secondary reactions. Consideration of linear C6H5 adds another intermediate elementary step to the mechanism of Bauer and Aten.' While Colket's mechanism is not at all established as the only channel for phenyl dissociation, it is consistent with observed product distributions from low-concentration experiments and is reasonable according to general chemical principles. Therefore we have used this approach in the interpretation of our data and in making calculations on the pressure dependence of rate constants.
Experimental Procedures Our apparatus and techniques for measurements behind reflected shock waves have been described in an earlier paper.' We used a stainless steel shock tube with a test section 7.6 cm in (3) Kern, R. D.; Wu, C. H.; Skinner, G. B.; Rao, V. S.; Kiefer, J. H.; Towers,J. A.; Mizerka, L. J. Symp. (Inr.) Combust. [Proc.],20, 1984 1985, 789. (4) Rao, V. S.; Skinner, G. B. J. Phys. Chem. 1984, 88, 5990. (5) Frenklach, M.; Clary, D. W.; Gardiner, Jr., W. C.; Stein, S. Symp. ( I n r . ) Combust. [Proc.],20, 1984 1985, 887. (6) Colket, 111, M. B. Presented at the National Meeting of the American Chemical Society, Division of Fuel Chemistry, New York City, April 13-16, 1986. (7) Chiang, C.-C.; Lifshitz, A.; Skinner, G. B.; Wood, D.R. J . Phys. Chem. 1979, 70, 5614.
diameter and 4.5 m long. Concentrations of H and D were measured earlier by resonance absorption behind the reflected shock wave, 2 cm from the end plate of the shock tube. For measurements behind the incident wave, the measurement station was not moved, but a 1.8-m extension was added to the tube so formation of the reflected wave was delayed beyond the desired test time. The microwave discharge lamp used to produce the Lyman-a radiation (source B of ref 7, with 0.1% H2 or D2 in helium at a lamp pressure of 2.5 Torr and with 40-W microwave power) had been characterized in terms of emitted line shape and also calibrated empirically. The calibration of most value for these experiments involves dissociation of very dilute mixtures of 2,2dimethylpropane (neopentane) which was shown by Tsang* to produce 0.9 f 0.1 atom of H per initial mole of reactant at temperatures near 1400 K, at which dissociation of the neopentane is essentially complete, but the products are stable. This method gives a calibration based on stoichiometry rather than kinetics, and we consider the absolute uncertainty in our calibration to be f20%. Knowledge of the profiles of the H and D profiles emitted by our lamp provide a basis for obtaining the temperature dependence of the calibration and the change in calibration when D rather than H is measured. We isolated the Lyman-a line by using the filter system described in ref 7 . Temperatures were calculated from the incident shock speed, while the incident shock pressure was also measured. Within our 2-3% accuracy of pressure measurement, the observed pressures were the same as those calculated from the shock speed, and pressure did not vary more than 2-3% throughout an experiment. Accordingly, we have estimated that the uncertainty in temperature is no more than 1.4%, or 20-30 K over the experimental range. Benzene-d6was from Kor Isotopes and was stated to have 99.96 atom % D. Chlorobenzene was reagent grade, from Fisher Scientific Co., with a boiling range of 131.7-132.0 "C. Bromobenzene was also from Fisher, with a boiling range of 155.4-156.4 "C. Iodobenzene, from Pfalz and Bauer, Inc., was 98% in purity with a boiling range of 70-72 "C at 12 Torr pressure. Bromobenzene-4-d and bromobenzene-2,4,6-d3 were from MSD Isotopes and said to be of 98% isotopic purity. All of the liquids were degassed by several freeze-pump-thaw cycles, and about onequarter was evaporated off before gas mixtures were made up. Argon was from Airco, Inc., Research Grade, 2 ppm total impurity, with less than 0.5 ppm hydrocarbons reported as methane.
Experimental Results Fifteen experiments were carried out on pyrolysis of 10 ppm benzene-d6 in argon, in the temperature range 1650-1 900 K and at an average pressure of 0.41 atm, the standard deviation in pressure being 0.04 atm. Because of the lower concentrations of benzene compared to our earlier experiments almost negligible corrections (about 1%) had to be made for absorption of Lyman-a radiation by the reactant. As before, we assumed that boundary layer cooling had no effect on our results. The only effect would be loss of a few percent of the atoms near the windows, and since the effect would also occur during our empirical calibrations, it seemed that the errors would largely cancel. The time constant of our optical system was 5 ps, but since the density ratio p 2 / p I was about 4 for our experiments, the time constant in terms of particle time was 20 1s. Particle times for complete experiments ranged from 200 to 1500 ps, during which pressures remained constant within expermental error. The general comments of this and the preceding paragraph also apply to the other results described in this section. For each benzene pyrolysis experiment, the graph of [D] versus time was nearly linear, although those at higher temperatures tended to be slightly concave downward (perhaps due to depletion of the reactant) and at temperatures in the middle of the range, slightly concave upward. It was not difficult to measure initial slopes of the graphs, from which rate constants could be calculated. (8) Tsang, W. J . Chem. Phys. 1966, 44, 4283.
