9352
J. Phys. Chem. 1996, 100, 9352-9359
Kinetic Study of the Reaction of the CFCl2CH2O Radical with O2 Fuxiang Wu and Robert W. Carr* Department of Chemical Engineering and Materials Science, UniVersity of Minnesota, Minneapolis, Minnesota 55455 ReceiVed: October 23, 1995; In Final Form: February 27, 1996X
The 2-fluoro-2,2-dichloroethoxy radical, CFCl2CH2O, is an intermediate in the mechanism of the tropospheric degradation of CFCl2CH3 (HCFC-141b), a chlorofluoromethane replacement in some large-scale industrial applications. In this work, the reaction of CFCl2CH2O with O2 was investigated at 10-35 Torr and 251341 K by UV flash photolysis and time-resolved mass spectrometry. CFCl2CH2O2 radicals were formed from the photolysis of CFCl2CH3/N2/O2 mixtures. The CFCl2CH2O radical is a product of the reactions of CFCl2CH2O2 with Cl and ClO and the self-reaction. The rate of formation and decay of CFCl2CH2O was followed by observations of the fragment ion CClCH2O+. The rate coefficient of the reaction of CFCl2CH2O with O2, determined from CHCl2CH2O decay in excess O2 by both pseudo-first-order analysis and nonlinear regression, can be expressed as (2.4 ( 0.5) × 10-15 exp[-(944 ( 55)/T] cm3 molecule-1 s-1. The half-life for removal of CFCl2CH2O radicals from the atmosphere by the title reaction is 6 ms in the mid-troposphere and 1 s in the mid-stratosphere.
Introduction Because of the January 1, 1996, ban on most technological uses of the chlorofluorocarbons (CFCs), alternative chemicals have been identified for use in many applications. Among these, HCFC-141b (CFCl2CH3) replaces CFC-11 (CFCl3) as a foam blowing agent in polyurethane foam insulation and is also used in some solvent and cleaning applications. This substance has been detected in the atmosphere since 1992, and measurements of its global distribution and mixing ratio growth have been reported.1 Since there is no known natural source of CFCl2CH3, it is clear that HCFC-141b has been in use for some time. Escape of these chlorine- and fluorine-bearing CFC replacements into the atmosphere is commonplace, making it imperative to understand their atmospheric chemistry. Reaction is initiated by H atom transfer from the hydrochlorofluorocarbon (HCFC) or hydrofluorocarbon (HFC) to atmospheric OH radicals, immediately followed by addition of O2 to the newly formed haloalkyl radical. The ensuing complex and only partially understood oxidative degradation mechanism involves halogenated alkoxy radicals as key intermediates. In this work we report on the stability of the CFCl2CH2O radical that is formed in the tropospheric oxidation of HCFC-141b and the kinetics of its reaction with O2. The stability of perhalomethoxy radicals has been studied by a number of research groups.2-6 It has been found that for many R-Cl-substituted oxy radicals the C-Cl bonds are very weak and unimolecular elimination of Cl is facile, even at the low temperatures characteristic of the upper troposphere. On the other hand, alkoxy radicals are thermally stable at atmospheric temperatures, and reaction with O2 is an important atmospheric removal mechanism. Investigations of the reaction with O2 have been reported for CH3O,7-13 C2H5O,9,14,15 and (CH3)2CHO16 radicals.
CH3O + O2 f CH2O + HO2
(1)
C2H5O + O2 f C2H5O + HO2
(2)
* To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(95)03116-9 CCC: $12.00
The CF3O radical is stable to C-F bond scission at atmospheric temperatures,4 and the reaction with O2 is very slow, with a reported upper limit k3 e 4 × 10-17 cm3 molecule-1 s-1 at 298 K.17
CF3O + O2 f CF2O + FO2
(3)
Catoire et al.18 reported that unlike CHCl2O and CCl3O, which rapidly eliminate Cl atoms, the CH2ClO radical reacts quantitatively with O2 to produce HO2 under ambient conditions,
CH2ClO + O2 f CHClO + HO2
(4)
in agreement with evidence from final product studies by Sanhueza and Heicklen19 and by Niki et al.20 Rayez et al.4 attributed the difference in the behavior of CHCl2O, CCl3O, and CH2ClO radicals to the differences in the potential barriers for chlorine atom elimination. Kaiser and Wallington21 have recently reported evidence for HCl elimination from the CH2ClO radical. The HCl unimolecular elimination will compete with the reaction with O2 at elevated temperatures. Reaction with O2, which can occur when an R-H atom is available, and dissociation by either C-Cl or C-C rupture are the principal expected atmospheric fates of halogenated ethoxy radicals. The relative importance of these paths depends mainly on the halogen substitutional pattern of the radical and on O2 concentration.21-27 For example, it was reported by Wallington et al.22 that at 296 K reaction of CH2FCFHO with O2, reaction 6, does not compete with C-C scission, reaction 5, even at a fairly high partial pressure of O2 (147 Torr).
