J . Phys. Chem. 1990, 94, 700-707
700
Flash Photolysis Study of the CH30, Ratios from 248 to 573 K
+ CH302Reaction:
Rate Constants and Branching
P. D. Lightfoot,* R. Lesclaux, and B. Veyret Laboratoire de Photophysique et Photochimie Molgculaire, UA 348 C N R S , UniversitZ de Bordeaux I , 33405 Talence Cedex, France (Received: February 21, 1989; In Final Form: June 13, 1989)
-
-
The reactions 2CH30, 2CH30 + O2 (la), 2CH302 CH30H + HCHO + 0, (lb), and 2CH302 CH300CH3 + O2 (IC)have been studied at temperatures between 248 and 573 K. At temperatures above 373 K, the resulting decay traces were distorted away from pure second order at short wavelengths (around 210 nm), owing to the presence of the hydroperoxy radicals formed via the nonterminating pathway (la) and the subsequent rapid step C H 3 0 + 0, HCHO + H 0 2 (2). This distortion enabled the nonterminating/terminating branching ratio, 0,to be determined. Combining the present results with previously published work on the branching ratios gave In (3 = 3.80 - 1470/T. Thus, although reaction 1 acts as a termination reaction under atmospheric conditions, it largely serves to convert CH302into H 0 2 under combustion conditions. The temperature dependence of 0enabled the real rate constant for the reaction, k l , to be. obtained over the entire experimental exp(365/n cm3molecule-’ s-I, with u2*/cm6molecule-2 = 2.00 X temperature range, giving k , = 1.3 X $E,R/K2 molecule-’ s-I = -5.61 X = 1712, and Absolute uncertainties, including contributions from both the experimental measurements and the dependence of k l on various analysis parameters, are estimated to be 22%, independent of temperature. No dependence of either the branching ratio or k , on the total pressure was found. The mechanism of the title reaction is discussed and the present results are compared with existing studies of alkylperoxy self-reactions. The implications for combustion and atmospheric modeling are also discussed. -+
-
Introduction The self-reactions of peroxy radicals are of both practical and theoretical interest. Peroxy radicals are known to be key intermediates in both the combustion1 and atmospheric2oxidation of hydrocarbons, and a detailed knowledge of the reactions between peroxy radicals would thus be an important contribution toward our understanding of these highly important and complicated processes. In general, such reactions display a negative temperature dependence and often several parallel reaction pathways, suggesting the intermediacy of an association complex, and a very complicated potential energy surface for the reaction. For example, the title reaction is believed to proceed via three pathways: CH302 + CH302 2CH3O + 0 2 (la) --* HCHO + CH,OH + 0 2 (1b)
-
Although the removal of methylperoxy radicals via reaction 1 has been much studied by use of direct techniques at temper-
atures appropriate to atmospheric ~ x i d a t i o n , ~no - ’ ~direct infor( I ) Cox, R. A. In Modern Gas Kinetics; Pilling, M. J., Smith, I . W. M . , Eds.; Blackwell Scientific: Oxford, 1987; Section C3. (2) COX,R. A. In Modern Gas Kinetics; Pilling, M. J., Smith, I. W. M.. Eds.; Blackwell Scientific: Oxford, 1987; Section C2. (3) Parkes, D. A.; Paul, D. M.; Quinn, C. P.; Robson, R.C. Chem. Phys. Lett. 1973, 23, 425. (4) Parkes, D. A. Int. J. Chem. Kinet. 1977, 9, 451. (5) Hochanadel, C. J.; Ghormley, J. A,; Boyle, J. W.; Ogren, P. J. J . Phys. Chem. 1977, 81, 3. (6) Anastasi, C.; Smith, I . W. M.; Parkes, D. A. J . Chem. Soc.. Faraday Trans. . . 2 ~ 1978. 74. 1693. (7) Kan, C: S.;’McQuigg, R. D.; Whitbeck, M. R.; Calvert, J. G. Int. J . Chem. Kinet. 1979, 11, 921 (8) Sanhueza, E.; Simonaitis, R.; Heicklen, J. Int. J . Chem. Kiner. 1979, 1 ., I . 907. . .. (9) Sander, S. P.; Watson, R. T. J. Phys. Chem. 1980, 84, 1664. ( I O ) COX.R. A.; Tyndall, G . J . Chem. Soc., Faraday Trans. 2 1980, 76, 153. ( I 1 ) Adachi, H.; Basco, N.; James, D. G. L . Int. J . Chem. Kinet. 1980, 12, 949. (12) Sander, S. P.; Watson, R. T. J . Phys. Chem. 1981, 85, 2960. (13) Kurylo, M. J.; Wallington, T.J. Chem. Phys. Lett. 1987, 138, 543. (14) McAdam. K.; Veyret, B.; Lesclaux, R. Chem. Phys. Lett. 1987, 133, 39. (15) Jenkin, M. E.; Cox, R. A.; Hayman, G.; Whyte, L. J. J . Chem. Soc., Faraday Trans. 2 1988, 84, 913. ( I 6) Simon, F.; Schneider, W.; Jenkin, M.; Moortgat, G. K. Presented at the 10th International Symposium on Gas Kinetics, Swansea, U.K., 1988. Simon, F.; Schneider, W.; Moortgat, G. Inf. J . Chem. Kinet. Submitted for publication. ~
~~
0022-3654/90/2094-0700$02.50/0
