1864
J . Phys. Chem. 1989, 93, 1864-1869
Formation of H and D Atoms in the Pyrolysis of Toluene-d, and ToIuene-a,a,a-ds behind Shock Waves V. Subba Rao and Gordon B. Skinner* Department of Chemistry, Wright State University, Dayton, Ohio 45435 (Received: February 13, 1987: I n Final Form: October 26, 1988)
Mixtures of 1-20 ppm of toluene-de and C6HsCD3in argon were pyrolyzed behind incident shock waves with a total pressure of -0.4 atm and a temperature range of 1450-1790 K. D atom concentrations were measured for the first compound and both H and D for the second. The data indicate that an appreciable fraction of toluene dissociates via C ~ H S C D ~C6H5 + CD3, [SHD], with kSHD = 2.0 X IOi5 exp(-94 kcal/Rn sei, while the rate constant for C6HsCD3 C6HSCD,+ D, [IHD], was found to be k l H D = 2.2 X lOI4 exp(46.4 kcal/RT), under experimental conditions. RRKM calculations were made to evaluate unimolecular falloff for these reactions and to calculate the corresponding rate constants for C7Hs. For C~HSCH, C6HS+ CH3, [ 5 ] , we find that k S = 1.5 X IOi5 exp(44.2 kcal/RT) s-', while for C6HSCH3 C6HSCH2+ H, [ l ] , we find k l = 2.5 X l O I 4 exp(-85.8 kcal/RT) s-I, both under the experimental conditions given above.
-
-
-
Introduction We have recently' reported results on the pyrolysis of toluene-d8 behind reflected shock waves, at an average total pressure of 3.2 atm and between 1410 and 1730 K. We interpreted our results in terms of the reaction C6DSCD3 ---* C ~ D S C D + ~D
(ID)
which has generally been taken to be the only important initiation step. For instance, in his mass spectrometric study Smith2 considered that C6HsCH3
-
-
+
C ~ H S C H ~H
(1)
accounted for at least 99.5% of the initial reaction, with C ~ H S C ---* H ~C6H5
+ CH3
(5)
accounting for less than OS%, in the temperature range 1000-1400 K. From the older literature using flow techniques at 900-1230 K, referenced in our earlier paper, Benson and 0 N e a l 3 had come to the same conclusion. In 1984 Colket4 reported that in single-pulse shock-tube studies around 1700 K, approximately 20% of the toluene dissociates via reaction 5. Very recently, Pamidimukkala et aLs state, on the basis of time-of-flight mass spectrometric and laser-schlieren shock-tube studies, that reaction 5 probably dominates over ( l ) , particularly at temperatures in the 1700-2200 K range. This change of mechanism is not altogether unexpected since, although reaction 5 should have a higher activation energy than ( l ) , based on the thermochemistry, it also has a larger Arrhenius A factor since two polyatomic species, rather than one polyatomic and one atom, are produced.6 Therefore, the importance of reaction 5 might be greater at high temperatures. Since our earlier paper was published, we have modified our shock tube so that measurements can be made behind incident waves, at pressures of 0.3-0.6 atm. We made measurements of C6DSCD3pyrolysis under these conditions so that we could consider the pressure dependence of toluene pyrolysis, comparing experimental results with different theories of unimolecular falloff. ~
~~~~~~~
(1) Rao, V . S.;Skinner, G. B. J . Phys. Chem. 1984, 88, 4362. (2) Smith, R. D. J . Phys. Chem. 1979, 83, 1553. (3) Benson, S. W.; ONeal, H.E.Kinetic Data on Gas Phase Unimolecular Reactions, NSRDS-NBS-21; National Bureau of Standards: Washington, D.C., 1970. (4) Colket, M. Symp. ( I n t . ) Combust. 1984, 20, 1032. (5) Pamidimukkala, K. M.; Kern, R. D.; Patel, M. R.; Wei, H. C.; Kiefer, J. H . J . Phys. Chem. 1987, 91, 2148. ( 6 ) Larson, C . W.; Patrick, R.; Golden, D. M. Combusr. Flame 1984, 58, 229.
0022-3654/89/2093-1864$01.50/0
Also, we have looked at C6H5CD3and by measuring both H and D concentrations have been able to learn something of the importance of reaction 5.
