J. Phys. Chem. 1985,89, 4713-4720 distances is unlikely may be biased by the lattice model, which does not allow the chain tilting which can m r even in the absence of chain torsional isomerism. It is precisely this kind of motional freedom in chains which directly result in the substantial chain tilting observed in a full molecular dynamics simulation.
4713
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, and to the Research Corporation for partial support of this research. S.H.N. is a recipient of an NIH/Research Career Development Award.
A Laser Flash Photolysis Study of the Reaction CH,
+ O2
---*
CH302at 298 K
Michael J. Pilling* and Martin J. C. Smith Physical Chemistry Laboratory, Oxford University, Oxford, OX1 3Q2,U.K. (Received: April 23, 1985)
+
The reaction CH3 O2 9CH302 has been studied at room temperature over a wide range of conditions (initial methyl radical concentration (co);oxygen concentration, and total pressure) by using 193-nm laser flash photolysis of azomethane, coupled with absorption spectroscopy. The rate constant, k l ,was measured under conditions of low c o / [ 0 2 ]where , the contribution ! 2CH30 was shown to be small (the limiting zero-pressure third-order rate constant with argon as a third body, kl" the limiting high-pressure rate constant, and r the relative stabilization efficiencies of oxygen and argon (Le., r = k l , o ~ / k l ~ Equation o). D demonstrates that kl,h may be obtained from a plot of In k l vs. [O,] and Figure 3 shows plots of In kl vs. [O,] for 32- and 53-torr total pressure. The extrapolated values ((2.00 f 0.10) X cm3 molecuIe-'s-' at 32 torr and (2.61 f 0.05) X cm-3 molecule-' s-I at 53 torr) differ little from the mean values of k , (all oxygen concentrations) of (2.07 f 0.04) X cm3 cm3 molecule-' s-' (32 torr) and 2.65 & 0.02) X molecule-' s-I (53 torr), where the quoted uncertainties are the standard deviations of the mean. At higher total pressures, where k l is closer to the limiting second-order value, no correlation was observed between In k l and [O,] and the values of k , returned from the original analysis were presumed to apply to a pure argon diluent. The analysis of the experimental fall-off curve, which will be described in the discussion section, enables kl,A: and kl" to be determined. Thus, the slope of the plots shown in Figure 3 may be employed to determine r (=kl,02/kl,Ar)the ratio of the stabilization efficiencies of 0, and Ar. Such an analysis gives r =
(17) Macpherson, M. T.;Pilling, M. J.; Smith, M. J . C. J. Phys. Chem. 1985, 89, 2268.
K.;Troe, J . Int. Symp. Combust. [Proc.],17, 1978 1979, p 5 3 5 .
(ka
-
kb)
= ak3effc0/ [O21
applies with a = 0.6. a is independent of the value used for k3eff in the range 4 < 10'1k3eff/cm3molecule-' s-' < 10. There is no systematic dependence of ( k , - k b ) on total pressure, suggesting that, within experimental error, k3 is indepedent of total pressure, p , over the range 53 < p/torr < 490. and a k3effvalue in the range (4-10) Provided co/[02] < X lo-'' cm3 molecule-1 s-I is employed, eq B returns accurate values for kl (Le., k b = k l ) . Thus the analysis described in the previous paragraph demonstrates that kl may be determined from the k, values obtained by using an analysis of data at low c o / [ 0 2 ] , via eq C
(18) (a) Troe, J . Ber. Bunsenges. Phys. Chem. 1983, 87, 161. (b) Luther,
4716
Pilling and Smith
The Journal of Physical Chemistry, Vol. 89, No. 22, 1985
_---
/---
1
I
.#"
I
I
I
100
200
300
1
400 500 Argon pressurelTorr
I
Figure 4. Dependence of k , on argon pressure; the error bars show the 95% confidence limits. The inset shows the data of Selzer and Bayes:' (-) best fit, using the Troe factorization method with k," = 1.05 X lo-', cm3 molecule-] s-', k10 = 4.8 X cm6 molecule-2 s-I, p', = 0.68; (---) fit using the best fit values of Cobos et (k," = 2.2 X 10-l2cm3 molecule-' s-l).