mation is available at temperatures above 417 K. In addition, studies of the branching ratios for the product channels at room t e m p e r a t ~ r e ” - show ~ ~ significant discrepancies and very little information is available on the temperature d e p e n d e n ~ e . ~ ~ , ~ ~ . ~ ~ Uncertainty in the branching ratios for the reaction impinges directly on the measured rate constant: all the direct studies of this reaction have monitored the apparent second-order rate constant, defined by -d[CH302]/dt = 2kObs[CH3O2l2, for the disappearance of the radical via its absorption around 250 nm. This apparent rate constant is greater than the real rate constant, k , , as the methoxy radicals produced in reaction l a react rapidly to produce H 0 2 , under the conditions of excess oxygen necessary in these studies to ensure the production of CH302: CH30
+ 02
-+
HCHO
+ H02
(2)
This H 0 2 in turn rapidly removes another C H 3 0 2radical on the time scale of reaction 1 : CH302 --*
+ HO2 HCHO
--*
CH3OOH
+ H2O + 0 2
+0 2
(3a) (3b)
( k 3 = 10k, at room t e m p e r a t ~ r e ’ ~ The ) . products of reaction 3 are all molecular; thus no further methylperoxy radicals are removed and the branching ratio for reaction 3 does not affect the rate of disappearance of CH302. We define the fraction of CH302 radicals which react via channel la as 0. For every CH302radical that reacts in this way, a further radical is rapidly removed via reactions 2 and 3. Thus, as long as reactions 2 and 3 take place quickly with respect to the time scale of reaction 1, the observed rate constant, kobs,is related to the real rate constant, k , , by kobs = ( I + ct)k,.I2 We also define the nonterminating/terminating (17) Anastasi, C.; Couzens, P. J.; Waddington, D. J.; Brown, M. J.; Smith, D. B. Abstract available at the 10th International Symposium on Gas Kinetics, Swansea, U.K., 1988. (18) Parkes, D. A., Proceedings of the 15th InternationalSymposium on Combustion, Tokyo, 1974; The Combustion Institute: Pittsburgh, PA, 1975; p 795. (19) Weaver, J.; Shortridge, R.; Meagher, J.; Heicklen, J. J . Photochem. 1975, 4, 109. (20) Weaver, J.; Meagher, J.; Shortridge, R.; Heicklen, J. J . Photochem. 1975, 4, 341. (21) Kan, C. S.; Calvert, J. G.; Shaw, J. H. J . fhys. Chem. 1980,84, 341 I . (22) Niki, H.; Maker, P. D.; Savage, C. M.; Breitenbach, L. P. J. Phys. Chem. 1981, 85, 877. (23) Alcock, W. G.; Mile, B. Combust. Flame 1975, 24, 125. (24) Selby, K.; Waddington, D. J. J . Chem. Soc., Perkin Trans. 2 1979, 1259.
0 1990 American Chemical Society
I
flash lamp
t
6
-+ per,
4
transient recorder
/
O
n
f
trigger flash lamp
Figure 1. Low-temperature apparatus.
branching ratio, Le., the fraction of C H 3 0 2radicals that react via channel l a divided by the fraction that react via channels l b and IC, as /3, where /3 = a / ( l - a). By determining the temperature dependence of the branching ratio, CY, of reaction 1 in this study, it was hoped to provide a more accurate estimate for the true rate constant, k l , than had previously been possible. We have recently studied the self-reaction of hydroperoxy radicalsZ5 at temperatures up to 777 K. It was shown that temperature dependence of k4, which is negative at low temperatures, becomes positive above 600 K, emphasizing the theoretical interest of such reactions and the importance of performing experiments over as wide a range of temperature as possible. This paper represents the second of a series of studies of peroxy radical reactions at elevated temperatures: a study of reaction 3 is presented in the following paper of this issue.26
Experimental Section The flash photolysis system consists of a deuterium lamp as the analysis light source, a reaction cell/temperature control combination, a pair of argon flash lamps, and a monochromator-photomultiplier assembly connected to a microcomputercontrolled transient recorder. Two sets of flash photolysis/UV absorption apparatus, differing chiefly in the design and construction of the photolysis cell and housing, were used, depending on the required temperature. At 373 K and below, a Pyrex cell fitted with a liquid-filled thermostat jacket was employed. At higher temperatures, an all-quartz cell situated in an electrically heated oven was used. The low-temperature apparatus is shown schematically in Figure 1; the details of the high-temperature cell and its housing are shown in Figure 2. Each flash lamp consists of a quartz tube, 0.85 m length, and 12 mm 0.d. For the high-temperature experiments, the flash lamps were surrounded by a second quartz tube, for better electrical insulation, and a removable Pyrex tube used to filter out radiation below 300 nm. For the low-temperature apparatus, these additional tubes were not necessary as the lamps were better isolated from electrically conducting parts of the apparatus and the cell itself was made of Pyrex. The electrodes are constructed from stainless steel and housed in custom-designed PVC supports. The flash is generated by passing a high-voltage discharge from a pair (25) Lightfoot, P. D.; Veyret, B.; Lesclaux, R. Chem. Phys. Lett. 1988, ISO, 120. (26) Lightfoot, P. D.; Veyret, B.; Lesclaux, R. J . Phys. Chem., following paper in this issue.
