J. Phys. Chem. 1996, 100, 8907-8912
8907
Atmospheric Lifetimes of HFC-143a and HFC-245fa: Flash Photolysis Resonance Fluorescence Measurements of the OH Reaction Rate Constants Vladimir L. Orkin,* Robert E. Huie, and Michael J. Kurylo Chemical Kinetics and Thermodynamics DiVision, Chemical Science and Technology Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 ReceiVed: January 22, 1996; In Final Form: March 12, 1996X
Rate constants for the reactions of hydroxyl radicals with CH3CF3 (HFC-143a) and CHF2CH2CF3 (HFC245fa) have been measured using the flash photolysis resonance fluorescence technique over the temperature range 273-370 K. A data analysis procedure is presented which should minimize rate constant errors introduced by the possible effects of radical diffusion. The following Arrhenius expressions have been derived for the reactions of OH with CH3CF3 and CHF2CH2CF3, respectively (in units of cm3 molecule-1 s-1): +0.21 +0.089 (0.95-0.17 ) × 10-12 exp{-(1979 ( 65)/T} and (0.632-0.078 ) × 10-12 exp{-(1331 ( 43)/T}. With these values, the atmospheric lifetimes for the two HFCs have been estimated to be 51 and 7.4 years, respectively. An error analysis is presented from which the rate constant uncertainty at any temperature can be calculated.
Introduction Chlorofluorocarbons (CFCs) are being eliminated from commercial production because their release into the atmosphere and subsequent photolytic degradation have resulted in decreases in the global abundance of stratospheric ozone. Partially halogenated alkanes (hydrochlorofluorocarbons or HCFCs and hydrofluorocarbons or HFCs) are among the leading CFC substitutes being introduced. Because of the presence of one or more C-H bonds, HCFCs and HFCs react with tropospheric hydroxyl radicals, resulting in shorter atmospheric lifetimes and transport of smaller amounts of reactive chlorine to the stratosphere. In addition to having shorter atmospheric lifetimes than CFCs, chlorine-free replacements like HFCs pose little risk to the Earth’s ozone layer due to the inability of their decomposition products to participate in catalytic ozone destruction cycles. Nevertheless, due to their strong absorption of the Earth’s outgoing infrared radiation (in absorption bands associated with C-F vibrations), HFCs can contribute to “global warming”. The quantification of the possible role as a “greenhouse gas” requires accurate and precise information on the compound’s residence time in the atmosphere, which is controlled primarily by reaction with the OH radical. Highly fluorinated hydrocarbons, which can be readily used as CFC substitutes due to their similar thermodynamic properties, are usually not very reactive toward OH and consequently their atmospheric lifetimes can be many years. The determinations of the absolute rate constants for such slow reactions are often compromised by the presence of reactive microimpurities in the samples studied. The measurements can also be complicated by other experimental artifacts such as OH loss by diffusion processes in the reactor. In this paper we present the results of our recent rate constant measurements for the reactions of OH with CH3CF3 (HFC-143a) and CHF2CH2CF3 (HFC-245fa). During the course of this study we developed a data analysis procedure to minimize the influence of extraneous OH loss processes on the determination of the rate constant of interest, thereby improving the precision * To whom correspondence should be addressed. Also associated with the Institute of Energy Problems of Chemical Physics, Russia Academy of Sciences, Moscow, 117829. X Abstract published in AdVance ACS Abstracts, May 1, 1996.
and accuracy of the technique in the measurement of rate constants as small as 10-16 cm3 molecule-1 s-1. Experimental Section24 Apparatus. The flash photolysis resonance fluorescence (FPRF) technique was used in this work and a detailed description of the apparatus has been given in previous papers from our laboratory.1-4 The principal apparatus component is a Pyrex reactor (of approximately 50 cm3 internal volume) thermostated with a fluid circulated through its outer jacket. Reactions were studied in argon carrier gas (99.9995% purity supplied by Spectra Gases Inc.) at a total pressure of 100.0 Torr (13.33 kPa). Flows of dry argon, argon bubbled through water thermostated at 276 K, and the HFC of interest (diluted with argon in some experiments) were premixed and flowed through the reactor at a total flow rate between 0.08 and 1.6 cm3 s-1, STP. Different HFC/argon mixtures were used to verify that the dilution process did not introduce any systematic error into the rate constant measurement. The concentrations of the gases in the reactor were determined by measuring both the mass flow rates using calibrated Tylan mass flow meters and the total pressure using an MKS Baratron manometer. Hydroxyl radicals were produced by the pulsed photolysis (0.2-4 Hz repetition rate) of H2O (introduced via the 276 K argon/H2O bubbler) using a xenon flash lamp focused into the reactor. The radicals were then monitored by their resonance fluorescence near 308 nm excited by a microwave discharge resonance lamp (1.5 Torr or 200 Pa of a 2% mixture of H2O in UHP helium) focused into the reactor center. The resonance fluorescence signal was recorded on a computer-based multichannel scaler (time channel width 30-100 µs) as a summation of 1000-15 000 consecutive flashes. This radical decay signal was analyzed as described below following the subtraction of a scattered light signal, taken as an averaged preflash signal, from each channel. The primary sample of HFC-143a (CH3CF3) used to obtain the k143a values presented in Table 1 was provided by PCR Corp. Using GC and GC-MS analysis we determined the sample to be 99.63% pure, with CO2 (0.012%) and CHF2Cl (0.36%) being the main impurities. Additional purification was carried out in order to remove possible olefinic impurities that might not have been resolved by the GC analysis.5 A second sample of HFC143a obtained from the NIST Thermophysics Division was also
S0022-3654(96)00188-8 This article not subject to U.S. Copyright. Published 1996 by the American Chemical Society
8908 J. Phys. Chem., Vol. 100, No. 21, 1996
Orkin et al.