TABLE I: Jhendence of k , on Argon Pressure at 298 K argon press./ 1 0 ' ~ k ~ / argon press./ 1013kl/ torr cm3 molecule s-I torr cm3 molecule s-' 31.9 2.00 f 0.220 218 4.90 f 0.26 52.6 2.61 f 0.10 286 5.60 f 0.17 84.4 3.44 f 0.21 376 6.11 f 0.22 127 4.11 f 0.07 488 6.48 f 0.17 163 4.46 f 0.24
"95% confidence limits
1.12 f 0.05 at 32 torr and 1 . 1 1 f 0.05 at 53 torr total pressure. Figure 4 shows a plot of k l vs. argon pressure; the error bars represent 95%confidence limits, and the values are listed in Table I. A minimum of four determinations was made at each pressure and a total of 102 separate experiments is incorporated in Figure 4. An estimated uncertainty of 2% in the oxygen pressure has been combined with the uncertainty in the fitted pseudo-first-order rate constants to determine the uncertainty limits for each determination of k l . 3 . The Determination of k3. The decay data obtained at co/ [O,] ratios greater than contains information which may, in principle, be used to obtain estimates of k3 with greater precision than the rather broad limits defined in section 2. Under these conditions, the analytic approximations contained in eq A and B are no longer valid and numerical integration techniques must be adopted. Under such circumstances, a full kinetic scheme, such as that defined in Table 11, should be employed. The reaction mechanism is designed to model the short time (C2 ms) behavior of the reaction system, and is based on the reaction schemes proposed by Parkes9 and by Adachi et al.ls (although the latter assumed reaction 3 to be terminating). The major reactions (1-8) involve the radicals CH3, CH3O2, and CH30. k l and k3 are of direct concern in the present work, kz has previously been measured in this l a b o r a t ~ r y , ' while ~ , ~ ~ values for k4 recommended by Baulch et aLi9and of k8 measured by Cox et aLZ0and Gutman et were employed. No measured rate constants have been reported for reactions 5 and 7 and the estimates of Adachi et al.,I5 Kan et and Parka9 were adopted; these reactions are, however, of limited importance. Reaction 6 is discussed in section 4; a considerably higher value than that previously estimatedzz was employed. Preliminary simulations of the decay profiles demonstrated that the concentration of the hydroperoxyl radical was low, typically,
-
(19) Baulch, D. L.; Cox, R. A.; Crutzen, P. J.; Hampson, R. F.; Kerr, J. A,; Troe, J.; Watson, R. T. J . Phys. Chem. Ref. Data 1982, 1 1 , 327. (20) Cox, R. A.; Derwent, R. G.; Kearsey. S. V.;Batt, L.; Patrick, K. G.
J . Photochem. 1980, 13, 149. (21) Gutman, D.; Sanders, N.; Butler, J. E. J . Phys. Chem. 1982,86,66. (22) Kan, C. S.; Calvert, J. G.; Shaw, J. H. J. Phys. Chem. 1980,84,3411. (23) Cox, R. A.; Tyndall, G. S . J . Chem. SOC.,Faraday Trans. 1 1980, 76, 153. (24) Sander, S. P.; Peterson, M.; Watson, R. T.; Patrick, R. J . Phys. Chem. 1982, 86, 1236.