IWULATION
ALUMWM F O L
J
/
OVEN
THERMOCWRES
4
\
ELEM
Figure 2. High-temperature cell and mounting.
of 1-pF CSI capacitors through the flash lamps filled with argon. Triggering is performed by sending a 30-kV impulse into a wire wrapped around the flash lamps. By use of voltages of up to 25 kV, flash energies of 625 J per flash can be achieved. The half-life for the light pulse is ;=8 ps, although problems with scattered light prevent data collection for approximately 200 ps after the flash. The time between flashes is usually 30-60 s, allowing for a complete replenishment of the cell contents every flash, in order to minimize interference from the reaction products. The radicals are monitored in real time using their characteristic UV absorption bands. The analysis light from a Hamamatsu L1636 "superquiet" low-pressure deuterium arc discharge lamp passes through the cell twice (path length = 140 cm) via external optics (plane and spherical mirrorsf= 1000 mm) and is focused onto the entrance slit of a Jobin-Yvon H20 monochromator (1or 2-nm band-pass) coupled to a Hamamatsu R928 photomultiplier. The signal from the photomultiplier is passed to a Hitachi VC-6020 digital storage scope (8-bit resolution, 1-ps minimum sampling period) in the high-temperature apparatus and to a Datalab DL902 transient recorder (8-bit resolution, 1-ps minimum sampling period) in the low-temperature apparatus. After digitization, the signal is transferred to a microcomputer via an interface for averaging, analysis, and storage. The microcomputer also controls the synchronization of the predelay, flash-lamp firing, and signal-recording sequence. Signal to noise ratios are improved by averaging the transient decays over 4-32 flashes. The lower detection limit of this technique toward the radical concentration is on the order of 5 X 10l2molecules The cylindrical high-temperature reaction cell, 80 cm in length and 4 cm in diameter, is constructed entirely of quartz. Two 5-cm evacuated end pieces result in a length of 70 cm for the photolysis region. Gas mixtures are preheated as they pass along the entrance tube, which runs along the entire length of the cell. The cell is situated in a cylindrical, electrically heated oven composed of four
702
The Journal of Physical Chemistry, Vol. 94, No. 2, 1990
semicylindrical pieces heated (Kanthal) in series and with a maximum total power rating of I .7 kW at 220 V. Temperature measurement is provided by three K-type thermocouples, situated as shown in Figure 2 and which act as sensors for the temperature controller (EireLec Ltd). I n order to compensate for the greater heat loss through the ends of the oven, the ends of the cell are additionally heated with resistance wire encased in quartz beads. I n this way, the temperature along the entire photolysis length can be kept uniform and stable to f l % at 800 K. The inner walls of the oven are covered with reflective aluminum foil to ensure a homogeneous light flux, and hence radical concentration, in the cell. The low-temperature photolysis cell, shown in Figure I , consists of three concentric Pyrex tubes, 75 cm in length, 8.5 cm total external diameter. The innermost, reaction, chamber is of 4.5 cm internal diameter and 70 cm in length. Its ends are sealed by “Suprasil I” windows to allow transmission of the analysis UV beam, which passes through the center of the cell. In this way, any wall effects arising from heterogeneous chemistry are avoided. Six entrances and exits in the cell allow transverse flow of reactant mixtures through the reaction chamber, ensuring a homogeneous distribution of reactants. The temperature of the cell is controlled by circulating ethanol (229-298 K) or ethylene glycol (298-403 K) from a Huber HS40 thermostated circulating bath through the middle jacket. The temperature is measured with a thermocouple with a precision of better than f0.5 K. The third jacket is evacuated to improve thermal insulation. At subambient temperatures the windows and cell walls are flushed with a flow of dry nitrogen, which prevents the formation of condensation or frost from interfering with the passage of the analysis beam. Methylperoxy radicals were generated by using the well-established source: CI, + hu CI + CI (5)
Lightfoot et al. discussed in some detail in the following paper;26we merely note here that the spectra are independent of the present experimental conditions of pressure and temperature. The only reaction products that absorb significantly in our experimental wavelength region are methyl hydroperoxide and hydrogen peroxide; the cross sections for both of these species were taken from the very recent results of Vaghjiani and Ravishankara.28