2444
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988
Rao and Skinner
T,K 1900
1800 I
I700 I
I
u)
n Y
1 0 ~, K1 ~ Figure 1. Initial rate constants for formation of D in pyrolysis of 10 ppm C6D6at an average total pressure of 0.41 atm. The line is for the least-squares Arrhenius expression through the points.
Time , microseconds Figure 2. Typical curves for formation of H and D from bromobenzene-4-d, 10 ppm in argon: (0)H atoms, 1541 K, total pressure 0.27 atm; (A) D atoms, 1552 K, total pressure 0.37 atm. Lines are values
calculated from kinetic model. These are shown in Figure 1. equation is
The least-squares Arrhenius
kD = 1.7 X l o i 5 exp(-107400 cal/RT) s-’ where the standard deviation of the points in terms of log k is 0.05, or a factor of 1.12. The 95% confidence level in E is 6 kcal. By the mechanism mentioned in the Introduction, part of the observed D comes from benzene directly, part from phenyl radicals. At the higher temperatures, phenyl radicals will dissociate quickly so the stoichiometric coefficient for D will be close to 2, but at the lower temperatures the second D may not be formed so soon, and the stoichiometric coefficient will be smaller. For this reason, the observed activation energy of 107.4 kcal may be greater than that for benzene dissociation. This point is addressed in the Discussion. Pyrolysis of chlorobenzene was studied in nine experiments with 10 ppm chlorobenzene in argon, a temperature range of 1600-1900 K, and a total pressure of 0.42 f 0.05 atm. It can be seen from the temperature range that chlorobenzene is not much more easily decomposed than benzene itself. The graphs of [HI versus time were slightly concave upward, the effect increasing at lower temperatures, as expected since the H is coming from a secondary reaction. However, the small curvature clearly shows that phenyl radicals dissociate much faster than chlorobenzene over the experimental range. The bromobenzene results were the most useful for the understanding of phenyl dissociation. We studied the pyrolysis of 5 ppm of C6HSBr, and 10 and 2 ppm of C6H,DBr-4-d and C6H2D3Br-2,4,6-d3,all in argon. For the last two compounds we measured formation of both H and D. Overall, a total of 66 experiments were carried out in the temperature range 1450-1800 K, at an average total pressure of 0.34 atm, with a standard deviation of 0.06 atm. In these experiments the upward curvature of the graphs of [HI and [D] versus time was quite noticeable, particularly at the lower temperatures, as shown in Figure 2, so that modelling could lead to better rate constants for phenyl dissociation than we could get from the chlorobenzene data. We were able to get direct information on the stoichiometry of phenyl radical dissociation in terms of hydrogen from our high-temperature data where H and D concentrations levelled off at longer times when all of the phenyl radical had decomposed. This had not been possible in our higher pressure runs since complete dissociation led to atom concentrations higher than we could measure, so we had made the assumption that 1 atom was produced per phenyl radical. From bromobenzene-4-d we found that at high temperatures 0.70 f 0.03 atom of H and 0.12 f 0.02 atom of D were produced per mole of bromobenzene or a total of 0.82 f 0.04. These uncertainties are based only on variations in analysis from one experiment to another, and if the uncertainties in calibrations and sample preparation are included, the overall stoichiometry might
0
4
c
P
9
IOPPM
1523 K ‘0
200 400 600 800 1000 2000
Time , microseconds Figure 3. Formation of H atoms in pyrolysis of iodobenzene: (0) 10 ppm, 1531 K, 0.36 atm, initial [C,H,I] = 28.7 X IO-’* mol cm-); (V) 10 ppm, average of two experiments at 1464 K, 0.38 atm, initial [C6H5J] = 31.6 X mol cm-); (0)1 ppm, 1523 K, 0.38 atm, initial [C,H,I] mol ~ m - Lines ~ , are empirical curves to show trends. = 3.04 X
best be reported as 0.8 f 0.3 atom of H and D per molecule of bromobenzene. This result is a fairly satisfactory one, although there are some natural questions that arise and are considered in the Discussion. For iodobenzene we studied 1 and 10 ppm mixtures of undeuteriated compound in the temperature range 1450-1800 K, the same range as for bromobenzene, at an average total pressure of 0.35 f 0.04 atm, with a total of 16 experiments. With 1 ppm iodobenzene, we found 0.75 f 0.3 atom H per molecule of initial iodobenzene at the higher temperatures. However, the iodobenzene results differed in two important ways from those for bromobenzene. First, at earlier times the graphs of [HI versus time were nearly straight, rather than being concave upward, and this was true even at the lower temperatures. Second, for all except the highest temperatures, the [HI values for 10 ppm experiments tended to level off, or to rise quite slowly, at longer times at values much less then expected if 0.75 atom of H is produced per iodobenzene molecule. Typical results showing these features are shown in Figure 3. The initial linear rise in all three curves is clearly seen. At 1200 ~ sthe , 1 ppm mixture had produced 0.43 atom per original molecule, the 10 ppm mixture at the same temperature (1 53 1 K) only 0.24. The 10 ppm mixture at 1464 K had produced only 0.09 atom per original iodobenzene at 1200 ps, yet the slope of the graph is much less than initially. The suggestion is that iodobenzene is dissociating by a different