Experimental Procedures Our apparatus and techniques for measurements behind reflected shock waves have been described in an earlier paper.7 We used a stainless steel shock tube with a test section 7.6 cm in diameter and 4.5 m long. Concentrations of H and D atoms 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% H, or D2 in helium at a lamp pressure of 2.5 Torr and with 40 W of 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 Tsang8 to produce 0.9 f 0.1 atom of H per initial molecule 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 lines emitted by our lamp provide a basis for obtaining the temperature dependence of the calibration curves and the change in calibration when D rather than H is measured. We isolated the Lyman cy 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 2-396 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. The toluene-d, was from Kor Isotopes and was stated to have 99.96 at. % D. Toluene-a,a,a-d, was from MSD Isotopes and was of 99% isotopic purity. Argon was from Airco, Inc., research grade, 2 ppm total impurity, with less than 0.5 ppm hydrocarbon reported as methane. (7) Chiang, C.-C.; Lifshitz, A,; Skinner, G. B.; Wood, D. R. J . Phys. Chem. 1979, 70, 5614. (8) Tsang, W .J . Chem. Phys. 1966, 44, 4283.
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 1865
Pyrolysis of Toluene-d8 and C6HSCD3
T , K
LI
E,
\
//’
.t
I
-
Q 1,000-
I
I
0
1500
I
-
v X
1600
i
7 v,
500-
n Y
200-
10050
200
0
400
600
800
-
1000
Time , microseconds Figure 1. Dependence of D atom concentration on time for incident shock-wave experiment with T = 1509 K, P2 = 0.46 atm, 10 ppm toluene-d8 in argon: (-) best estimate of initial slope; (---) calculated concentrations by using a four-reaction scheme.
Pyrolysis of toluene was studied in mixtures of 1, 5 , 10, and 20 ppm toluene-d8 and 3 and 10 ppm toluene-a,a,a-d3, in argon. Because of the lower total concentrations, absorption of Lyman a by toluene and reaction products was considerably smaller than in the earlier experiments. Using the absorption coefficient of toluene-d8 vapor at Lyman a (121.5 nm) and 1300 K of (4.4 f 0.5) X lo7 mol-’ cm2 found earlier, we calculate that the 20 ppm mixture at 0.35 atm and 1300 K would absorb only 2% of the Lyman a. This fraction is barely detectable at our signal-to-noise ratio, so that corrections for molecular absorption and the question as to whether products absorbed to the same extent as reactants were of little concern. As before, we assumed that boundary layer cooling had no effect on the 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 (which we repeated under incident wave conditions), it seemed reasonable 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 just under 4 for most of our experiments, the time constant in terms of particle time was 20 p s . Particle times for complete experiments ranged from 300 to 1500 W S , during which pressures remained constant within experimental error. At longer times pressures would decrease, and at much longer times (4OOO-psparticle time) amval of the sample/driver interface would be signaled by an increase of Lyman a intensity to its original value.
Experimental Results While our total data analysis took into consideration all of our measurements over the experimental times, it seemed worthwhile to make a first estimate of the rate constant for toluene-d8 dissociation from the initial slopes of the curves of [D] versus time. Such a graph is shown in Figure 1. Determination of initial slopes was easier here than in our earlier data on toluene-& because most of our graphs resembled Figure 1 in having a nearly linear dependence of [D] on time for the first several hundred microseconds, compared to 100 p s or less for many of our earlier curves. This happened because less D was lost by reaction with toluene (reaction 2D) because of the lower concentrations of toluene. Figure 2 shows these first-order rate constants determined from initial slopes, along with a least-squares line. The average pressure for all 39 experiments was 0.41 atm, with a standard deviation of 0.05 atm, and the temperature range was 1450-1790 K. The least-squares Arrhenius equation based on the initial slopes of the graphs of [D] versus time is
kD = 2.8
X
lo” exp(-94.6 kcal/RT) s-’
where the standard deviation of the points from the line in terms of log k is 0.12, or a factor of 1.3. The 95% confidence level in E is 6 kcal. Since it is understood that the observed [D] probably
10 5.6
5.8
6.0
6.2
6.4
6.8
6.6
1 0 ~, K1 ~
Figure 2. Initial rate constants for the formation of D in pyrolysis of toluene-d8in argon at 0.41 atm: 0, 20 ppm; 0, 10 ppm; A, 5 ppm; V, 1 ppm. Line calculated by least-squares method. I
I
I A A
I
/
0
200
400
Time
600
800
1000
1200
, microseconds
Figure 3. Dependence of D and H concentrations on time for two similar experiments with 10 ppm C6HSCD3in argon: 0,1611 K, 0.46 atm of total pressure, D atom concentration; A, 1605 K, 0.46 atm of total pressure, H atom concentrations. Curve A, calculated H concentrations by using best fit data, k , = 9.0 X loi3exp(-84 kcal/RT), k, = 2.7 X IOi5