Results and Discussion Experimental Conditions. Experiments were performed at temperatures between 248 and 573 K. The majority of the experiments were performed at atmospheric pressure, although some were performed at 210 Torr. The concentration of oxygen was maintained sufficiently high to ensure that the conversion of C H 3 0 into H 0 2 via reaction 2 was very fast on the time scale of reaction 1 ( k 2 [ 0 , ]varied from 6 X IO3 s-] at 248 K to 2.5 X IO4 s-I at 573 K29). No systematic dependence of the results on the flash-lamp energy, chlorine concentration, or the concentrations of methane and oxygen was noticed, suggesting the absence of unforseen chemistry. In particular, no evidence for the reaction of the various radicals present with molecular chlorine was found over the present temperature range. Above 600 K, however, there was evidence for a chain process involving the reaction of C H 3 0 with molecular chlorine and for the thermal decomposition of the CH4/CI2/air mixtures on the time scale of the residence time of the mixture in the cell. Further work in this interesting temperature region is planned, using more thermally robust chemical systems to generate CH30, radicals. Over the temperature range of this study, no problems associated with the thermal decomposition of either the reactants or the products were noticed. In addition, the results obtained using two flash lamps were identical with those obtained with a single flash lamp, within experimental error, validating our earlier experiments on the H 0 2 + H 0 2 reaction, in which only a single flash lamp was used.2s Branching Ratios. The branching ratios for reaction 1 have CI CH4 CH3 + HCI (6) been measured by a number of groups; the results are summarized CH3 0 2 + M --* CH302 + M (7) in Table I . Although several studies have been performed at nonambient temperatures, only the very recent study of Anastasi Conditions were chosen so that the time for the generation of the et aLk7was performed as a function of temperature. In each case radicals (7 = 40 ps) was always short compared to the time for where channel I C was observed, via the dimethyl peroxide product, their decays ( T = 40 ms). Particular care was taken to ensure it made only a very minor contribution to the overall rate constant. that the concentrations of methane and oxygen were sufficient Where the dimethyl peroxide product was not observed, the to prevent complications due to secondary reactions during the measured quantity was /3, the ratio of the radical ( l a ) to the generation period, thus ensuring the quantitative conversion of molecular (( 1b) (IC)) producing channels, Le., the ratio of the chlorine atoms into methylperoxy radicals. nonterminating to terminating channels. It is clear that significant Reaction mixtures were prepared using a standard Pyrex discrepancies exist between the various measurements. vacuum system fitted with Teflon taps. The usual reactant In view of the these discrepancies and, in particular, the paucity concentrations employed were as foliows in units of molecules ~ m - ~ : of data on the temperature dependence of the branching ratio, [O,] = (2.5-5.9) X IO”; [CH,] = (0.8-3.9) X loi8; [CI$ = we performed time-resolved experiments with the aim of observing (2.6-7.5) X IOk6; balance N,. All reagents were introduced into the HO, product of reactions l a and 2 by its UV absorption. The the cell via calibrated flow controllers; mixing occurred before UV spectra of H 0 2 and C H 3 0 2are broad and overlap strongly entry to the cell. Methane, oxygen, nitrogen, and methanol all but differ significantly in the position of their maxima: the H 0 2 flowed through Tylan FC 260 mass-flow controllers. Before and spectrum peaks at around 205 nm, where u(H02) = 5.3 X after each experiment, the concentration of chlorine was detercm2 m o l e c ~ l e - and ~ , ~ monotonically ~ decreases with increasing mined spectroscopically, using its absorption at 330 nm. wavelength, whereas the CH3O2 spectrum increases with waveOxygen, nitrogen (I’Air Liquide, purity >99.5% and 99.995%, length from 205 nm to its peak at around 235 nm, where urespectively), air (I’Air Liquide, 80% N,, 20% 02,same purities (CH302)= 4.8 X cm2 molecule-’,27and then decreases with as above), methane (I’Air Liquide, purity >99.5%), and chlorine increasing wavelength. Thus, at 210 nm, the HO, absorption cross ( 5 % in nitrogen, I’Air Liquide) were all used without further section is around a factor of 2 greater than that of CH302,whereas purification. at 240 nm, the C H 3 0 2absorption cross section is the greater by Decay traces were analyzed by nonlinear least squares, using around a factor of 3.27 Simulations showed that the presence of numerical integration of the appropriate system of chemical significant quantities of H 0 2 radicals should produce a distortion equations. Because of the problem of overlapping spectra, inherent of the C H 3 0 2decay trace at short ( H 0 2 >> CH,OOH >> H202. At 260 nm, the absorption due to CH,OOH and H202is negligible. The greater fractional absorption at the shorter wavelength enables the nonterminating/terminating branching ratio for the reaction to be determined. (a) 210 nm, full time scale 51.2 ms; (b) 210 nm, full time scale 5.12 ms; (c) 240 nm, full time scale 51.2 ms; (d) 240 nm, full time scale 5.12 ms.
studies of Jenkin et al.I5 and Simon et a1.16 have systematically varied the analysis wavelength. At this temperature, however, the concentration of H 0 2 relative to CH302never builds up to a significant level, due to both the dominance of the molecular channels of reaction 1 over the radical-producing channel and the great difference between the rate constants for reactions 3 and I . Using an average value of cy at room temperature, taken from Table I and literature values'4 for k3 and k l , simulations showed that any such distortion of the decay traces should be within reasonable experimental noise, as confirmed by the constancy of kobsas a function of wavelength in ref 15. Previous studies of reactions 330 and 112,'3 suggest, however, that the ratio k 3 / k l (30) Dagaut, P.; Wallington, T. J.; Kurylo, M. J. J . Phys. Chem. 1988, 92, 3833.