0 Oo-
-00o0 lo'tis
10'tis
Figure 5. Decay profiles of the fractional absorption at 216.36 nm. (a) c,, = 3.01 X 1014cmT3,[O,] = 2.62 X 10l6~ m -best ~ , fit for k3 = 5.09 f 0.38 X lo-" molecule-' s-I, x2 = 1.81; (b) co = 7.44 X 10" ~ m - ~ , [O,]= 2.04 X 10l6 ~ m - best ~ , fit for k3 = (4.81 f 0.38) X IO-'' molecule-' s-I, x2 = 0.85. (-) fit using the full kinetic scheme; ( - - - ) calculated curves, using eq A, with the same values for k , , k2,co, and [02l.
-
-
[HO,] 5X [CH30] [CH302]. Thus reactions 9-1 2, although included, are of minor significance. Reactions of minor products in the initial photolysis (H, CH2)179zswere also included in the kinetic scheme, but played an insignificant role. Decay profiles were recorded at a total pressure of 123 torr, C -4 ~X 1014 and 2 in an argon diluent, with 3 X 1013 C ~ ~ / c m X 10l6 C [ O , ] / C ~ -C~4 X 10l6.Approximately 100 data points were employed in the fits describing 95-99% of the methyl radical decay. The numerical integration program FACSIMILE^^ was used to determine the time-dependent radical concentrations for input values of k3 and co. The concentrations were converted to fractional absorptions via the equation AI/Zo = 1 - exp(-~ui[Xi]I) i
where the Xi are the species CH3, CH,O2, and HO,, with absorption cross sections at 216.36 nm, oi of 4.12 X lo-'' cm', 3.6 X cmz (section l ) , and 6.5 X cmz.z7 k3 and co were then varied to minimize the sum of squares of the residuals between simulated and observed fractional absorptions. Constant weighting factors, calculated from the standard deviation of the pretrigger base line, were applied to the experimental data, since the fractional absorptions were small. Reduced x2 values in the range 0.85-1.81 were obtained for the final fits. Figure 5 shows fits to the decay profiles for the extreme values of xz.The figure also shows decay traces, calculated for the same values of kl, k2, co, and [O,], but omitting reaction 3 from the reaction scheme (i.e., calculated by using eq A). Table I11 shows the best fit values for k3 for a ninefold variation in co/[02]. The values are randomly scattered, despite the wide variation in the contribution of reaction 3 to the decay. The external estimate of the standard deviation of the mean of the k3 values was about 4 times greater than the internal estimate suggesting that nonrandom errors are present (in, for example, the rate constants assumed in the fit-see below). Under these circumstances, an unweighted (as opposed to reciprocal-variance-weighted) estimate of the mean is more valid, giving k 3 = (4.54 f 0.33) X lo-" cm3 molecule-] s-I, where the quoted uncertainty limits are the standard deviation of the mean. In order to estimate the uncertainty more realistically, the effects of errors in the other rate constants must be assessed. As a first step, a sensitivity analysis of the simplified kinetic scheme (reactions 1-8) was performed by using the Green's function method,28via the program CHEMSEN.29 The reduced sensitivity (25) Baggott, J. E.; Brouard, M.; Coles, M. A,; Davis, A,; Macpherson, M. T.; Pilling, M. J., to be published. (26) Chance, E. M.; Curtis, A. R.; Jones, I . P.; Kirby, K. R.
'FACSIMILE: A Computer Program for Flow and Chemistry Simulation and General Initial Value Problems"; H.M.S.O.: London, 1977; No. C13. (27) Hochanadel, C. J.; Ghormley, J. A,; Ogren, P. J. J. Chem. Phys. 1972, 56, 4426. (28) Hwang, J. T.; Dougherty, E. P.; Rabitz, S . ; Rabitz, H. J. Chem. Phys. 1978, 69, 5180.
The Reaction CH3
+0 2
-.