exp(-95 kcal/RT); other rate constants from Table I. Curve B, calculated H concentrationswith A , = 0. Curve C, calculated H concentrations with A , = 1.0 X loi5. Curve E, calculated H concentrations with A , = 2.0 X loi5. Curve D, calculated D concentrations with best-fit data. comes from more than one chemical reaction, this rate constant kD has no mechanistic significance. For C6HSCD3we carried out 31 experiments, measuring D concentrations in 17 and H concentrations in 14. As far as possible we used identical conditions for H and D measurements. The average total pressure was 0.50 f 0.07 atm, and the temperature range 14%-1770 K. Typical results from two similar experiments, shown in Figure 3, show that the production of D is nearly linear with time in the early stages of the reaction, just as it was from C7De,while the production of H shows upward curvature, suggesting that at least part of the H comes from a relatively slow secondary reaction. Qualitatively, such curves could arise from formation of D directly via reaction 1, followed by formation of H by dissociation of benzyl radicals. From the initial slopes of the D atom graphs we calculated rate constants for the formation of D atoms. These results are shown
1866 The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 TABLE I: Elementary Reactions Found Important in Toluene Pyrolysis no. reaction" 1 C6Hz,CH3 C6H5CH2 + H
----
1HD ID 2HD
i
C ~ H S C D ~C6H5CD2 f D C6D5CD3 C6DjCD2 + D H + C6H5CD, C6Hz,CD2+ HD H + C~DSCD, C6D5CD2 HD D + C6H5CD3 C6H5CD2 + D2 D + C6Dz,CD3 C6D&D2 + D2 D + C6Hz,CD, C6HdDCD3 + H C~HSCH, C6H5 + CH3 C~HSCD, C6H5 + CD, C6DsCD3 C6D5 + CD3 C6H5 C2D2 + C4D2 + D C6D5 --+ C2D2 + C4D2 + D C6H5CD2 H, D, other prod C6DSCD2 D, other prod +
I i
-+
2D 2D2 4DH 5 5HD 5D
+
+
i i
+
6
6D 7HD 7D
i
Rao and Skinner A , moP cm3 s-1
E , kcal
ref this work
1014
85.8 86.4
this work
1.8 x 1015
14.6
I , 9, this work
1.5 x 1015
15.0
I , 9, this work
2.8 x 1 0 1 3 1.5 x 1015
3.7 94.2
1, 9 this work
2.0 x 1015
94.0
this work
9.0 X 10I2
73.0
10
5.4 x 10'6
100.0
11
2.5 x 2.2 x
1014
'For unimolecular reactions these rate coefficients are for temperatures of 1400-1800 K and a total Ar pressure of 0.4 atm (300 Torr or 4 X IO4 Pa). For reactions 1 and 5 results from the RRKM calculations that match the best-fit modeling results are given. energies shown in Table I. These values are uncomfortably high and did not quite match with lower temperature data taken by R a ~ i s h a n k a r a . ~When we included reactions 5 and 6 in our modeling calculations for the earlier data, the A values could be lowered about 30% to those in Table I, with no reduction in the fit to the data. These lower values work well with our new data and intersect the Ravishankara curves at 1050 K, as is desirable. At that temperature kzHD= 1.62 X 1 O l 2 and kZD2 = 1.14 X 10l2 mol-' cm3 s-', respectively, while k2 (for H + C6H5CH3 C6H5CHz H2) is 2.23 X 10" mol-' cm3 SKI, from our earlier paper. This last value is in excellent agreement with the value of 2.35 X 10l2 mol-' cm3 s-I given by the equation of Robaugh and Tsang,21k2 = 1.2 X lOI4 e x p ( 4 . 2 kcal/RT) mol-I cm3 s-l, from a single-pulse shock-tube study at 950-1 100 K. However, our rate constants in our higher temperature range are larger by a factor of about 2 than those obtained by extrapolation of Robaugh and Tsang's Arrhenius equation or even of a non-Arrhenius equation with a T2.5 term that matches their E at 950-1 100 K. We require these higher rate constants to get a good match to our experimental data, but we have estimated uncertainties of a factor of 1.2 in the Robaugh and Tsang equations and at least 1.3 in our Table I data for reaction 2. The different sets of data can be reconciled well within that uncertainty range if the Arrhenius activation energy for Robaugh and Tsang's data is increased from 8.2 to 10.0 kcal for the temperature range 950-1 100 K, keeping the absolute value of k2 constant at the midpoint of their range. Combining rate constants at the ends of their range with a P5term yields the equation k2 = 6.8 X lo5 p 5exp(-4.84 kcal/RT) mol-' cm3 s-'. This seems to be the best equation on the basis of currently available data. Actually, the experimental results of this paper do not depend very much on k2, since the concentrations of toluene are lower by a factor of about 10 from those in our earlier paper. Lowering kZHD and kzDby even a factor of 2 from the values of Table I affects the rate constants for reactions 1 and 5 only a few percent. Conversely, of course, the data of this paper are not helpful in determining the rate constants of kz and its isotopic variants in our temperature range. In our earlier paper we considered a reaction 3, in which H (or D) added to the ring and CD3 was eliminated. This process was important in some lower temperature experiments in that paper but not in the higher temperature experiments reported here, for reasons discussed in the earlier paper. Reaction 4, in which D adds to the ring and H is eliminated, is of some importance here. It occurred in the opposite sense in the earlier paper ( H adding and D being eliminated), so the value in Table I has been modified slightly from the earlier one. We have made a study of reaction 6 (ref 10) by following H atom formation in the pyrolysis of chlorobenzene and bromobenzene, from which phenyl radicals are formed. We found almost one atom of H (experimentally 0.82 i 0.2) formed per molecule
1 T , K
I0,OOO
1500
1700
+
56
58
60
62
64
66
68
IO~IT , K
Figure 4. Initial rate constants for the formation of D in pyrolysis of toluene, C6H5CD3,in argon at 0.50 atm: 0, 10 ppm; V, 3 ppm. Line calculated by least-squares method. Upper line same as that shown in Figure 2 for C6D5CD3.