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988 2445
Pyrolysis of Benzene mechanism than chlorobenzene and bromobenzene. We did obtain a least-squares Arrhenius curve for the first-order rate constant for initial formation of H atoms from iodobenzene
kH = 2.8
X
lo1*exp(-69.4 kcal/RT)
TABLE I: Important Reactions in Pyrolysis of Benzene, Chlorobenzene, and Bromobenzene, 0.4 atm, 1500-1900 K reaction
s-l
the 95% confidence level in the activation energy being 7.6 kcal and the standard deviation of the points in terms of log k being 0.12, or a factor of 1.3. Both 1 and 10 ppm data fitted equally well to this equation for initial slopes, although they would not have if longer time behavior had been considered.
Discussion In considering our results it should be kept in mind that, at our very low concentrations of reactants, unimolecular reactions dominate over bimolecular ones. Most of the processes that are important at higher concentrations can be neglected under ours. For example, the data of Nicovich and Ravishankarag and ourselves4 show that abstraction of H from benzene by H atoms is unimportant. The most important bimolecular process is addition of H to the ring, followed (rapidly, at our temperatures) by elimination of an atom. If D is added to C6D6 and another D lost, of course no detectable reaction occurs, but if H adds to bromobenzene, it might be reasonable to expect that Br would be eliminated, since the C-Br bond is about 30 kcal weaker than the C-H bond in this situation.I0 The same argument would apply less strongly to chlorobenzene. We have assumed that H atoms add at equal rates to benzene and the halobenzenes, and that halogens are eliminated. Using the rate constant for addition of H to benzene from our earlier paper, we find that up to 10% of the H or D atoms can be lost this way in an experiment with 10 ppm chlorobenzene or bromobenzene. With lower initial concentrations of reactants, the losses are corresponsingly lower. This is the only bimolecular reaction that we believe affects the H or D atom concentrations by more than 1%. Dissociation of phenyl radical should be considered first, since that result can then be used in analysis of benzene dissociation. The chlorobenzene and bromobenzene data are both good for this purpose, the latter being somewhat better since they go to lower temperatures. The iodobenzene data are not what we expected, and to understand them we had to assume that other products besides phenyl radicals and I atoms are produced from iodobenzene. To proceed with the analysis an assumption needs to be made about the stoichiometry. We could assume that 1 hydrogen is produced per bromobenzene (and chlorobenzene) and correspondingly 1 per phenyl, the experimental value of 0.82 being close enough, within experimental error. There are, though, some reasons why the ratio might not be exactly 1: (a) Perhaps some of the halobenzenes go to products other than phenyl radical plus halogen atom that do not lead to H formation. (b) Perhaps some of the phenyl radical goes to a product other than linear C6H5, which does not produce hydrogen. (c) Perhaps some of the linear C6H5decomposes in such a way that H is not produced. Actually, since according to Colket’s model6 the linear C6H5decomposes very quickly, we cannot distinguish between suggestions (b) and (c) in our experiments. So, since it seems best to stay as close to the experimental results as possible, and to make the simplest assumptions, we have assumed that 18% of the phenyl radical dissociates in some way without formation of H, while the rest does produce H, presumably via linear C6H5. In the worst case, this assumption could produce a 20% error in our calculated rate constants. Pyrolysis of chlorobenzene and bromobenzene could be modelled quite well by using the data for reactions 2-9 of Table I. We found that the same rate constant could be used for dissociation of the variously deuteriated phenyl radicals we produced, which was to be expected since the rate-limiting reaction consists pri(9) Nicovich, J. M.; Ravishankara, A. R. J. Phys. Chem. 1984, 88, 2534. (10) McMillen, D. F.; Golden, D. M. Annu. Reu. Phys. Chem. 1982, 33, 493.