The Journal of Physical Chemistry, Vol. 89, No. 22, 1985 4717
CH302
TABLE I 1 Kinetic Scheme for the CH3/02 System'
---
1. CH, + O2 CH302 2. CH3 + CH3 C2H6 3. C H 3 + C H , 0 2 2CH,O 4a. 2 C H 3 0 2 inert products 4b. 2CH,02 2 C H 3 0 + O2 5. C H 3 C H 3 0 products 6. CH,O C H 3 0 2 products 7. 2 C H 3 0 products 8. CH,O O2 products
-+ -+ - + + -+ +
9. CH, H 0 2 products 10. C H 3 0 2 H 0 2 products 1 1. CH,O H 0 2 products 12. 2 H 0 2 products
" Rate constants of pressure-dependent
range of variation rate constant/ of rate constant cm3 molecule-' s-I in fit A. Reactions of Major Species 4.1 x 10-13 5% 5.7 x 10-1' 5% 4.5 x 10-1' 2.2 x 10-13 1.5 x 10-13 3 x 10-11 (1-6) X lo-'' 1 x 10-11 (0.1-10) x 10-12 3 x 10-1' (1-6) X lo-" 1.3 x 1 0 4 5 B. Reactions Involving Minor Species 3 x 10-1' 6X 2 x lo-" 1.8 X 10-l2
20% 5%
this work 16, 17 this work 19 19 9, 15, 22b this work 9, 15, 22' 20, 21
10% total
15' 23 15' 24
lglSl
*
-2
"95% confidence limits assuming only random errors in the fit (see text).
0
1.0
0
1.0
coefficient for substance X with respect to rate constant ki is defined by Figure 6 shows sensitivity coefficients for C H 3 and CH3O2 over 99% of the methyl radical decay for typical experimental conditions. The sensitivity analysis demonstrates that both the methyl and methylperoxy concentrations are most sensitive to the values employed for the well-defined rate constants, k l and kz, and the fitted rate constant, k,, confirming the validity of the approach adopted in this section to determine k3. The sensitivity coefficients for the estimated rate constants (Table 11) are much smaller. The uncertainty in the fitted value of k3,arising from uncertainties in the rate constants employed in the model, was determined by varying k , , k2, k5,k6,and k7 over the ranges shown in Table 111. The sensitivity analysis demonstrated that the effect of the other rate constants included in the analysis is negligible. The resulting uncertainties in k3, from each of the sensitive rate constants, are also shown in Table 111. Combining these estimates with the error intrinsic in the determination of k3 from the experimental data gives a total uncertainty in the region of 25% and a final estimate for k3 of (4.5 1.1) X lo-" cm3 molecule-' s-l. 4 . The Time Dependence of [ C H 3 0 z ] .The time dependence of the methylperoxy radical concentration was monitored concurrently with that of the methyl radical, in order to test further the mechanism developed in sections 1-3. The monitoring beam was split after leaving the reaction cell, and about 10% passed through a 254-nm interference filter to a photomultiplier. Typical time scales employed were 0.4-2 ms. HOZis the only other species formed in the proposed kinetic scheme which also absorbs at 254 nm; Hochanadel et al.6,27obtained cr(HO,)/a(CH,O,) = 0.2 at this wavelength. Seven, separate, dual-monitoring experiments were performed over a range of initial conditions: 4 X lOI3 < cO/cm-, < 4 X 1014 and 2 X 1OI6 < [ O , ] / C ~ < - ~4 X 10l6. The 216-nm absorption was analyzed as described in section 3. Radical concentrations,
ref
1
reactions refer to 127 torr. bEstimate.
TABLE 111: Best Fit Values for k q as a Function of cn/[O21 103co/ 10"k3/ 103co/ 10"k3/ ro,i cm3 molecule-' s-l 10,1 cm3 molecule-' s-I 1.4 3.34 1.40" 3.1 5.90 f 0.75 1.9 6.30 f 0.70 3.6 4.81 f 0.38 2.3 3.21 f 0.69 9.2 4.16 f 0.11 2.7 3.46 f 0.50 11.5 5.09 f 0.19 2.9 4.50 f 0.27 12.5 4.60 f 0.16
typical resultant uncertainty in k?