CH2FCFHO f CH2F + HC(O)F
(5)
CH2FCFHO + O2 f CH2FC(O)F + HO2
(6)
In the case of CF3CFHO radicals produced from HFC-134a (CF3CFH2) at the same experimental conditions, 20% react with O2 and 80% undergo C-C bond rupture.23,24 However, the sole atmospheric removal mechanism of CH3CF2CH2O and CF3CHOCF3 radicals has recently been reported to be reaction with O2, and unimolecular dissociation is of negligible atmospheric © 1996 American Chemical Society
Reaction of the CFCl2CH2O Radical with O2
J. Phys. Chem., Vol. 100, No. 22, 1996 9353
importance.25,26
CH3CF2CH2O + M f CH3CF2 + HCHO + M
(7)
CH3CF2CH2O + O2 f CH3CF2CHO + HO2
(8)
We have previously reported mass spectrometric observations of the CFCl2CH2O radical on the time scale of several milliseconds.28 In this investigation, CFCl2CH2O observation times were extended to 100 ms, and the kinetics of the CFCl2CH2O reaction with O2 was studied by mass spectrometrically monitoring CFCl2CH2O decay in the photolysis of CFCl2CH3/ O2/N2 gas mixtures. To the best of our knowledge, this is the first direct determination of the reaction of a haloalkoxy radical with O2. The CFCl2CH2O radical is shown to be sufficiently stable at atmospheric temperatures, and reaction with O2 is the primary atmospheric removal mechanism. Experimental Section The experimental apparatus and procedures were given in detail earlier.28 Kinetic experiments were carried out by broad band flash photolysis, approximately 1 µs flash duration at 5 Hz, and with time-resolved electron ionization/quadrupole mass spectrometry via pinhole sampling of the jacketed, temperaturecontrolled reactor ((1 °C). The xenon flashlamp (6 kV discharge voltage) was pulsed at 5 Hz. The reactants flowed through the reactor, a 6.6 cm long × 0.53 cm wide square channel milled into a stainless steel block, at 12 cm/s for purging between flashes. The irradiated volume of the reactor was approximately 0.9 cm long, centered on the pinhole. Ion counts from a Daly detector were preamplified, discriminated, and signal averaged with a multichannel analyzer. Gaseous mixtures of CFCl2CH3 and N2 were prepared and introduced into the reactor. A separate inlet line mixed in O2 just upstream of the reactor. At each total reactor pressure, the partial pressure of O2 could be controlled at either 0.5, 1, 1.5, or 2 Torr. The reaction was initiated as in our previously reported investigation of the flash photolysis of HCFC-141b/O2/N2 mixtures.28 Atomic chlorine was generated by the photodissociation of CFCl2CH3 through Suprasil optics. The initial concentration of Cl atoms was determined by NOCl actinometry and was in the range (2-8) × 1013 cm-3. Typically, [Cl]0/ [CFCl2CH3] was in the range (1-1.3) × 10-4 depending upon the flash intensity and the focusing optics position. CFCl2CH2O2 was formed by reactions 9 and 10:
CFCl2CH3 + Cl f CFCl2CH2 + HCl
(9)
CFCl2CH2 + O2 f CFCl2CH2O2
(10)
The Cl atoms are a stand-in for OH radicals, which initiate the atmospheric reaction, since they are easier to generate in the laboratory and are more reactive with 141b. The removal of CFCl2CH2O2 radicals, and the formation of CFCl2CH2O radicals, occurred by the following reactions:
CFCl2CH2O2 + Cl f CFCl2CH2O + ClO
(11)
CFCl2CH2O2 + ClO f CFCl2CH2O + ClOO
(12)
2CFCl2CH2O2 f 2CFCl2CH2O + O2
(13)
In the atmosphere, CFCl2CH2O is formed primarily from CFCl2CH2O2 + NO. Reactions 11 and 12 were previously investigated by monitoring the formation of CFCl2CH2O via a signal
Figure 1. Experimental m/z ) 77 signal at 341 K and 25 Torr total pressure. Gas mixture: 57.4% HCFC-141b in N2. [O2]: 1.4 × 1016 cm-3. Gas flow rate: 12 cm s-1.