A , mol cm3 SKI E , kcal 9.3 x 1014 io6 5.0X lOI4 105 5.0 x 1013 73 3.2 X 10” 85 1.5 X 10” 72 7.2 x 1013 3.4
calcd from 1D this work this work this work this work 1
4.8 x 1013
1
2.2 x 1015
3.4 38
Same rate constants used for isotopic variants.
ref
6 Same as reaction
5. ‘Same as reaction 7.
marily of the breaking of a C-C bond. Similarly, loss of Br from bromobenzene was not appreciably affected by deuterium substitution on the ring. It is understood that all of the unimolecular reactions are in the intermediate falloff region, and the Arrhenius parameters of Table I are appropriate under our experimental conditions (1400-2000 K, -0.4 atm). For the iodobenzene results we found it necessary to introduce additional reactions to model the data. In a very recent paper, Robaugh and Tsang‘ measured the conversion of iodobenzene into benzene by pyrolyzing it in the presence of a large excess of cyclopentane, so that whenever a phenyl radical was produced it would immediately react with cyclopentane to produce benzene. Their rate constant for dissociation of iodobenzene to phenyl radicals and I atoms near 1100 K and at 2-6 atm total pressure is given by klo = 8.6 X lo4 exp(-32821/T) s-’. If this expression and the Table I expression for reactions 2 and 9 are used to model our iodobenzene data, a poor fit is obtained. The calculated [HI values are somewhat above the observed ones at the beginning of the experiments and become progressively worse at longer times due to the curvature of the graphs, as shown in Figure 3. Reasonable reductions in k l oto allow for unimolecular falloff in going to our experimental pressure of 0.4 atm made no noticeable improvement. We could match the data quite well by assuming that some of the iodobenzene dissociates to C6H4and HI. This would not be inconsistent with Robaugh and Tsang’s work since C6H4should also be converted to C6H6 in an excess of cyclopentane. We assumed that C6H4produces H atoms rather slowly, and that HI reacts with H in the normal way.’, We should note that the rate of dissociation of iodobenzene is much faster than the rate of formation of H, so in these experiments all the iodobenzene disappears at the beginning of the experiment and an analogue of eq 5-8 for the reaction of H with iodobenzene is not needed. A good fit (standard deviation of the ratio of observed to calculated [HI of 20%) was obtained by using the Robaugh and Tsang expression for overall dissociation of iodobenzene, assuming a product distribution of 27% C6H5 I and 73% C6H44- HI along with the following rate constants:
’
-+ + - +
k2(C6H5
l-C6H5) = 3.0 X loi3 exp(-73 kcal/RT) s-l
k9(l-C6H5
kll(C6H4 k12(H
HI
+
H
products), same as Table I
other products) = 2 X l o i 3 exp(-77 kcal/RT) s-l
H,
I) = 5.0 X 10” exp(0.7 kcal/RT) mol-’ cm3 s-’
with k , , taken from ref 12. The best value for k2 is 0.6 of the Table I value, not too bad agreement, and if the Table I value (11) Robaugh, D.; Tsang, W. J . Phys. Chem. 1986, 90, 5363. (12) Kerr, J. A.; Moss, S. J. In CRC Handbook of Bimolecular and Termolecular Reactions; CRC: Boca Raton, FL, 198 1 .
2446
Rao and Skinner
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988
H
/ ”i
+
H/
6
t H
Figure 4. Mechanism for dissociation of phenyl proposed by Frenklach,
Clary, Gardiner, and SteinSand Colket6 is used in the model with optimum values of the original product distribution and kll, the standard deviation increases only to 22%. Because of the speculative nature of adding C6H4to the model for iodobenzene pyrolysis, we do not want to use the derived rate constant to modify the results of Table I, but simply note that the iodobenzene results give general support to the Table I values. The rate constant for reaction 2 in Table I is for the total disappearance of phenyl radicals by all channels. The experiments with partially deuteriated bromobenzenes were for the purpose of learning in more detail what these channels are. We found that, from bromobenzene-44, we obtained 0.71 f 0.4 mol H and 0.11 f 0.02 mol D per mole of reactant, while from bromobenzene-2,4,6-d3 we obtained 0.41 f 0.04 mol H and 0.39 f 0.04 mol D per mole, with 0.18 mol of reactant in each case producing neither D nor H , as discussed above. The stated uncertainties are relative ones reflecting reproducibility of the data among experiments, while absolute uncertainties are 25-30%. These ratios reproduced all of the data from low to high temperatures (small to essentially complete dissociation of phenyl radical) which indicates that isotope scrambling due to movement of hydrogen atoms is either very fast, so that scrambling is complete before appreciable dissociation occurs, or relatively slow. If it is assumed that the H and D atoms scramble slowly, then one calculates that we get 0.1 1 atom from C4, 0.14 from each of C2 and c6, and 0.205 from each of C3 and C5(see Figure 4). This would indicate that several processes are happening simultaneously. If reaction is assumed to occur initially to form linear C6H5,as shown in Figure 4, then dissociation to C2H2,C4H2, and H, the main Colket mechanism, would release H from carbons 6 and 2. Linear C6H5could itself lose an H from the 4 position to form C6H4. Loss of H from carbon 5 (or the equivalent carbon 3) would seem to require at least momentary