decreases with temperature, owing to the stronger negative temperature dependence of reaction 3. Thus, any H 0 2 produced via reaction l a should be more easily seen at high temperatures. Significant differences between the forms of our experimental decay traces collected at different wavelengths were observed at temperatures above 373 K. Figure 3 shows a set of decay traces collected at 473 K; the difference in the forms of the decays collected at 210 and 240 nm is very apparent, particularly at short reaction times. Under identical conditions of temperature and pressure, sets of four decays were typically collected, two at shorter wavelength (usually 210 nm) and two at a longer wavelength (usually 240 nm); at each wavelength, one decay was collected on a short time scale, where distortions due to the presence of H 0 2 were greatest, and the other was collected on a much longer time scale (typically an order of magnitude), where the overall decay
704
Lightfoot et al.
The Journal of Physical Chemistry, Vol. 94, No. 2, 1990
TABLE II: Analvsis Parameters absorption cross sections, 1018 a/cm2 molecule-’ 27,28 H02 CH302 H202 CH3OOH 0.31 5.3 2.5 0.37 0.13 0.06 I .8 4.8 0.06 0.03 0.3 3.6 Rate Constants/cm3 molecule-I s-’ k 3 = 4.4 X IO-” exp(780/T) (ref 26) k4 = 3.8 X exp(58O/T) + 1.2 X 10-”[M] exp(ll50/T) 7.1 X IO-’’ exp(-3730/T) (ref 25, 26) 210 n m 240 n m 260 n m
+
of CH302 was dominant. In this way, it was possible to extract information on both the nonterminating/terminating branching ratio, @, and the total rate constant, k , . In order to allow for small (6%) fluctuations in the flash intensity or relative radial absorption cross section between experiments, initial concentrations were optimized with respect to each decay trace. Global parameters, such as rate constants, were optimized with respect to the whole set of curves. The parameters used in the fitting procedure are summarized in Table 11. A typical fit to the data is shown in Figure 3. The total absorption at 240 nm is almost entirely due to C H 3 0 2 ,whereas there is a significant contribution from HO, at 210 nm. The difference between the forms of the decays at the two wavelengths is thus essentially that between the C H 3 0 2 absorption at 210 nm and the total absorption at the same wavelength. The present experiments only measure the total absorption as a function of time and thus do not directly measure the individual concentrations of each of the absorbing species. It is therefore important to demonstrate that all the absorbing species have been accounted for and that the distortion of the C H 3 0 2decay traces is caused by the presence of HO,. (i) The reaction scheme used to analyze the present decay traces (reactions 1-4) is consistent with our current knowledge of the chemistry of this system: we know that H 0 2 is produced in the title reaction. (ii) C H 3 0 0 H and H z 0 2 are the only stable products that contribute significantly to the observed decay profiles and then only to a minor extent. The absorption due to other molecular species involved in the production or subsequent reactions is negligible compared to that of the peroxy radicals. (iii) Although most experiments were done at 210 and 240 nm, some were performed with other pairs (one short, 230 nm) of wavelengths between 200 and 260 nm. No dependence of the results on the choice of wavelengths was noticed. The further species distorting the C H 3 0 , decay traces thus has a spectrum entirely compatible with that of HOz. (iv) The extent and time dependence of the H 0 2 contribution to the CH,O, decay traces is entirely compatible with our own studies of the CH3O2 + H 0 2 reaction:26 a approaches but does not exceed unity. In addition, our branching ratio ties in well with end product analysis work at lower temperatures. It was possible to extract useful information on the branching ratio for reaction 1 from the highest temperature reported here, 573 K, down to around 373 K. At lower temperatures, the decreasing importance of channel l a and the increasing rate of reaction 3 relative to reaction 1 resulted in decay traces at short wavelengths with forms similar to those at longer wavelengths. It is emphasized that our technique can only be used to distinguish between the terminating ((lb) (IC)) and H02-producing ( l a ) channels of the reaction; no differentiation between channels l b and I C is possible. However, all previous results suggest that channel I C represents only a small fraction of the total reaction. The value of p increased strongly with temperature. No dependence of (3 on total pressure was noticed. Our results are summarized in Table 111 and compared with previous studies in Figure 4. Despite the scatter in the various measurements, the general agreement is reasonable, given the difficulty of the measurement and the very different techniques used. Our own value at 388 K seems rather low, but this point represents the lower
+
TABLE 111: Present Results for a,8, and k I no. of a’ p exptb T / K .press./Torr . 573 760 0.82 4.42 4 8 523 760, 210 0.79 4.39 0.64 1.84 12 473 760, 210 0.49 0.97 4 423 760 0.29 0.41 4 388 760 0 373 760 0 368 760 0 298 760 0 273 760 0 248 760
1013k,c
2.58 f 0.16 2.40 f 0.19 2.77 f 0.1 1 2.94 f 0.30 3.37 f 0.30 3.41 f 0.33 3.23 f 0.42 4.53 f 0.74 4.74 f 0.31 5.47 f 0.56
no. of expt IO 8 18 4 4 6 4 14
4 7
“See text for a discussion of the uncertainties in a. * a and /3 were generally determined from a smaller number of experiments than kl. (Units of cm3 molecule-’ s-’. Errors are la, including a Student’s f.