in Figure 4. The least-squares Arrhenius equation based on these initial slopes is
k~= 3 8.2 X 10" exp(44.7 kcal/RT)
S-'
where the standard deviation of the points from the line in terms of log k is 0.07, or a factor of 1.17, and the 95% confidence level in E is 5 kcal. The least-squares line for C7D8dissociation is also shown. The gradual separation of these lines at higher temperatures should be noted and will be considered in the discussion.
Discussion Because of the low concentrations of reactants that we used, the number of elementary steps of importance in determining H and D concentrations was relatively small. They are listed in Table I, where it can be seen that isotopic variants of some are needed because of the use of C6H5CD3. For the unimolecular reactions we have given Arrhenius parameters that apply to the experimental pressures of this paper, -0.4 atm. Of the seven reactions given in Table I, only (1) and (5) were considered to have freely adjustable rate constants. The others were known and either fixed or adjusted within narrow limits. We will first review the sources of information on the known reactions and then concentrate on those of main interest, reactions 1 and 5. Reaction 2 was important in our earlier study of toluene pyrolysis.' To model our earlier data, we used AzD = 2.5 X lOI5 and AzDz = 2.1 X lOI5 mol-' cm3 s-I, with the same activation
(9) Ravishankara, A. R., private communication
-
Pyrolysis of Toluene-d8 and C6H5CD3 of original chlorobenzene, and so along with reaction 6 we assume another reaction with rate constant 0.18/0.82 times k6, by which phenyl dissociates without producing H atoms. In Ref 10 we explain the rationale for including this parallel reaction. While we do not know its nature and are not even sure it exists, we consider that including it leads to the most direct relationships between observed and calculated atom concentrations. We made RRKM calculations that indicate an appreciable pressure dependence of reaction 6. At 1600 K the rate constant is about 1.4 times faster at 3.2 atm, the average for our earlier studies, than at 0.4 atm, the average for these. We assume the reaction is controlled by breaking one of the C-C bonds in the ring, so the rate constant will not be significantly affected by replacement of H with D. We have also made a study of benzyl dissociation by measuring formation of H and D atoms in pyrolysis of ethylbenzene, CgH5CD2CH3." This decomposes to form benzyl and methyl radicals, after which the former decompose further with formation of mainly H and a little D. The mechanism is not known, but a likely possibility is again breaking of the ring and loss of H from one or more products, so again we assume no deuterium isotope effect. We have used our data directly for the studies with C6H5CD3,and for C6D5CD3we have added together the rate constants for H and D formation. We hesitated to make RRKM calculations for benzyl decomposition because the mechanism of the reaction is so incompletely known. Since it is nearly the same size as toluene, we used the same falloff effect as we found for toluene (see below). The difference in rate constant between 0.4 and 3.2 atm is estimated to be only about a factor of 1.2. Our results are not the only ones on benzyl dissociation. The first published study was by Astholz and Troe,I2 who used ultraviolet absorption behind shock waves to follow the reaction. At 0.4 atm and 1600 K their results give a first-order rate constant of 530 s-l for benzyl dissociation. Our results' give 1200 s-I, so we are a factor of 2 higher. More recently, Muller-Markgraf and Troe" reported a new study that gave much larger rate constants for benzyl dissociation: about 15 000 s-I at 1600 K and 4 atm of pressure. This result was quite surprising, since the general view has been that benzyl should dissociate more slowly than phenyl, because of its resonance stabilization, and we measure k for phenyl under the same circumstances to be 5300 s-I. It may be that with our different techniques the two studies measured different reactions. What is needed to reconcile the data is for toluene to be converted rapidly to an intermediate with an absorption spectrum different from that of benzyl, without formation of H atoms, followed by a slow dissociation of this intermediate to form H atoms. Our assumption, paralleling what seems to be happening with phenyl, is that benzyl first reacts to form linear C7H7. This may lose H or may further dissociate, and the next level of products produces H, leading to formation of about one H atom per benzyl, which is what we have observed at the upper end of our temperature range. The nature of our results