formation of a diradical, followed by a hydrogen migration. This seems a less likely process, yet appears to be the most popular pathway. Since the above product distribution seems rather odd, we think that isotope scrambling does occur rapidly on phenyl radicals, so that our distributions are not meaningful for determining reaction pathways. We had hoped to obtain clear evidence for a particular reaction channel, and have not done so. Perhaps, though, our data will prove meaningful in the future when combined with other information. A brief comment should be made concerning reaction 9, which we adopted from Colket.6 Reaction 9 is too fast to affect the modelling results, or to have its rate constant determined from our data. We consider that once linear C6H5is formed, all of it dissociates immediately to form products, including H atoms. Colket’s equation gives k9 = 1.4 X 1O’O sT1 at 1600 K, which would certainly suggest rapid disappearance of linear C6H5. Interestingly, though, in his analysis he chose a substantially larger value of k2 (1.3 X 1O’s-I at 1600 K, 25 times our value of 5.3 X lo3s-I) and from the equilibrium constant K2 he found k_2to be 3.1 X 1 O l o
s-l. Therefore, according to his view about 2/3 of the linear C6H5 formed goes back to phenyl radical, and only to later products, so the effective rate constant for conversion of phenyl radical to final products is only ‘/3k2. With our smaller k2 and the same equilibrium constant, our value of k-* is less than 10%of k9 and therefore has little effect on the course of the reaction since only a small fraction of linear C6H5will go back to phenyl radical. In comparing our k2 to Colket’s, we should then consider several points: (a) As described above, his “effective” value for k2 is only (at 1600 K) of the nominal value of 1.3 X lo5 s-’. (b) His data were at 7 atm total pressure, so a higher value would be expected (but not a factor of 8 higher). (c) Our experience in modelling was that the rate of formation of D (and presumably of other products) is not affected strongly by k2, because even with our value the reaction is limited by klD. Perhaps Colket’s data could be fitted almost as well by use of somewhat smaller k2 values. Since we have now determined rate constants for some of the unimolecular reactions of Table I at more than one pressure, and since others have made measurements at still different pressures, it is worthwhile to consider their pressure dependence using the RRKM approach. We have used a program similar to that described by Stein and Rabinovitch,13 with the Beyer and Swinehart a l g ~ r i t h m ’to~ provide an exact count of densities of quantum states (in our case assuming harmonic oscillators). An important consideration is the collisional efficiency of the argon diluent, which is a very weak collider for intermolecular energy transfer. We have used Troe’s15 equation Pc
1 - PC‘I2
= -- ( A E ) FEkT
to evaluate the collisional efficiency, P,. In the equation, ( A E ) is the total average energy transferred per collision, which has been shown to be about 130 cm-I for transfer of energy between vibrationally excited toluene molecules (not too different from the species we are studying) and argon.16 FE is the ratio of the area under the Boltzmann distribution curve above the energy needed for reaction, E,, to RT times the Boltzmann factor at Eo. This can be obtained easily as part of the RRKM calculation. It is close to 1 for small molecules, but for our molecules it lies between 2 and 4 at 1700 K. This is about as large a value of F E for which Troe’s equation is valid. The calculated values of P, are all in the range 0.02-0.04. The general nature of the RRKM calculations can be described briefly. For reactions 1, lD, 3, and 4, an appropriate stretching vibration was taken as reaction coordinate. Two bending frequencies associated with the leaving atom were substantially lowered (factor of 0.3) from those of the molecule, and two other bending frequencies were somewhat lowered. Energies of reaction (converted to 0 K) were taken from McMillen and Goldenlo with a zero-point energy difference calculation for C6D6. Vibrational frequencies of C6H6 and C6D6 were taken from S h i m a n o ~ c h i ’ ~ and of C6H5C1and C6H5BT from Whiffen’* and Kidoh, Ishii, Iwamoto, and F ~ k u s h i . ’ For ~ phenyl a vibrational spectrum was generated mainly by removing one stretching and two bending frequencies from that of benzene, and then making some small changes based on the calculations of Pacansky and Schrader” comparing ethane and the ethyl radical. For reaction 2 a ring deformation frequency was taken as reaction coordinate, and several other ring and bending frequencies moderately reduced. (13) Stein, S. E.; Rabinovitch, B. S. J . Chem. Phys. 1973, 58, 2438. (14) Beyer, T.; Swinehart, D. F. Commun. ACM 1977, 16, 379. ( 1 5 ) Troe, J. J . Chem. Phys. 1977, 66, 4758. (16) Hippler, H.; Troe, J.; Wendelken, H. J. J . Chem. Phys. 1983, 78, 6709. (1 7 ) Shimanouchi, T. Tables of Molecular Vibrational Frequencies; Consolidated Vol. 1, NSRDS-NBS-39; National Bureau of Standards: Washington, DC, 1972. (18) Whiffen, D. H. J . Chem. SOC.1956, 1350. (19) Kidoh, K.; Ishii, T.; Iwamoto, Y . ;Fukushi, S. Chiba Kogyo Daigaku Kenkyu Hokoku, Riko-hen 1980, 25, 5 .