at m/z ) 77 which was identified as (CClCH2O)+, a fragment ion of CFCl2CH2O.28 In this work, the decay of CFCl2CH2O was followed for as long as 100 ms in the presence of deliberately varied partial pressures of O2. Linde extradry grade nitrogen and Northern Cryogenics oxygen (99.99%) were used from cylinders without further purification. Research grade chlorine was obtained from Linde and was dried by distillation from -78 to -196 °C. Nitric oxide was supplied by Matheson with a minimum purity of 99.0% and was degassed and stored in a glass bulb. NOCl was prepared and purified using the method described previously.28 CFCl2CH3 (HCFC-141b) was purchased from PCR, Inc., with a minimum purity of 97% and was degassed before use. Results Pseudo-First-Order Analysis. Figure 1 shows the time dependence of the signal at m/z ) 77, revealing that CFCl2CH2O rises to a maximum in about 10 ms and then decays away in about 100 ms. The rise time is controlled by reactions 9-13. The decay rate was found to increase with increasing [O2], and this was attributed to reaction 14.
CFCl2CH2O + O2 f CFCl2CHO + HO2
(14)
Although atomic oxygen is formed by photolysis of O2 in amounts proportional to [O2]0, the oxy radical decay cannot be accounted for by reaction with the low levels of O atoms encountered here, since the O atoms must react predominantly with HCFC-141b and ClO. The kinetics of the former reaction has not been reported, but if the rate coefficient is estimated from O + CH3CH2Cl and O + CH3CHCl2 (each equal to 2.5 × 10-15 cm3 molecule-1 s-1 at 321 K)42 and the O + ClO ) Cl + O2 rate coefficient reported in ref 30 is applied, the halflife of the O atoms would be approximately 0.5 ms. At lower temperatures the latter reaction may dominate, but the O atom lifetime would still be less than 1 ms. Since [O]0 was estimated at approximately 2 × 10-11 cm-3 (see ref 28 and Table 3), there are not enough O atoms remaining after the maximum of [CFCl2CH2O] to significantly influence its decay. Numerical simulations, with the mechanism given in Table 3, showed that other reactive intermediates are not present in sufficient concentration to contribute measurably to the oxy radical decay. Further numerical simulations showed that the OH radicals
9354 J. Phys. Chem., Vol. 100, No. 22, 1996
Wu and Carr
Figure 2. First-order plot of CFCl2CH2O decay signal at 341 K and 25 Torr total pressure. Gas mixture: 57.4% HCFC-141b in N2. [O2]: 1.4 × 1016 cm-3. Gas flow rate: 12 cm s-1. (O) Experimental data; (s) linear fitting.
Figure 3. k14′ vs O2 at different total pressures and at 341 K. Gas mixture: (50-58)% HCFC-141b in N2. At each given total pressure, the partial pressure of O2 is controlled to be either 0.5, 1, 1.5, or 2 Torr, respectively: (b) 35 Torr; (O) 25 Torr; (9) 20 Torr; (0) 10 Torr.
generated by the O + 141b reaction react almost exclusively with 141b. However, the additional oxy radicals formed by these side reactions only contribute 0.2% to the yield formed by the main 141b photolysis path and are of negligible consequence.