Q
c
1
3
2
1000/T
4
.,
Figure 4. Arrhenius plot for /3, where p is the ratio of CH302radicals that react via channel l a to those that react via channels l b and IC: this work; 0,ref 17; ref 18; ref 19 and 20; 0, ref 21; 0, ref 22; *, ref 23; X, ref 24. Solid line shows the unweighted best fit to the data; dotted line shows approximate 1 a uncertainties. Uncertainties in the present values are discussed in the text.
+,
+,
temperature limit for the use of our technique to determine 0and is subject to greater experimental uncertainty than the points at higher temperatures. It is clear that, whereas the molecular channels are clearly dominant under atmospheric conditions, at temperatures above 400 K, the radical channel l a leading to H 0 2 is the most important. Thus, although reaction 1 acts as a termination step for peroxy radicals in atmospheric oxidation systems, it serves to convert C H 3 0 2into HO, in combustion systems. The unweighted data in Figure 4 were fitted to an expression of the form In (3 = A + B / T , giving In p = 3.80 - 1470/T
(El)
The variances and covariance for A and B are given by dA= 0.92, u ~ ~ =/ 1.1 K 1~ X lo5, and a2AB/K = -3 13; approximate 1u uncertainties in In are shown in Figure 4. Transforming (El) gives the corresponding result for a ( a = p/(1 + p)): a = 1/(1
+ exp(1470/T)/45)
(E2)
The dependence of a on temperature, with approximate l a uncertainty limits, calculated by use of the method of propagation of errors, is shown in Figure 5. The sensitivity of a to changes in the analysis parameters is discussed below. Rate Constants. The values of a deduced from (E2) were used in the analysis of the decay traces at temperatures of 373 K and below. In these cases, single decay traces were analyzed, returning values of the total rate constant k l and the initial concentration. No systematic dependence of k , on wavelength was found, confirming that the values of a used were not significantly in error. The present results at room temperature are compared with previous measurements, corrected for differences in absorption cross sections, in Table IV. There now seems to be generally good agreement on kobs/cat ambient temperature. Similarly, the absorption cross section at the maximum of the CH3O2 spectrum
Flash Photolysis Study of the CH302 1.0
+ CH3O2 Reaction I
1
The Journal of Physical Chemistry, Vol. 94, No. 2, 1990 705 TABLE V Comparison of Temperature-Dependent Studies of k," T/K press./Torr Ab -E/R' ref 248-417 60-700 N2 9.7 f 1.4d 438 f 47 12 9.4 f 1.4 414 f 37 13 228-380 50-400 481 f 102 17 760 7.8 f 2.4 250-450 248-573 200-760 air 12.7 f 1.4 365 f 41 this work
"Corrected to the present values of a(CH302). The kob values of other workers have been corrected to k , by dividing by 1 cy at each temperature (E2) and refitting to an Arrhenius expression. bunits of cm3 molecule-I SKI. 'Units of K. dErrors lo.
+
1000/T
Figure 5. Dependence on temperature of a,the fraction of CH302radicals that react via channel la. a = p/(l + 8). Symbols have the same meaning as in Figure 4. TABLE IV: Comparison of Measurements of khbaat Room Temperature k..k/@ X/nm techniaueb knhC ref 3.6 f 1.2 3 7.5 f 2.5d 240 MMS MMS 4.8 f 0.9 4 10.0 f 1.8 238 FP/UVA 5.8 f 1.0 5 13.1 f 2.3 248 6 235-240 3.8 f 1.0 8 f 2 7 20.5 f 2.5 265 FP/UVA 6.4 f 0.8 8 FP/UVA 5.9 f 0.5 14.4 f 1.2 254 9 FP/UVA 4.9 f 0.3 245 10.6 f 0.7 9 FP/UVA 7.2 f 0.9 270 28.4 f 3.6 5.9 f 1.0 10 250 MMS 13.3 f 2.3 FP/UVA 5.0 f 0.4 11 10.5 f 0.8c 212.5-280 FP/UVA 5.2 f 0.7 12 11.8 f 1.6 250 FP/UVA 4.9 f 0.6 13 250 1 1 . 1 f 1.4 FP/UVA 5.9 f 1.0 14 250 13.4 f 2.3 MP/UVA 4.9 f 0.5 15 11.1 f 1 . v 210-270 MP/UVA 4.8 f 0.2 16 I 1.6 f 0.d 220-270 5.3 f 1.5 17 MMS 11.0 f 3.1 240 FP/UVA 5.6 f 0.9 this work 11.7 f 1.v 2 10-260
" Units of IO5 cm2 molecule-'. bAbbreviations: MMS, molecular modulation spectrometry; FP/UVA, flash photolysis/UV absorption; MP/UVA, modulated photolysis/UV absorption. 'Corrected to the present values of o(CH302). dErrors lo. c240 nm. f250 nm. found in recent studies is in good agreement, with o,,,(CH302) = (4.8 f 0.4) X IO-'* cm2 m o l e c ~ l e -and ~ , the ~ ~absolute ~ ~ ~ ~value ~~ of kob at room temperature can also be considered as well-defined. The dependence of k , on the presence of up to 12.8 Torr of water vapor at room temperature was also briefly studied; no significant dependence was found, in agreement with the work of Kan and Calvert3I and Sanhueza et aL8 Fitting to all the present results gives k,/cm3 molecule-'
s-I
= 1.27
X
exp(365/T) (E3)