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988 2447
Pyrolysis of Benzene
TABLE 11: Calculated Falloff Parameters for Unimolecular Reactions of Table I reaction property
1
En, kcal high-press. Arrhenius parameters, 1700 K A,, s-I E,, kcal Arrhenius parameters, 1700 K, 300 Torr of Ar A , s-’ E , kcal &, 1700 K k 3 ~ ) ~ ~ 1700 ~ ~ /Kk ~ FE, -1700 K
-
- -
2
1D
3
4
108.6
110.3
80.0
95.0
79.7
1.3 X 1OI6 113.6
1.2 x 1016 114.5
1.3 x 1015 81.3
1.4 x 1015 96.9
3.5 x 1014 81.0
8.5 x 1014 105.9 0.036 0.69 2.5
1.1 x 1015 107.6 0.034 0.74 2.6
1.7 x 1013 69.5 0.028 0.45 3.2
1.9 x 1014 91.1 0.031 0.78 3.0
1.3 x 1013 71.5 0.025 0.60 3.7
k, , C 6 H 6 , Troe
T I
c
‘ I t
I
Log P
,
torr
Figure 5. Falloff curves for unimolecular dissociation of C6H6and C6D6 highly diluted in argon: ---, R R K M method; -, Troe method. (0) Experimental for C6D6, this work and ref 1, factor of 1.5 error bars.
Y, i I
I
2
I
3
I
I
4
Log P , torr
Figure 6. RRKM falloff curve for dissociation of C6HShighly diluted in argon. Experimental points: (0)this work and ref 4; (A)ref 25; ( 0 , V) ref 6.
respectively, and the average overall energy transfer per collision The energy of reaction was estimated to match the experimental at 130 cm-I, as before. data. By a calculation based on thermochemical kinetics20 it was The results of the calculations for benzene dissociation are found that the heat of reaction from phenyl to linear C6H5is 56 shown in Figure 5 on a large scale so the two calculations can f 5 kcal. The activation energy may well be considerably above be compared. The error bar for our point in the middle of the this, since the formal number of bonds in the product is the same figure has been set at a factor of 1.5 to show the scale. The other as in the reactant, and a bond must be broken when going from experimental point is from our earlier paper, also for C6D6, so linear C6H5to phenyl radical. Colket6 used 65 kcal, but our higher while it looks like it belongs on the C6H6 curve it really does not. value of 80 kcal is just as reasonable. Over the entire range shown, the two methods of calculation To match the RRKM curves to our data, we adjusted the agree within 35%, and between 100 and 10000 Torr, where data lowered frequencies until the RRKM rate constants matched the have been obtained, within 10%. Although the Troe curves have experimental ones in Table I at 1700 K. Details of the RRKM a smaller slope, they lead eventually to larger k , values, factors parameters are given in Appendices I-V. It should perhaps be Of 1.22 for C6H6 and 1.17 for C6D6. For both Troe and RRKM, mentioned that, although some of the R R K M parameters have the curves for C6H6 and C6D6 approach at lower pressures on the been set somewhat arbitrarily, the falloff behavior is not highly graph. Eventually they cross so that in the low-pressure limit ko sensitive to the specific choice of parameters, provided the values for C6H6 is about half that for C6D6. In our approach we have of the calculated rate constants are not changed. Since our not changed the shapes of the RRKM curves but simply moved calculated values do match experiment at out moderate pressures, them to higher pressures by factors of l/&. Once this has been the calculated high-pressure rate expressions should be nearly as done for the ko lines (so the falloff curves remain asymptomatic accurate as the experimental ones. to them) the ko value by Troe’s formulation is 34% higher for C6H6 Some of the results of the calculations are shown in Table 11. and 55% for C6D6 compared to RRKM, not too serious disFor the three reactions where we chose Eo directly from the agreement. The difference is due to the “broadening” of the falloff thermochemistry, the experimental activation energies matched curves due to the