data permit the rate coefficient to be expresed as
With [O2] 2-3 orders of magnitude larger than [CFCl2CH2O], the decay of the oxy radical was assumed to be pseudo-firstorder. Figure 2 is an example of a first-order plot of the m/z ) 77 signal from 45 to 80 ms. Data from shorter times could not used, since the formation rate of the oxy radical interfered, while at times longer than 100 ms the purge flow swept the radicals away from the sampling region. Over the limited time available, linear least squares fits, shown by the line in Figure 2, were done. Although there is visually detectable curvature of the first-order plots, the pseudo-first-order assumption proved to be satisfactory. The good agreement between the results obtained by the pseudo-first-order method and the nonlinear regression analysis described below shows that serious errors are not introduced by the pseudo-first-order assumption. At a given temperature and a given total pressure, pseudofirst-order decay rate constants of reaction 14, k14′, were calculated from these fits. Experiments were conducted over a range of [O2] at different total pressures and different temperatures, and values of k14 were determined from k14′ vs [O2] plots. Figure 3 is such a plot for several pressures at 341 K, from which it is apparent that there is no systematic variation of the slope with pressure. The intercepts show that there is a significant O2 independent component of the decay that depends upon total pressure. This is analyzed below and is shown to be due primarily to combined diffusion and flow out of the sampling region. The 341 K bimolecular rate coefficients listed in Table 1 reveal that the reaction is somewhat slow, and although the values of k14 showed some variability, they are sufficiently in accord that no clear pressure dependence of k14 can be discerned. The data in Table 2 confirm the absence of a pressure dependence at other temperatures. Table 2 also shows that the reaction has a modest temperature coefficient, the values of k14 increasing by less than a factor of 3 over the 90° range from 251 to 341 K. These data are presented in the Arrhenius plot of Figure 4 as the filled circles. Linear regression of these
k14(T) ) (2.7 ( 0.7) × 10-15 e[-(973(91)cal/T] cm3 molecule-1 s-1 where the statistical errors are reported as 2σ. Nonlinear Regression Analysis. Because the oxy radical decay range available for the pseudo-first-order analysis is less than one decade and the first-order kinetic plots have discernible nonlinearity, the data were also analyzed by one-parameter nonlinear regression as an alternative determination of k14. The reaction mechanism on which the regressions were done was developed in our investigation of the reactions of Cl and ClO with CH3CFClO2 and CFCl2CH2O2 radicals.28 A modified version was also employed in our work on the reaction of NO with these peroxy radicals.31 In both studies the reactions were initiated by flash photolysis of HCFC-141b/O2/N2 mixtures, as in this work, but here lower purge flow rates were used in order to increase the observation time available before the reacting mixture was swept away from the pinhole. The reaction mechanism is listed in Table 3. Values of all of the rate coefficients except reactions 14 and 25 are available from the literature.28,30,32-36 Oxy radical loss by flow through the pinhole and by wall reaction are included as a lumped first-order process. The apparent rate coefficient, k25, was experimentally determined as described in the next section. The calculations were done on an Apollo workstation. Figure 5a illustrates the quality of the fits over the first 40 ms, demonstrating that the mechanism is capable of giving very good results over this time interval. An indication of the sensitivity of the fits is given in this figure by the dotted lines, which are the results of numerical simulations in which k14 was varied by (50%. The values of k14 obtained by fitting 35 Torr, 321 K data over five different time intervals are listed in Table 2. The results obtained by regression over the first three time intervals, up to 40 ms, are in agreement with the values of k14 determined by the pseudo-first-order plotting method. However, the fitted values of k14 become larger than those from the pseudo-firstorder method if data beyond 40 ms are used. Thus, the mechanism of Table 3 is inadequate at longer times, and an additional decay mechanism, or mechanisms, must come into play. This is illustrated in Figure 5b by the divergence of a
Reaction of the CFCl2CH2O Radical with O2
J. Phys. Chem., Vol. 100, No. 22, 1996 9355
TABLE 1: Experimentally Determined First-Order Rate Constants of Reaction 14, k14′, at Different Total Pressures and at 341 K k14′ (s-1) O2 concentration (1016 molecules cm-3) 1.42 2.83 4.25
total pressure (Torr)
0
35 25 20 10
36.0 ( 0.3 28.8 ( 0.3 20.5 ( 0.2 17.8 ( -.2
39.1 ( 0.3 29.9 ( 0.3 21.3 ( 0.2 20.6 ( 0.2
38.5 ( 0.4 33.4 ( 0.3 24.8 ( 0.2 22.49 ( 0.2
42.0 ( 0.4 32.9 ( 0.3 27.3 ( 0.3 23.2 ( 0.2
5.67
k14 (10-16 cm3 molecule-1 s-1)
45.4 ( 0.5 36.3 ( 0.4 29.1 ( 0.3 24.9 ( 0.2
1.54 ( 0.6 1.27 ( 0.4 1.62 ( 0.3 1.19 ( 0.3
times. The results are in good agreement with the pseudo-firstorder analysis. These rate coefficients are plotted in Figure 4 as the open circles. A linear least squares fit of all of the data from both methods of analysis gives the Arrhenius expression
k14(T) ) (2.4 ( 0.5) × 10-15 exp[-(944 ( 55/T)] cm3 molecule-1 s-1
Figure 4. Arrhenius plot of experimentally determined rate constants of reaction 14: (O) experimental results from nonlinear regressions; (b) experimental results from first-order plot method; (s) linear fitting.