indicated that these later steps are fast compared to the ring-breaking step, since graphs of H appearance versus time consisted of nearly straight lines, while two or more steps of comparable rate would produce curved plots. Since benzyl is so stable thermodynamically, it is difficult to think of an intermediate species to which benzyl would be converted rapidly, followed by slow dissociation of the intermediate to produce H. For example, a thermochemical kinetics calculation using Benson's methods14 indicates that linear C7H7 (H2C= C=CH-CH=CH-CH=CH, formed by breaking the ring C-C bond next to the CH2 group) is very unstable compared to benzyl, so if the linear species did not dissociate rapidly it would soon reach a steady-state concentration at a very small fraction (10) Rao, V. S.;Skinner, G. B. J . Phys. Chem. 1988, 92, 2442. ( 1 1 ) Rao, V. S.; Skinner, G. B. Symp. (In?.)Combusr. 1986, 21, 809. (12) Astholz, D. C.; Troe, J. J . Chem. SOC.,Faraday Trans. 2 1982, 78, 1413.
(13) Muller-Markgraf, W.; Troe, J. Symp. (Inr.) Combust. 1986, 21, 875. (14) Benson, S.W. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1976.
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 1867 of the benzyl concentration. If it dissociated slowly, then benzyl would have to disappear slowly also. Still, there are substances and reactions in the total process of benzyl dissociation that are not well understood, and we do not know just how they are formed. It seems logical, for the present purpose of clarifying the first step of toluene pyrolysis, to use our data for formation of H and D from C6H5CD2, and by simple combination, of D from CgD5CD2, with the expectation that the future will provide a mechanism for explaining why two ways of looking at benzyl dissociation provide such different numerical results. Our model needs to know not how fast benzyl disappears but how fast atoms are formed from it, and we feel sure we know this, at least within a factor of 2. However, although we are sure this is the right approach, we also tried putting Muller-Markgraf and Troe's rate constant into our modeling calculations, with results that are described briefly later in this section. Having considered those reactions that had fixed or nearly fixed values throughout the modeling process, we can now look at the other two, reactions 1 and 5. Since 5 was not included in our earlier analysis, we started by setting its rate constant to zero to see if the results for C6H5CD3could be explained without it. Briefly, the deuterium data could be modeled quite well, but the hydrogen data could not. We have shown this result in Figure 3, where it can be seen that without reaction 5 (curve B) the calculated concentration of H rises much too slowly. Benzyl radicals are formed in approximately equal numbers to the D atoms but are too stable to provide enough H atoms. When reaction 5 (curve B) is introduced, the H atoms appear much faster from phenyl dissociation, so the calculated concentrations approach those observed. The D concentrations continue to be matched fairly well, but not so well as the H, the calculated graphs having too much curvature, as shown here. The best fit to the data, represented by the rate constants of Table I, indicates that approximately half of the toluene dissociates by reaction 5, less at low temperatures than at high temperatures, because of the difference in activation energies. The accuracy with which we know k5 is suggested by Figure 3, in which the fit of H for A5 = 2 X lOI5 s-l (74%of the best fit value) is not bad and certainly no worse than the best-fit value for D, so an uncertainty of f50% seems reasonable for k5. When Muller-Markgraf and Troe's high value of k7 is used in the model, H is produced almost immediately from benzyl, and the H atom curve can be modeled quite well without the use of reaction 5. The best value of klHD in this situation is 20% less than that of Table I. The calculated D graphs still have more curvature than the data. Including reaction 5 leads to too much H, so if k7 is larger than we think, then the conclusion would be that reaction 5 is less important. There seems to be no counter argument with respect to reaction 1 . Our data are very clear that D is produced from C6H5CD3directly, in a first-order fashion, to a major extent. Generally this channel accounts for at least half the initial dissociation in our temperature range, although in laser-schlieren experiments at very high temperatures5 reaction 5 would become more important. The smaller yield of D atoms from C6H5CD3compared to C6D5CD3,shown in Figure 4, and the increase in the difference between the two curves with increasing