weak collisions, a special feature of Troe’s quite well with those calculated at experimental conditions, the method. farthest off being 6.1 kcal for chlorobenzene, and the others being There still exists a difference between our data and those obwithin 4 kcal. These numbers are comparable to our ability to tained by two recent investigators. Hsu, Lin, and Lin,24whose measure activation energies because of our limited temperature experimental temperature range overlapped ours, obtained a rate range and analytical uncertainties. We note that the activation constant of 69 s-l for C6H6 dissociation at a pressure of 2.3 atm. energies under experimental conditions are appreciably below Eo From our graphs, we obtain 28 s-‘ from Troe and 29 s-’ from (and even more below E,) even though the actual falloff is not RRKM, a little more than a factor of 2 lower. Kiefer, Mizerka, very great, between factors of 0.45 and 0.78 below k,. We also made falloff calculations using Troe’s method15~22~23 Patel, and WeiZ5agree with Hsu, Lin, and Lin quite closely. Knowing of this discrepancy, we have checked over our procedures for C6H6 and C6D6. Again, the calculation was adjusted t o match and calculations carefully but have found no reason to change our the experimental data at 1700 K and 0.4 atm (300 Torr or 4 X findings. Although all the methods that have been used involve lo4 Pa), the looseness parameter being set at 0.37 and 0.32, some assumptions, ours seems t o be a very straightforward one. (20) Pacansky, J.; Schrader, E.J. Chem. Phys. 1983, 78, 1033. (21) Benson, S. W. Thermochemical Kinetics, 2nd Ed.;Wiley: New York, 1976; p 21. (22) Troe, J. J. Phys. Chem. 1979, 83, 114. (23) Troe, J. J. Chem. Phys. 1981, 75, 226.
(24) Hsu, D. S. Y.; Lin, C. Y.; Lin, M. C. Symp. (Inr.) Combusr., [Proc.], 20, 1984 1985, 623. (25) Kiefer, J. H.; Mizerka, L. J.; Patel, M. R.; Wei, H.-C. J. Phys. Chem. 1985, 89, 2013.
2448
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988
In figure 6 we show the RRKM falloff curve for dissociation of C6H5,plotted on a smaller scale so other values can be shown. Our data point from this work is again the control point for the curve and is shown with an error bar of a factor of 2 (as are the other points). Our earlier value at higher pressure is in excellent agreement, and Kiefer, Mizerka, Patel, and Wei's value at 740 Torr is within a factor of 2 of our curve. We have also shown Colket's estimates, both k2 itself and also the "effective" k , which allows for reverse reaction when k2 is large. If we try values of k 2 a factor of 10 larger than ours in our calculations, we obtain almost straight line graphs for production of H atoms from bromobenzene, instead of the characteristic concave upward ones such as shown in Figure 2. Conclusions We have measured rate constants for dissociation of C6D6, C6H5,C6H5CI,C6H5Br,and C6H51behind incident shock waves, and calculated corresponding values for C6H6. To the extent that they overlap, these data are in good agreement with earlier results we obtained behind reflected waves. Our results for benzene dissociation are a factor of 2 lower than two other recent studies, but we are in agreement with one recent result for phenyl dissociation.