TABLE 2: Determined Rate Constants k14 (10-16 cm3 molecule-1 s-1) for the Reaction of CFCl2CH2O with O2 at Different Temperatures and Pressures First-Order Plotting Method temp (K)
35 Torr
25 Torr
20 Torr
10 Torr
average
341 321 317 302 290 270 255 251 251
1.54 1.35 1.1 1.21 0.95 0.84
1.27 1.24 1.31 1.15 0.81 0.64 0.46 0.62 0.60
1.62 1.18 1.2 1.21 1.14 0.79 0.46 0.71 0.65
1.19 1.27 1.25 1.07 1.11 0.68 0.58 0.41 0.45
1.41 ( 0.20 1.26 ( 0.07 1.2 ( 0.10 1.18 ( 0.07 1.0 ( 0.15 0.74 ( 0.09 0.50 ( 0.10 0.58 ( 0.10 0.57 ( 0.08
Nonlinear Regression Method (0-20 ms Data Were Used) temp (K)
pressure (Torr)
341 338 290 270
35 35 35 35
average
k14 1.39 1.04 0.99 0.66
1.70 1.32 1.14 0.81
1.82 1.83 0.97 0.84
1.37 1.23 0.96 0.76
1.57 ( 0.22 1.36 ( 0.34 1.01 ( 0.09 0.77 ( 0.08
Nonlinear Regression Results at Different Time Scales (35 Torr, 321 K) time range of data point k14
0-10 ms
0-20 ms
0-40 ms
0-60 ms
0-99.5 ms
1.26
1.29
1.44
1.89
2.51
numerical simulation of the calculated CFCl2CH2O profile from the data at long times. We show below that the additional decay mechanism comes from the combined effects of diffusion and purge flow. Table 2 also lists values of k14 obtained by numerical regression at several experimental conditions. The regressions were done over the time interval from 0 to 20 ms to avoid the mass transport effect on oxy radical concentration at longer
This is in good agreement with the Arrhenius expression from the pseudo-first-order method, confirming that the experimental limitations do not introduce significant errors into the pseudofirst-order analysis. We recommend this Arrhenius equation since it is derived from both methods of data analysis. Numerical simulations with this mechanism also permitted examination of predicted concentrations of intermediates as a function of time in order to assess possible interferences in the pseudo-first-order analysis. The calculated concentration profiles of CFCl2CH2O2 and CFCl2CH2O shown in Figure 6 indicate that enough CFCl2CH2O2 is present even at 20-30 ms to cause significant formation of CFCl2CH2O. This shows that the experimental data points for the pseudo-first-order analysis should only be taken after 40 ms. It was estimated that the error will be less than 5% if the data points after 40 ms are used to determine k14 by the pseudo-first-order method, and it will be greater than 20% if data points before 40 ms are used. Effect of Mass Transport. Four processes, other than reaction with O2, which can influence oxy radical decay are (1) flow from the reactor into the ion source chamber through the pinhole, (2) axial diffusion of CFCl2CH2O from the center into unirradiated regions toward the ends of the reactor, (3) passage of a region of decreasing [CFCl2CH2O] past the pinhole due to the purge flow (there is a symmetrical axial gradient of [CFCl2CH2O] due to the light intensity distribution from the flashlamp and also due to diffusion), and (4) heterogeneous removal. If these are described as first-order loss processes, the observed first-order rate constant, k14′, would be given by the sum