with u2A/cm6molecule-2 s - ~= 2.00 X uZEIR/K2= 1712, and (T2AE/R/Cm3molecule-' s-I = -5.61 x IO-'3. The present results and values of k , , derived from the three previous temperature-dependent studies of kobsby dividing kobs by ( 1 + a ) at each temperature and refitting the resulting data set to an Arrhenius form, are compared in Table V and Figure 6. I n each case good agreement with our own results over their common temperature range is observed, although the derived Arrhenius parameters are somewhat different, emphasizing the importance of performing experiments over as wide a range of temperature as possible. The value of k , was independent of pressure between 210 and 7 6 0 Torr at 4 7 3 and 5 2 3 K, in agreement with previous work at room t e m p e r a t ~ r e . ' ~ Also shown in Figure 6 are our values of kob and the dependence of kobson temperature, calculated from (E2) and (E3), using kobs =(1 a ) k l . It is interesting to note that the Arrhenius plot of kobs should be slightly nonlinear over our temperature range, although any such nonlinearity is well within the experimental scatter. Below 250 K, where a is very small, kobsshould be very
+
(31) Kan, C. S.; Calvert, J. G. Chem. Phys. Lett. 1979, 63, 1 1 1
=
I
1,
10-131
1
2
3 1000/T
4
5
Figure 6. Arrhenius plot for k , and kob. k , : -, m, this work, error bars represent experimental l o uncertainties,including a Student's t; - - -,ref 12; -.-, ref 13; -, ref 17. kob: -, 0,this work. The kob values for ref 12, 13, and 17 have been corrected to values of kl, using the present expression for (Y (E2). See text for details.
close to k , and thus display the same temperature dependence. At higher temperatures, the increase in a with temperature partially offsets the overall reduction in k , with temperature and kobsdisplays a weaker temperature dependence. Above 700 K, where a changes very little with temperature, kob i= 2kl and should again display approximately the same temperature dependence as k , . Sensitivity Analysis. Owing to the rather indirect method used to determine the branching ratio and thus the real rate constant in this study, it is important to assess the effects of possible changes in the analysis parameters on the derived results. Artificial decay traces were generated with the same rate constants and absorption cross sections employed in the actual analysis (see Table 11) and values of a and k , taken from ( E 2 ) and (E3), respectively. Randomly distributed noise, with a root-mean-square deviation of 3% of the peak absorption, corresponding to typical experimental conditions, was added to the decays, which were than analyzed in exactly the same manner as the experimental traces, but with analysis parameters that differed from those in Table I1 by *20%. Sensitivity parameters were not derived for a at low temperatures, where a was not determined experimentally. The results are summarized in Table VI. It is clear that the derived parameters, a and k , , are sensitive to the value of k3. For example, at both 573 and 373 K, an increase in k3 results in an equally large increase in a. Physically, a larger value of k3 would reduce the concentration of H 0 2 , resulting in a less pronounced distortion of the simulated trace, and in order to reproduce the observed distortion, the optimum value of a would need to be increased. The corresponding sensitivity of k , to k3 is large at high temperatures but decreases rapidly with decreasing temperature, as might be expected. Changes in the absorption cross sections of H 0 2 at 210 and 240 nm are included to allow for changes in the spectrum of H 0 2 relative to CH302. The value of a is very sensitive to such changes; k3 is less so, particularly at the lower temperatures. The sensitivities of a and k l to k4 were negligible under all experimental conditions. Allowing for errors of approximately 25% in k326and 10% in our relative spectra of HOz and CH302 results in a 28% uncertainty in our values of a, essentially independent of temperature. This uncertainty, based on possible systematic errors, is much greater than the experimental scatter on a . The corresponding
706
Lightfoot et al.
The Journal of Physical Chemistry, Vol. 94, No. 2, 1990
TABLE VI: Sensitivitv Parameters. S. ,."for a and kl a(H0,,210
and 240 nm)
k3
T IK 573 313 213
a
k,
a
k,
0.96
-0.64
-1.33
-0.42
-1.26
0.56 0.34 0.06
1 .os
-0.04
nSi, = In (dai/aio)/ln( ~ Q ~ / Q ~ where '), ai refers to the derived parameter, a, to the analysis parameter, and ' to the original value. The fractional change in a or k , is given by the fractional change in the analysis parameter, multiplied by the appropriate sensitivity coefficient.