temperature are consistent with the idea that reaction 5 is occurring. The curves are close at low temperatures because the benzyl radicals are stable and only a small fraction of toluene dissociates by reaction 5. At high temperatures, more of reaction 5 occurs, and an appreciable fraction of benzyl dissociates, so we end up getting about twice as much D from C6D5CD3as from C6H5CD3.This mechanism also explains why the activation energy for kD (94.6 kcal) is larger than those for klD(86.4 kcal) and kSD(94.0 kcal). This happens because the secondary reactions 6D and 7D cause production of increasing numbers of D atoms per reacting molecule as the temperature increases. However, Muller-Markgraf and Troe's rate expression also leads to a generally similar result. Even with their high rate constant for benzyl dissociation, only a small fraction of the benzyl dissociates in the first few hundred microseconds of our lower temperature experiments, while all of it
1868 The Journal of Physical Chemistry, Vol. 93, No. 5, 1989
Rao and Skinner TABLE 11: Calculated Falloff Parameters for Reactions 1 and 5
reaction" 5 Eo. kcal 86.5 88.0 100.0 high-pressure Arrhenius parameters, 1600 K A,, s'I 2.8 x 1015 2.4 x 1015 6.7 X 10l6 E,, kcal 92.5 93.2 104.2 Arrhenius parameters, 1600 K, 300 Torr of Ar A , s-I 2.5 x 1014 2.2 x 1014 1.5 x 1015 E , s-l 85.8 86.4 94.2 Arrhenius parameters, 1600 K, 3000 Torr of Ar A , s-' 1.1 x 1015 1.0 x 1015 1.4 X 10l6 E , s-I 89.9 90.5 99.8 &, -1600 K 0.024 0.021 0.024 k 3 W T o r r l k , , -1600 K 0.76 0.76 0.59 property
x-
I
Log P
, torr
Figure 5. Observed and calculated rate constants for toluene dissociation at 1600 K: 0, data from this work and ref 1 for reactions 1HD and 1D; A,this work, reaction 5 HD; V, Muller-Markgraf and Troe,Iotaken as sum of 1 and 5 ; -, RRKM curves for reactions 1 and 5 for C,H,; ---, RRKM curves for reactions 1 and 5 for C7Ds.
dissociates quickly at higher temperatures. Unfortunately, then, the trend of Figure 4 does not make a clear distinction between the two cases. We also modeled our older high-pressure (3.2 atm) C7Ds pyrolysis data using our new mechanism. Since one could not really distinguish reactions 1 and 5 in those experiments, we simply used the same activation energies as in Table I and kept the ratio A1/A5 constant. The best-fit values of A , and A , were a factor of 1.56 higher than for the lower pressure data. This is the kind of change to be expected but is somewhat larger than we found from RRKM calculations. The value of k l Dobtained by this model at 1600 K is only 0.68 of that found in our earlier paper, because we also get some D via reaction 5. The sum of klD + kSDis 1.32 greater than the earlier k , , so the total rate of disappearance of toluene is somewhat faster by the new model. Because of the different temperature dependences of the reactions, the ratio of the new to old rates of disappearance increases with rising temperature. We have shown the two sets of values in Figure 5, along with the RRKM curves. For RRKM calculations we used the exact-count method developed by Stein and Rabinovitch,', assuming harmonic oscillators. We used vibrational models with no active internal rotations other than those mentioned below, since we had used ones of this nature for dissociation of methane16 and ethane,17 in both cases fitting not only our shock-tube data but lower temperature data obtained by other techniques. In developing the models, one could think of toluene as phenylmethane for reaction 1 and as an ethane where one CH, is substituted by phenyl for reaction 5 . Vibrational frequencies for toluene, including deuterated species, have been worked out by Hitchock and Laposa,18 and we used bond-dissociation energies given by McMillen and Golden,lg adjusted to 0 K and also adjusted for isotope effects. Some details of the RRKM calculation for C6HSCH3are as follows: (a) The molecule has 38 vibrational degrees of freedom, and the C6H5-CH3 rotor was considered to be free. (b) For the C6H5CH2-H complex, a 2950-cm-' C-H stretching frequency became the reaction coordinate, and bending frequencies of 1455 and 1040 cm-l were lowered to 355 and 245 cm-l, respectively. The C6H,-CH3 motion became a torsional vibration of 190 cm-'. In the complex, two external moments of inertia increased by a (15) Stein, S . E.; Rabinovitch, B. S. J . Chem. Phys. 1973, 58, 2438. (16) Chiang, C.-C.; Baker, J. A,; Skinner, G. B. J. Phys. Chem. 1980,84, 939. (17) Skinner, G. B.; Rogers, D.; Patel, K. B. Int. J . Chem. Kinet. 1981, 13, 481. (18) Hitchcock, A. P.; Laposa, J. D. J . Mol. Specrrosc. 1975, 5 4 , 223. (19) McMillen, D. F.; Golden, D. M. Ann. Reo. Phys. Chem. 1982, 33, 493.