k14′ ) k14[O2] + ke + kd + kw
(15)
where ke is the rate coefficient for decay caused by flow through the pinhole, kd is a lumped rate coefficient accounting for diffusion and bulk gas flow through the reactor, and kw is the wall removal rate coefficient. Equation 15 predicts that k14 can be obtained from the slope of a plot of k14′ vs [O2], while the mass transport mechanisms giving rise to the last three terms would account for the intercept. To investigate this aspect of the experiments and to deepen our understanding of this complex reaction system, models for pinhole flow and axial diffusion were used to estimate ke and kd for comparison with the intercepts. Additional experiments, designed to provide an estimate of kw, were also done. The pinhole flow rate coefficient, ke, can be expressed as
ke ) A0Veff/V
(16)
where A0 is the area of the pinhole, V is the exposed volume of
9356 J. Phys. Chem., Vol. 100, No. 22, 1996
Wu and Carr
TABLE 3: Reaction Model for Nonlinear Regressions (321 K, 35 Torr of Total Pressure)a 9. 10. 11. 12. 13. 14. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.
CFCl2CH3 + Cl f CFCl2CH2 + HCl CFCl2CH2 + O2 f CFCl2CH2O2 CFCl2CH2O2 + Cl f CFCl2CH2O + ClO ClO + CFCl2CH2O2 f ClOO + CFCl2CH2O 2 CFCl2CH2O2 f 2 CFCl2CH2O + O2 CFCl2CH2O + O2 f CFCl2CHO + HO2 CFCl2CH2o f loss CH3CFCl + O2 f CH3CFClO2 CH3CFClO2 + CFCl2CH2O2 f CH3CFClO + CFCl2CH2O + O2 2CH3CFClO2 f 2CH3CFClO + O2 CH3CFClO2 + Cl f CH3CFClO + ClO ClO + ClO f product ClO + ClO + M f Cl2O2 + M ClO + O f Cl + O2 ClO + CH3CFClO2 f ClOO + CH3CFClO Cl + O2 + M f ClOO + M CH3CFClO f CH3CFO + Cl Cl + Cl f Cl2 Cl + ClOO f Cl2 + O2 Cl + ClOO f 2ClO ClOO + ClOO f product ClO + HO2 f HOCl + O2 Cl + HO2 f HCl + O2
kb
ref
4.8 × 10-15 1.0 × 10-11 5.3 × 10-11 7.2 × 10-12 3.7 × 10-12 1.26 × 10-16 8.8c 9.6 × 10-13 3.7 × 10-12 3.7 × 10-12 1.3 × 10-11 1.6 × 10-14 8.6 × 10-16 3.7 × 10-11 7.2 × 10-12 8.8 × 10-16 1 × 105 c 2.1 × 10-14 2.3 × 10-10 1.2 × 10-11 1.6 × 10-11 5.2 × 10-12 3.2 × 10-11
30, 32 30 28 28 33, 34 this work see text 30 33, 34 33, 34 28 30 30 30 28 30 6 35 30 30 36 30 30
a Initial concentrations: CFCl2CH3 6.16 × 1017 cm-3; Cl 8.13 × 1013 cm-3; CH3CFCl 8.13 × 1013 cm-3; O2 3.03 × 1016 cm-3; O 1.93 × 1011 cm-3. Calculated maximum concentrations: [CFCl2CH2O]max 1.07 × 1014 cm-3; [CFCl2CH2O2]max 5.2 × 1013 cm-3. b Unit: cm3 molecule-1 s-1. c Unit: s-1.
the reactor, and Veff is the linear flow speed through the pinhole. Xiong and Carr37 have shown that for flow which is in the transition between bulk flow and free molecular flow, which is the situation in these experiments, Veff is given by the interpolation formula of eq 17.