2.0
104tls
2.0 104t/s Figure 6. Reduced sensitivity coefficients for (a) CH, and (b) C H 3 0 2 over 99% of the CH, decay for co = 3.4 X 1014cm-) and [O,] = 3.7 X 10I6~ 3 1 7 ~The ~ . circled numbers refer to the reactions listed in Table 11.
*
(29) Kramer, M. A,; Rabitz, H.; Kee, R. J. Sandia Tech. Rep. 82-8230, 1982. Kramer, M. A,; Calo, J. M.; Rabitz, H.; Kee, R. J. Sandia Tech. Rep. 82-9231, 1982.
/
OO
1
2
4
3
104tls
Figure 7. Buildup and decay of the absorption signal at 254 nm,due, primarily, to C H 3 0 2 : (-) fit to data by using the mechanism shown in Table I1 with u(CH,O,),~, = 3.4 X cm2 and k7 = 1 X lo-'' cm3 molecule-' s-I. The other parameters (co, k,) were determined by fitting to the absorption at 216.36 nm,which was recorded concomitantly. (---) first order fit to the long-time decay.
calculated with the best fit values of k3 and co for the 216-nm absorption, were fitted to the 254-nm absorption with the cross
4718
The Journal of Physical Chemistry, Vol. 89, No. 22, 1985
Pilling and Smith
TABLE I V Rate Parameters Describing the Decay of CH302 kobsd/S-l
103c0/[021
353 139 137 186 139 71 93
9.2 3.6 3.1 2.9 2.7 2.3 1.9
[CH3021ma,/ ioi3 11.3 3.9 4.6 6.2 3.4 3.2 4.6
" D = {kobpd - 2k4[CH,0,],,,l/[CH30].
[CH3Olmax/ 10" cm-3
[Hod ma,/ 10" cm-'
3.5 0.86 1.1 1.1 0.45 0.36 0.88
0.06 0.03 0.04 0.04 0.02 0.02 0.04
Units = lo-" cm3 molecule-'
section for CH3O2, u(CH302)254 as the only adjustable parameter. Allowance was made for absorbance by H 0 2 although its contribution to the total absorbance was very small (6 10.0 k 0.5 2.6 f 0.05
1.7 2.2 1.2 f 0.6
(4)
of the decay was followed, it is reasonable to define an apparent first-order decay constant, kobsd,even if the decay is second order in radicals, since the concentration of the latter are approximately constant. Table IV shows values of kow for the seven experiments, which covered a factor of 4 in co/ [O,]. The maximum CH302, C H 3 0 , and H 0 2 concentrations, determined from the FACSIMILE fits, are also shown. kobd is a factor of 2-5 times greater than the maximum pseudo-first-order rate constant for reaction 4. Even if the maximum reported value for k4 is employed (5.8 X cm3 molecule-' s-I),l5 the decay is still far too rapid to be explained by this channel. C H 3 0 is the only other radical present in significant concentrations on these time scales, and Figure 6 demonstrates that [CH302]is sensitive to k6 if a rate constant in the region of IO-" cm3 molecule-' s-' is employed. The final column in Table IV lists values of D = (kow - 2k4[CH302]man)/[CH30], which is an estimate of k6 if the discrepancy in the CH302 decay rate can be ascribed entirely to reaction 6. Although the D values are somewhat scattered, their variation is random and uncorrelated with [CH30],,,, which covers a tenfold range. Thus the reaction C H 3 0 C H 3 0 2 products (6)
-
-
provides a reasonable and consistent explanation of the enhanced methylperoxy decay, provided k6 1 X lo-" cm3 molecule-' s-'. Figure 7 shows a fit to the absorbance at 254 nm using this mechanism. Alternative interpretations (reaction with H 0 2 , CH3N2CH3, or HCHO, wall reaction, or photolysis by the monitoring beam) were considered quantitatively but shown to be unimportant. An alternative explanation can be provided, which is consistent with the low literature value for k6(