1
5D
1D
OOT
1
8.3 X 10l6 104.2 2.0 x 1015 94.0 1.7 X 10I6 99.8 0.021 0.60
"See Table I for equations of reactions. factor of 1.1. The reaction path multiplicity was 3, and the energy of reaction, Eo,was 86.5 kcal. (c) For the C6H5-CH3complex, a vibrational model was also used. The 1208-cm-' stretching frequency became the reaction coordinate, while bending frequencies of 1040, 1040,347, and 217 cm-I became 145, 135,60, and 60 cm-', respectively. The C6H5-CH3 rotor remained free. Two external moments of inertia increased by a factor of 2.0. The reaction path multiplicity was 1, and the energy of reaction, Eo, was 100.0 kcal. We calculated the collisional efficiency p, for argon-toluene collisions using the method described by Luther and Troe,*O although with this large molecule at our high temperatures, we are approaching the limit of validity of their approximations. Representative results of these calculations including limiting highpressure Arrhenius parameters are shown in Table I1 and Figure 5 , in which experimental results are shown with error bars for a factor of 1.5. As expected, the falloff for this large molecule is fairly small down to 300 Torr of total pressure, even allowing for a very low collisional efficiency. The calculated value of 0,is probably somewhat lower than the correct one,2obut the actual value is not likely to be much more than 0.03, so the effect on the results is small. Our RRKM calculation was made with a program that included the two channels together, so that at lower pressures the falloff of reaction 5 was greater because the energized molecules were removed by reaction 1. We probably did not account for quite all of this effect because we included the weak collider efficiency p, after the main calculation, by translating the curves along the pressure axis. However, with the small extent of falloff in our experimental range, errors from this source should be correspondingly small. It is interesting to note that the isotope effect in going from C7D8to C7H8 leads to an increase in k l but a small decrease in ks, changes that are not unexpected from the mechanisms of the reactions. The result is that reaction 5 becomes less important under similar conditions for C7H8 than for C7D8. We have also shown a point from Muller-Markgraf and Troe's recent study,13 which lies a factor of nearly 3 above our calculated curve. Since they did not consider reaction 5 and were giving a rate constant for the dissociation of toluene, a better comparison with their data would be with the sum of k l + k,. In this case the difference lies within a factor of 2. Our data can be compared with those of Pamidimukkala et al., in terms of the relative importance of reactions 1 and 5 and in terms of the rate constants of the reactions. Their data extend down to 1600 K, the center of our experimental range. At 1600 K and 0.5 atm of pressure they find that k5 is 1080 s-' and estimate k , at 40% of k,. That is, they consider reaction 5 the more important reaction and find the sum of the two to be 1500 s-l, (20) Luther, K.; Troe, J. In Reactions of Small Tramient Species; Fontijn, A., Eds.; Academic Press: New York, 1983. (21) Robaugh, D.; Tsang, W. J . Phys. Chem. 1986, 90, 4159.
A., Clyne, M. A.
1869
J . Phys. Chem. 1989, 93, 1869-1876 compared to our sum under similar conditions (from our RRKM calculations) of 720 s-I, a difference of a factor of 2 in the same direction as our difference with Muller-Markgraf and Troe. The RRKM results are similar, That is, they consider reaction 5 the more important reaction and find the sum of the two to be 1500 SI, compared to our sum under similar conditions (from our RRKM calculations) of 720 s-l, a difference of a factor of 2 in the same direction as our difference with Muller-Markgraf and Troe. Similarly, the RRKM calculations of Pamidimukkala et al. give the high-pressure limit of ( k , k,) at 1600 K as 2190 s-l (assuming k , = 0.4k5), whereas we found ( k , + k2) to be 1060 s-l, with k l = 1.7k5. In our earlier paper’ we compared our data with those of Price,22 who made his study at substantially lower temperatures. We noted that his data seem to be of good quality. For purposes of comparison with our data they can be concisely summarized as giving a rate constant for dissociation of toluene ( k , k 5 )of 1.3 x s-I at 1050 K near the high-pressure limit. Our RRKM calcus-l, with 90% lations lead to a ( k , k,) value of only 0.2 X of the dissociation of toluene oqcurring by reaction 1. The dominance of reaction 1 at this temperature is expected because of its lower activation energy, but the factor of 6 in the rate constant values shows that our model, with fixed activation energy and molecular parameters, cannot be used over such a wide temperature range. The conclusions to be drawn from this work on the relative importance of reactions 1 and 5 must be tentative. If we accept our data on the role of formation of H from benzyl and phenyl, then our data require a substantial contribution, about 40-50%, of reaction 5 in the dissociation of toluene-d8 and C6H5CD3near 1600 K. For C7H8this would drop to about 30%, in reasonable agreement with Colket’s4 observation. If we consider the limits of uncertainties in measuring H and D in the experiments described in this paper and in those on ethylbenzene” and benzenelo that provide rate constants for H formation from benzyl and
+
+
+
(22) Price, S.J. Can. J . Chem. 1962, 40, 1310.