Veff ) (1 - β)(〈V〉/4) + β(RVs)
(17)
In eq 17, β ) r/(λ + r), r is the radius of the pinhole, λ is the mean free path, 〈V〉 is the molecular average speed, R is an empirical parameter which is equal to 0.95,37 and Vs is the speed of sound. Parameters for eq 17 and calculated values of Veff and ke at 341 K and at different total pressures are listed in Table 4. To determine kw, photolysis experiments with a 58% HCFC141b in N2 mixture (with a trace of oxygen present) were conducted at 35 Torr and 284-346 K. The low O2 level is sufficient for rapid and quantitative conversion of CFCl2CH2 radicals to CFCl2CH2O2, but the reaction of CF2ClCH2O with O2 is negligible. Also, the purge flow was slowed to about 5 cm s-1 so that it will not affect the CF2ClCH2O decay. Under these experimental conditions the oxy radical decay is due to pinhole flow and wall loss. At 35 Torr and over the temperature range 284-346 K, ke + kw was found to be 8.5 ( 0.3 s-1. Using the calculated values of ke the wall rate coefficient can be obtained. At 35 Torr and 341 K kw ) 5.8 s-1, in good agreement with kw ) 6.3 s-1 found at 340 K and over the pressure range 12-35 Torr in another investigation.38 These data are given in Table 4. The increase of ke + kw with pressure appears to be entirely attributable to ke. Experimental values of ke + kw were used in the nonlinear regressions. The value given in Table 3, k25 ) ke + kw ) 8.8 s-1 is an average from this work and from ref 38. Further numerical work showed that an uncertainty of 10% in kw will cause an error of 17% in the determination of k14 by nonlinear regression. The statistical error in kw is only 5%. The experimentally determined nonzero intercepts from Figure 3 are listed in Table 4. It is evident that pinhole flow and wall reaction can only account for a portion of the observed
intercept in the higher purge flow rate experiments. The remainder of the intercept is expected to be due to the combined influence of diffusion and flow. To test this hypothesis, a simple mathematical model was developed. The following factors were considered. The length of the most intensely irradiated region of the reactor is about 9 mm. The extent to which light intensity varies in the axial direction is not known, although from the geometry of the flashlamp and lens it cannot be very large. Accordingly, this was modeled as a 9 mm long uniformly exposed region, centered on the pinhole. The initial concentration of Cl atoms was considered to be uniform within this volume. The exposed region is sampled by the pinhole, and diffusion of reactive species from there into the less strongly irradiated region, with its lower radical concentrations, causes loss of CF2ClCH2O radicals from the sampling region. Furthermore, after about 40 ms (at the gas flow velocity of 12 cm s-1) the purge flow has moved the initially uniform region downstream and positioned the boundary between the irradiated and unirradiated regions at the pinhole. The initial concentration distribution is now broadened due to axial diffusion, and as the concentration gradient sweeps across the pinhole, an additional apparent oxy radical loss process is observed. An estimate of kd was obtained from a solution of the onedimensional diffusion equation describing the rate of diffusional spreading of a component of concentration, C, in the axial direction, x, given by eq 18.
∂C/∂t ) D∂2C/∂x2
(18)
Considering the ends of the illuminated region of the reactor to initially have concentration discontinuities of reactive intermediates, the initial and boundary conditions are
}
t ) 0, C(x) ) C0, -l e x e l (19) C(x) ) 0, -l < x > l, t ) 0 ∂C/∂x ) 0, x ) 0, t > 0 where t is time, x is distance from the pinhole sampling point, l is the half-length of the region, C is the concentration, and C0 is the uniform initial concentration within the region.
Reaction of the CFCl2CH2O Radical with O2
J. Phys. Chem., Vol. 100, No. 22, 1996 9357
Figure 6. Calculated concentration profiles of CFCl2CH2O2 and CFCl2CH2O at 35 Torr and at 321 K using k14 determined in Figure 5a. Reaction model and initial concentrations are listed in Tabl3 3. (s) CFCl2CH2O2; (-‚-) CFCl2CH2O.