Acknowledgment. This work was supported by the U S . Department of Energy under Contract DE-AC-02-76-ER02944. We gratefully acknowledge very helpful discussions with Wing Tsang, M. B. Colket, John Kiefer, M. C. Lin, and R. D. Kern. We also acknowledge the assistance of Mr. John Dreyden in the preparation of the figures. Appendix I Details of R R K M Calculation f o r c$6 C6H, H . Frequencies (multiplicities) of molecule: 3068 ( I ) , 3063 (2), 3062 ( l ) , 3047 (2), 1596 (2), 1486 (2), 1326 ( l ) , 1310 ( l ) , 1178 (2), 1150 ( l ) , 1038 (2), 1010 ( l ) , 995 ( l ) , 992 ( l ) , 975 (2), 849 (2), 703 ( l ) , 673 ( l ) , 606 (2), 410 (2) cm-'. Frequencies (multiplicities) of complex: 3068 ( l ) , 3063 ( l ) , 3062 (l), 3047 (2), 1596 (2), 1486 (2), 1326 ( l ) , 1310 ( l ) , 1178 ( l ) , 1150 ( l ) , 1038 ( l ) , 1010 ( l ) , 995 ( l ) , 992 ( l ) , 975 ( l ) , 849 ( l ) , 703 ( I ) , 673 ( l ) , 606 (2), 410 (2), 272 ( l ) , 204 (l), 834 ( I ) , 706 (1) cm-'. In complex, two external moments of inertia increased 10% over those of molecule. Reaction path multiplicity, 6. Collision diameter, C 6 H 6 - ~ r 4.4 , A. No internal rotors in either molecule or complex. Energy of reaction, E,, 108.6 kcal. +
-
+
Appendix I1 Details of R R K M Calculation f o r C6D6 C6D5 D. Frequencies (multiplicities) of molecule: 2293 ( l ) , 2292 ( l ) , 2287 (2), 2265 (2), 1552 (2), 1335 (2), 1286 ( l ) , 1037 ( l ) , 969 (1), 943 ( l ) , 867 (2), 827 ( l ) , 824 (l), 814 (2), 795 (2), 662 (2), 601 ( l ) , 577 (2), 497 ( l ) , 352 (2) cm-I. Frequencies (multiplicities) of complex: 2293 ( l ) , 2292 ( l ) , 2287 (1). 2265 (2), 1552 (2), 1335 (2), 1286 ( I ) , 1037 ( I ) , 969
+
Rao and Skinner (l), 943 (l), 867 (l), 827 ( l ) , 824 ( l ) , 814 (l), 795 (I), 662 (l), 601 (l), 577 (2), 497 (l), 352 (2), 200 (l), 160 ( l ) , 680 ( l ) , 550 (1) cm-]. In complex, two external moments of inertia increased 15% over those of molecule. Reaction path multiplicity, 6. Collision diameter, C 6 D 6 - ~ r4.4 , A. No internal rotors in either molecule or complex. Energy of reaction, E,, 110.3 kcal. Appendix 111 Details of R R K M Calculationf o r C6H5(Phenyl Radical) -, Linear C6H5.Frequencies (multiplicities) of phenyl radical: 3068 ( l ) , 3063 ( l ) , 3062 ( l ) , 3047 (2), 1596 (2), 1486 (2), 1038 ( l ) , 1326 (l), 1310 ( l ) , 1150 (l), 600 (2), 1010 (l), 995 ( l ) , 992 ( l ) , 975 (l), 849 (2), 703 (l), 700 (l), 606 (2), 673 (l), 410 (2) cm-l. Frequencies (multiplicities) of complex: 3068 ( l ) , 3063 ( l ) , 3062 ( l ) , 3047 (2), 794 (l), 1193 (l), 606 (l), 250 (l), 895 (l), 562 ( l ) , 1035 ( l ) , 764 (2), 350 ( l ) , 1189 ( l ) , 934 ( l ) , 540 ( l ) , 800 ( l ) , 1277 ( l ) , 630 ( l ) , 485 (2), 878 ( l ) , 328 (1) cm-I. In complex, three external moments of inertia taken as 1.6 times those of reactant. Reaction path multiplicity, 2. Collision diameter, C6H5-Ar, 6.0 A. No internal rotors in either reactant or complex. Energy of reaction, E,, 80.0 kcal.
-
Appendix I V Details of R R K M Calculation f o r C6H5Cl C6H5 + Cl. Frequencies of molecule: 3069, 3050, 3029, 307 1, 3052, 158 1, 1582, 1478, 1444, 1324, 1267, 1174, 1157,1068, 1025, 1002,986, 965,902, 831, 740,682,616,400, 1084,702,416,297,467, 196 cm-'. Frequencies of complex: 3069, 3050, 3029, 307 1, 3052, 158 1, 1582, 1478, 1444, 1324,1267, 1174, 1157, 1068, 1025, 1002,986, 965, 902, 831, 740, 682, 616, 400, 1084, 250, 100, 260, 65 cm-'. In complex, two external moments of inertia taken as 2.5 times those in molecule. Reaction path multiplicity, 1. Collision diameter, C6H5CI-Ar, 6.0 A. No internal rotors in either molecule or complex. Energy of reaction, E,, 95.0 kcal.
-
Appendix V Details of R R K M Calculation f o r C6HjBr C6H5 4- Br. Frequencies of molecule: 3069,3069,671,3056,3050,3029, 1264, 1176, 1070, 1158,1068, 1020,989,963,254,903,832,736,1578, 1578, 1472, 1443, 1321, 1001,459,681,615, 314,409, 181 cm-I. Frequencies of complex: 3069, 3069, 3056, 3050, 3029, 1264, 1176, 1070, 1158, 1068, 1020,989,963,95,903,832,736, 1578, 1578, 1472, 1443, 1321, 1001,459,681,615, 314,409,65 cm-'. In complex, two external moments of inertia taken as 2.4 times those in molecule. Reaction path multiplicity, 1. Collision diameter, C6H5Br-Ar, 6.0 A. No internal rotors in either molecule or complex. Energy of reaction, Eo 79.7 kcal.