phenyl radicals, then the contribution of reaction 5 could be as low as 10% and as high as 50% under our conditions. It is unlikely that reaction 5 is the dominant reaction at 1600 K, but its importance will increase, as expected a d as shown numerically by our R k K M calculations, at higher temperatures. In light of the similarities and differences between the most recently published ~ o r k ~and , ~our q ~own, ~ we can perhaps prepare a composite picture of toluene dissociation that emphasizes the most definitive parts of each study. First, we can deduce a k , expression for the sum of k l + k5 that includes Price’s value of 1.3 X s-l at 1050 K and a value of 1600 s-l at 1600 K. The Auhenius equation through these points, k , = 1.8 X 1015exp(-85100 callR7‘) s-l, should be accurate within a factor of 1.5 from 1000 to 2000 K. Second, both experiment and calculation show that unimolecular falloff in this temperature range is moderate, even when argon, a very weak collider, is the main one present. As noted in Table 11, we find k / k , at 300 Torr and 1600 K to be 0.76 for reaction 1 and 0.59 for reaction 5, while Pamidimukkala et aL5 find k / k , to be 0.68 for the sum of k l and k5 at 380 Torr and 1600 K, a very similar result. So there is not a great deal of falloff in the range of interest for most combustion problems, and both RRKM calculations give similar results. Third, the fraction of toluene dissociation occurring by reaction 1 decreases with temperature. We suggest values in the highpressure limit of about 90% at 1000 K, 78% at 1200 K, 64% at 1400 K, 50% at 1600 K, 40% at 1800 K, and 32% at 2000 K. These are based on our observations and RRKM calculations but reduced somewhat in consideration of the results of ref 5. The percentages will increase with decreasing pressure, but as long as k / k , is above 0.5 the changes will be small.
Acknowledgment. This work was supported by the U S . Department of Energy under Contract DE-AC-02L76-ER02944. We also acknowledge the assistance of John Dryden in preparation of the figures. Registry NO. C ~ H S C H108-88-3; ~, C ~ D S C D2037-26-5; ~, C~HSCD~, 1124-18-1.
Study of the High-Temperature Pyrolysis of Propene by Determination of H and D Atoms Formed from Partially Deuterated Propenes Heated behind Shock Waves V. Subba Rao and Gordon B. Skinner* Department of Chemistry, Wright State University, Dayton, Ohio 45435 (Received: August 19, 1987; In Final Form: August 8. 1988)
Very dilute mixtures of CD2CHCH3,CH2CDCH3,and CH2CHCD3were pyrolyzed at 1500-1800 K behind incident shock waves at an average pressure of 0.42 atm and behind reflected waves at 2.8 atm. Analysis for H and D using resonance absorption spectroscopy showed that propene dissociates partly by formation of hydrogen atoms and allyl radicals, (l), and partly by formation of vinyl and methyl radicals, (2). Both of these unimolecular dissociation reactions of propene are in the intermediate falloff region at our pressures and temperatures. For (1) we find kl = 3.5 X 10l2exp(-75 kcal/RT) s-I at 0.42 atm and kl = 3.6 X 10” exp(-lO kcal/RT) s-l at 2.8 atm. For (2) we find k2 = 8.2 X 10l2exp(-80 kcal/RT) s-l at 0.42 atm and k2 = 2.3 X 10” exp(-80 kcal/RT) s-l at 2.8 atm. Estimated uncertainties are factors of 1.5 in (1) and 2 in (2).
Introduction The goal of this study has been to learn about the unimolecular initiating steps in propene pyrolysis. The two reactions that have been most considered are CH2CHCH3
-
-+
CH2CHCH3
CH2CHCH2 CHzCH
+H
+ CH3
(1)
(2)
Other possibilities are loss of H 2 by reactions such as 0022-3654/89/2093-1869$01.50/0
CH2CHCH3 CH2CHCH3
-
+
CHCCH3 + H2 CH2CCH2 H2
+
(3)
(4) Earlier shock-tube studies have not been able to distinguish among the possibilities, although reaction 2 has generally been said to be the main initiating step. The single-pulse studies of Chappell and Shawl and Burcat2 in the temperature range (1) Chappell, G.A,; Shaw, H. J . Phys. Chem. 1968, 72, 4672.
0 1989 American Chemical Society