errors for k , are 17% at 573 K, decreasing to 11% at 373 K. At lower temperatures, the effects of k 3 and the relative spectra on k , are negligible and a was not determined. Combining these derived uncertainties in k , with the experimental scatter results in 1 cr uncertainties for k , of 17%, approximately independent of temperature over our experimental range. This uncertainty does not allow for possible errors in the absolute calibration of our spectra (Le., both HO, and CH302). Changes in this calibration would not affect C Y . although k l would scale linearly. Using an estimated uncertainty of 15% for the absolute values of the absorption cross sections increases the uncertainty on k , to 22% as quoted in the abstract. Owing to the dependence of a and k , on the value of k3, the final analysis of the present data, as well as that used to determine k 3 in the following paper26was performed iteratively: the values of k , and a found here were used in the analysis of k 3 and the value thus obtained reentered into the analysis of k , and a. Fortunately, this procedure rapidly converged and only two iterations were required to give results which were stable to well within the 1 u experimental uncertainties for each parameter. Mechanism and Comparison with Other Alkylperoxy Radicals. The weak negative temperature dependence and values well below the collisional limit of the overall rate constant suggest the formation of an association complex that can redissociate to reactants or go on to form products. In addition, the lack of sensitivity of the measured parameters to the total pressure suggests that the association complex is thermalized under the conditions of our experiments. This initially formed moiety is thought to be dimethyl tetroxide, CH304CH3. Infrared absorption features attributed to this species were observed by Ase et aL3, on annealing argon/oxygen matrices containing methylperoxy radicals. No evidence for the production of CH,OH, C H 3 0 0 H , CH302CH3,or HCHO was found, demonstrating that the tetroxide was stable at 35 K in the matrix. This observation also suggests that all the reaction products observed at ambient temperature are produced via the same tetroxide intermediate. No observations of tetroxides in the gas phase have been reported, and the UV absorption spectra of such species are unknown. Indeed, it is unlikely that the tetroxide is thermally HO, reaction is also stable at our temperatures. The HO, thought to proceed via a tetroxide intermediate. In order to reproduce the experimental dependence of the overall rate constant on pressure and temperature, using RRKM methods, Patrick et al.33were obliged to postulate weak (30-60 kJ mol-') H02-02H bonding. Under such conditions, the redissociation of the thermalized H 0 4 H intermediate into reactants is very rapid, on the millisecond time scale, around ambient temperature. The presence of two methyl groups instead of hydrogen atoms should not greatly affect the barrier to redissociation, and redissociation in the present case should thus also be rapid on our experimental time scale. That redissociation to reactants competes very effectively with rearrangement to products in the present case can be inferred from the experimental rate constant, k , , which decreases with temperature and which is around a factor of 50 below the rate constant for association of the isoelectronic n-propyl radical at room temperat~re.~~
+
(32) Ase. P.; Bock, W.; Snelson, A. J . Phys. Chem. 1986, 90,2099. (33) Patrick, R.; Barker, J. R.; Golden, D. M. J . Phys. Chem. 1984, 88. 128.
*3-'8Lp--.--
J-
2
3
-_... - ~ - ~
-~
5
:003/-
Figure 7. Arrhenius behavior of several alkylperoxy radical self-reactions. (a) CH302;(b) C2H502;(c) i-C3H702;(d) t-C4H,O2. -, koh; - - -, k , (=k,b,/(l
+ C Y ) ) ; ..., akl.
The fact that, with increasing temperature, one product channel increases rapidly at the expense of the others whereas the overall rate constant changes only slightly provides further strong evidence for a common intermediate for the various product channels. Equation E l can thus be equated to the ratio of the Arrhenius forms of the rate constants for the unimolecular decomposition of the thermalized intermediate species CH304CH3via channels l a and l b + IC. Assuming that channel IC is not significant, then A,,/A,b = 45 and E,, - Elb = 12 kJ mol-,. At this point it is important to note that the increasing importance of channel l a with temperature does not indicate a peroxy radical self-reaction with a positive temperature coefficient as the total rate constant k , decreases with increasing temperature. This negative temperature dependence presumably arises because the redissociation of the tetroxide adduct increases more rapidly with temperature than the sum of its reactions to give products. A comparison of the present results with those obtained for other alkylperoxy radicals is instructive. The dependence on temperature of the observed second-order rate constant and of the branching ratios have been studied for the e t h y l p e r ~ x y , ~isopropylper~-~~ OXY,^^,^ and t e r t - b u t y l p e r ~ x y ~ J ~radicals. , ~ ~ * ~ ' In the latter case, channel l b is not possible as there are no hydrogen atoms bonded to the peroxy carbon atom. The results for these three radicals are compared with the present results for methylperoxy in Table VI1 and Figure 7. There are several results to note: (i) The temperature dependence of the total rate constant, k , , is negative for CH3O2; for the other peroxy radicals, the temperature dependence is positive, the activation energies increasing with radical size. For i-C3H702and t-C4H902,the temperature ranges studied are not sufficient to allow an accurate determination of their A factors. (ii) In each case where the two channels la and 1b are possible, they are effectively competing with each other over the temperature range studied. For example, at 298 K, a = 0.25, 0.39, and 0.14 for CH302,C2H502,and i-C3H702,respectively, despite the fact that the total rate constants vary greatly. (iii) The contributions of channel l a to the overall reaction, a k l , shown in Figure 7 , all show a positive temperature dependence, increasing in magnitude in the order C H 3 0 2C C2H502 < i-C3H702(
