J. Phys. Chem. 1988, 92, 2971-2974
Computational Study of the CH,
2971
+ 0, Chain Branching Reaction
R. Zellner* and F. Ewig Institut fur Physikalische Chemie, Uniuersitat Gottingen, Tammannstrasse 6, 3400 Gottingen, FRG (Received: June 11, 1987)
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Rate constants and branching ratio for the reaction channels CH3 + O2 C H 3 0 + 0 (la) and CH3 + O2 C H 2 0 + OH (1b) have been derived from RRKM theory by assuming a common CH302intermediate. The computation is based on a 160 kJ/mol isomerization barrier between CH302and C H 2 0 0 H as derived recently in direct studies of the reverse C H 3 0 + 0 reaction at low temperatures. In contrast to most previous conclusions, channel l b is predicted to dominate over channel la at all temperatures below 2800 K, with the individual rate coefficients being k l , = 1.1 X lo1, exp(-l3990/T) and k l b = 3.4 x 10'' exp(-6Oo/T) cm3/(mol.s).
Introduction Due to its thermal stability, the methyl radical plays an important role in the oxidation of hydrocarbons. Whereas larger radicals decompose rapidly prior to their oxidation, methyl radicals have thermal lifetimes long enough to encounter direct oxidation by either 0 atoms or 02.Whereas the reaction with 0 atoms is important under radical-rich conditions (Le., flame propagation), the reaction with O2becomes dominant in radical-poor situations during ignition and induction peri0ds.I The reaction between C H 3 and O2 has two channels, viz. CH3
+ O2
-
+
CH30+ 0
AHR = +119 kJ/mol
(la)
+ OH
AHR = -222 kJ/mol
(lb)
CH2O
In here the formation of CH30 is usually followed by rapid decomposition to yield CHzO H, such that the reaction becomes chain branching. Next to the overall rate coefficient (kla + k l b ) the branching ratio ( k l b / ( k l a klb)) is of extreme importance to the rate of growth of the free-radical concentration in the induction period of hydrocarbon oxidation. This has long been recognized, and as a consequence a large number of experimental studies2-'2 have been devoted to the kinetics of this reaction. Whereas there is reasonable agreement between the various degiving activation terminations of the rate coefficient kla,2-9-11 energies between 109 and 130 kJ/mol in close proximity to the endothermicity of this channel, the determinations of k l b scatter by almost 2 orders of magnitude between 1500 and 2000 K. The limits available for k l b render this reaction from dominant7J1to absolutely negligible3s9at the lower end of this temperature range. Moreover, activation energies reported for klbdiffer by almost 100 kJ/mol, with the lowest value being only 38 kJ/mol." This situation is highly unsatisfactory since most sophisticated experimental techniques have been used in the most recent studies,%" and not much improvement can be expected along this line. In the present work we report results from a computational study using RRKM theory together with the assumption of a
+ +
(1) Wamatz, J. In Combustion Chemistry; Gardiner, W. C., Ed.; Springer: New York, 1984; p 197. (2) Brabbs, T. A.; Brokaw, R. S.Symp. (In?.) Combust., [Proc.], 15th
1975, 893. (3) Dean, A. M.; Kistiakowsky, G. B. J . Chem. Phys. 1970, 54, 1718. (4) Jachimowski, C. J. Combust. Flame 1974, 23, 233. (5) Tsuboi, T.; Wagner, H . Gg. Symp. (In?.) Combust. [Proc.],15th 1975, 833. (6) Bowman, C. J. Symp. (In?.) Combust., [Proc.],15th 1975, 869. (7) Olson, D. B.; Gardiner, W. C. Combust. Flame 1979, 32, 151. (8) Tabayashi, T.; Bauer, S.H. Combust. Flame 1979, 34, 63. (9) Bhaskaran, K. A.; Frank, P.; Just, Th. Proc. Znt. Symp., Shock Tubes Waves, 13th 1981, 503.
(IO) Shu, D. S.Y.; Shaub, S. M.; Creamer, T.; Gutman, D.; Lin, M. C. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 909. (11) Saito, K.; Ito, R.; Kakumeto, T.; Imamura, A. J . Phys. Chem. 1986, 90, 1422. (12) Baldwin, A. C.; Golden, D. M. Chem. Phys. Lett. 1978, 55, 350.