TABLE 4: Estimated Parameters at 341 K parameter
10 Torr
20 Torr
25 Torr
35 Torr
intercept from Figure 3 (s-1) λ(×10-4 cm) β Veff(×104 cm s-1)a ke (s-1) kw (s-1) ke + kw (s-1)
18.4 19.8 0.56 2.07 2.1 6.3 8.4
20.1 9.91 0.72 2.55 2.5 6.3 8.8
28.6 7.62 0.77 2.60 2.6 6.3 8.9
Di,m (cm2 s-1)b kd (s-1)c ke + kw + kd (s-1)
4.55 13.9 22.3
2.28 20.3 29.1
1.82 23.7 32.6
35.8 5.50 0.82 2.72 2.7 6.338 9.038 8.5 ( 0.3 (this work) 1.3 30.5 39.5
a Values of 〈V〉 ) 2.19 × 104 cm s-1 and V ) 3.43 × 104 cm s-1 were used in the calculations using eq 17. b Estimated by standard method from ref 39. c Calculated using eq 20 with x ) Vrt and Vr ) 12 cm s-1.
Figure 5. Curve fitting of numerically calculated CFCl2CH2O profiles to experimental m/z ) 77 data at 35 Torr total pressure and at 321 K (gas flow rate: 7 cm s-1). Reaction model and initial concentrations are listed in Table 3. Part a: (O) experimental data up to 40 ms; (s) calculated CFCl2CH2O profile using determined k14; (- - -) calculated CFCl2CH2O profile using 1.5k14; (-‚-) calculated CFCl2CH2O profile using 0.5k14. Part b: (O) experimental data up to 100 ms; (s) calculated CFCl2CH2O profile using k14 determined by nonlinear regressions using 0-40 ms m/z ) 77 data.
The solution of eq 18 with these initial and boundary conditions is39
{
}
l-x l+x C1 ) C0/2 erf + erf 2xDt 2xDt
(20)
The diffusion coefficient of CFCl2CH2O was estimated by standard methods.40 The values are listed in Table 4. With the convective flow accounted for by x ) Vt, where V ) 12 cm s-1, C/C0 was calculated by eq 20. When ln C/C0 was plotted vs t over the interval from 40 to 100 ms, the plots were very nearly linear, indicating that the CFCl2CH2O decay could be approximated as an exponential. Values of the first-order decay constant, kd, obtained from these plots, are given in Table 4. Justification for eq 15 can be found in the form of the solution of eq 21, the equation of change for diffusion with irreversible
first-order reaction, since if C1 is a solution of eq 18, then eq 22 is a solution of eq 21.39
∂C/∂t ) D∂2C/∂x2 - kC
(21)
C ) k∫0 C1e-kt dt + C1e-kt
(22)
t
Thus, eq 22 gives C as a sum of exponentials, to a good approximation, and kd can be included in the sum of eq 15. The estimated intercepts of the k14′ vs [O2] plots, given by ke + kw + kd, are given in Table 4 for comparison with the experimental values. The estimates are all high, but considering the approximations in the calculation of kd, the agreement must be considered reasonable. In fact, kd must be overestimated, since the model assumption of a step function for [CFCl2CH2O]0 gives a driving force for diffusion that is too large. The concentration gradients of CFCl2CH2O at the boundaries of the irradiated region must be finite initially due to the axial gradient of flashlamp intensity. This will give slower diffusion rates and correspondingly smaller values of kd. Since the spatial flashlamp intensity distribution is not known, a more accurate analysis could not be done. Nevertheless, the approximate analysis shows that axial diffusion, superimposed upon the purge flow, is the dominant contributor to the intercepts of Figure 3,
9358 J. Phys. Chem., Vol. 100, No. 22, 1996
Wu and Carr
TABLE 5: Comparison of Rate Constants for Reactions of Oxy Radicals with O2 A-factora
E/R ( (∆E/R)
k (298)a
ref
C2H5O
3.9 × 10-14 (5.5 ( 2.0) × 10-14 3.6 × 10-14 1.1 × 10-13 6.3 × 10-14
900 ( 300 1000 880 1038 550
CF3O
(7.1 ( 0.7) × 10-14 (3.0 ( 1.0) × 10-14