0022-3654/88/2092-2971$01SO/O
common intermediate, C H 3 0 0 , with a two-channel fragmentation, viz. CH, O2 9 CH3O2 C H 3 0 0 (la)
+
--
+
-
CH200H CH2O + O H (1b) The impetus of this work comes from a recent experimental study, performed in our laboratory, on the rate constant and O H product yield of the C H 3 0 + 0 reaction a t low temperature^.'^,'^ This study has confined the energy barrier of isomerization (AEiso) between CH3O2 and CHzOOH to 160 kJ/mol, whereupon the energetics of channel l b is much better quantified than has previously been the case. Even in the most recent computational study of reaction 1,15 the authors were led to treat AEisoas a variable quantity.
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Energetics of the Reaction Whereas the thermochemistry of reagents and products and hence AHR 2f the overall reaction are well-defined (for a summary of thermodynamic data used see Table I), there is considerable uncertainty as to AHf for CH200H and the corresponding transition state of its formation from CH3O2. Based on an activation energy for reaction l b of E,b = 145 kJ/mol, the C H 3 0 2 CH200H isomerization barrier (AEiso) was previously assumed to be -260 kJ/mol.I0 A recent redetermination of E:, however, led to a much smaller value (38 kJ/mol"), inferring AEi, 160 kJ/mol and AHf* 180 kJ/mol. Moreover, independent confirmation of a low AHf* value also came from two recent ab initio calculations which predicted 20516 and 22317 kJ/mol. In recent work in our own laboratory we have determined both the absolute rate coefficient and the branching ratio for the reverse reaction, viz. C H 3 0 + 0 CH3O2 CH3 + O2 (-la) CHZOOH CH20 OH (lb) Values of = (1.5 f 0.4) x IO1, cm3/(mol.s) and k-lblk-1 = 0 . 1 2 3 2 at T = 298 K were ~ b t a i n e d . ' ~ . By ' ~ use of RRKM theory, the result for the branching ratio was found to be in agreement with AHf* 180 kJ/mol, corresponding to an isomerization barrier of AEia = 160 kJ/mol. As a consequence there appears to be sufficient information, obtained from independent sources,11,14,16,17 which suggests that AEisois near 160 kJ/mol, considerably smaller than has been previously assumed. The standard heat of formation of CHzOOH has been accepted as 65 kJ/mol, a value intermediate to what has been obtained in an ab initio calculation (69.8 kJ/mol16) and what can be estimated from group additivity rules (54 f 10 kJ/m01~~-'*).It should be
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+
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(13) Rhasa, D.; Zellner, R. Chem. Phys. Lett. 1986, 132, 474. (14) Ewig, F.; Rhasa, D.; Zellner, R. Ber. Bunsen-Ges. Phys. Chem. 1987, 91, 708. (15) Dean, A. M.; Westmoreland, P. R. In?. J . Chem. Kine?. 1987, 19, 207. (16) Melius, C. F., private communication, 1986. (17) Kamiya, K.; Matsui, H.; Asaba, T., private communication (cited in ref 11).
0 1988 American Chemical Society
2912 The Journal of Physical Chemistry, Vol. 92, No. 10, 1988
Zellner and Ewig
TABLE I: Summary of Thermodynamic Data and Their Temperature Dependence Relevant to the Reaction between CH3 and O3 species/reaction 298 K 500 K 1000 K 2000 K 3000 K CH3 CHI0 0
2
CHZOOH CHI02 CH2OOH ( A H f * ) +
CH3 CH3
+ +
CH3
+ 0 2 + CH3O2
0 2
0 2
+
+
CH3O CH2O
+0 + OH
146.9e 16.5' 17.6 65b 180'
155.3 25.4 30.7
AHf', kJ/mol 181.6 58.6 76.0
248.8 147.7 190.2
325.4 248.7 316.2
119 -222
118 -222
AH,", kJ/mol 118 -223
115 -224
101 -225
7.5 x 10'0
K,,d cm3/mol 2.6 x 104
13.0
1.1
6.6 X
IOl9
"Accepted value; average of the data reported, Batt et *Accepted value; average of values obtained by an a b initio technique16 and from ?~~ dTemperature dependence calculated from group additivity rules.14*'* Accepted value based on experimental"^'^ and t h e o r e t i ~ a l ' ~evidence. = 17.6 kJ/mol.I9 'Reference 17. fReference 21. NASA polynomials of BurcatZ4but adjusted to give agreement with AHf0298(CH302)
where i = a, b. In here k,(T) and k-,(T) are the thermally averaged rate coefficients for the dissociation (a, -1) and isomerization (b) channels of CH302. They are obtained from the corresponding specific rate coefficients k , ( E ) and the thermal distribution function
f(E) = p(E) exP(-E/RT)/Qvlb
(3)
via k,(T) =
QV,b-'L,
kl(E) P(E) exP(-E/RT) d E
(4)
where i = a, b, -1. Since for all temperatures below 3000 K ( k , + kb)