TABLE 1: Summary of the Results Obtained for the Reactions of OH with HFC-143a and HFC-245fa molecule (HFC) CH3-CF3 (HFC-143a)
CHF2-CH2-CF3 (HFC-245fa)
[HFC] range, 1015kHFC,a 1015 temp, no. of cm3 K molecules/cm3 experiments molecule-1 s-1 298 318 330 353 370 273 284 298 313 330 350 360 370
12.5-63 5.9-35 5.6-22 5.3-16 2.5-10 1.6-8.8 1.5-7.3 1.1-10.0 1.0-6.3 0.87-6.0 0.82-4.7 0.79-3.1 0.40-5.3
5 1 1 1 2 4 4 9 4 4 4 1 7
1.24 ( 0.03 1.88 ( 0.11 2.49 ( 0.10 3.44 ( 0.32 4.51 ( 0.30 4.73 ( 0.17 5.86 ( 0.55 7.24 ( 0.021 9.26 ( 0.65 11.4 ( 0.49 14.0 ( 0.5 15.5 ( 0.5 17.2 ( 0.9
a Error bars are levels of confidence of 95% and do not include estimated systematic errors.
studied at room temperature as a check for possible effects of reactive impurities. This latter sample had a purity of 99.97% with CO2 (0.024%) and CH2F2 (0.010%) being the main impurities. The sample of HFC-245fa (CHF2CH2CF3) was provided by Allied-Signal Corp., who found no impurities using both GC-MS and GC-FID techniques with a detection limit of better than 1 ppm. We further tested the sample for the presence of olefins (using absorption spectrophotometry near 160 nm) and found less than 0.0005%. FPRF Data Treatment. The flash photolysis resonance fluorescence technique has been widely used in different modifications (including the use of laser-induced fluorescence detection) to measure the rate constants of elementary gas reactions since the initial work by Braun and Lenzi.6 The rate constant of the reaction
Figure 1. Examples of FP/RF experimental data and data treatment for the reaction of OH with HFC-143a. (a) Time dependence of RF signal. Reference decay (upper set), [CH3-CF3] ) 2.45 × 1016 and 5.0 × 1016 molecules/cm3 (intermediate and lowest sets, respectively). (b, c) Residuals from the fitting procedure (see text).
kA
R + A 98 products is usually determined by monitoring the change in concentration of a reactive transient, R, generated by flash photolysis in the presence of a large excess of reactant, A. Under these conditions, the decay of the resonance fluorescence signal, which is proportional to the decay of the concentration of R, is given by the following expression:
∂(RFsignal) ∂[R] ∝ ) -τdiff-1[R] - τ0-1[R] - kA[A][R] ) ∂t ∂t -{(τdiff-1 + τ0-1) + kA[A]}[R] (1) In this expression, kA is the rate constant for the reaction being studied and (τdiff-1 + τ0-1) is a background decay rate associated with diffusion out of the viewing zone (τdiff-1) and reactions of R with reactive impurities in the carrier gas mixture (τ0-1). Normally, a concentration of added reactant A is chosen which results in an overall signal decay rate much faster than the decay rate due to diffusion and to reaction with impurities, that is, kA[A] . (τdiff-1 + τ0-1). Under these conditions, the exact nature of this background decay is not important and an exponential behavior is usually assumed. However, extremely high concentrations of reactant are often not acceptable because they can result in a change in τdiff or can quench the radical fluorescence signal. Hence, for very unreactive compounds the accessible decay rates due to the reaction under study may be similar to the background decay rate and the nature (i.e., functional form) of this background can become important in the kinetic analysis.
To determine rate constants accurately for slow reactions when the rate of loss of OH due to reaction with the HFC is not much greater than the rate of loss due to diffusion and other background processes, we derived a procedure whereby the firstorder decay coefficient due to reaction with A (τA-1) is obtained by the simultaneous treatment of the data obtained in the presence of A, IA(t), and in the absence of A, I0(t):
τA-1 ) kA[A] )
{ }
I0(t) ∂ ln ∂t IA(t)
(2)
The derivation and suitability of this equation are discussed in the Appendix. The second-order rate constant kA is then obtained from a plot of τA-1 versus [A]. Results and Discussion Figure 1a displays resonance-fluorescence decays typically obtained during our study of the reaction of OH with HFC143a. The reference decay (I0) is shown as the top data set, while the other two sets are decays of the OH resonancefluorescence signal at two different HFC concentrations. Reference decays were always measured at both the beginning and the end of a series of experiments. These data were fit as discussed above and in the Appendix, and values of τA-1 were derived. Figure 1b,c shows plots of the residuals from the fitting procedure for the data at the two different HFC concentrations. The random distribution of the residuals indicates that the analysis procedure provides a reliable estimate of the exponential decay due to OH reaction with the added HFC. Data obtained
Atmospheric Lifetimes of HFC-143a and HFC-245fa
J. Phys. Chem., Vol. 100, No. 21, 1996 8909
Figure 2. Plot of τ143a-1 versus [CH3CF3] for the reaction of OH with HFC-143a at T ) 298 K. (Solid line is the linear least-squares fit to the data and dashed lines are its 95% confidence intervals.)
over a range of HFC concentration were treated in a similar manner to generate a first-order decay rate vs concentration plot as shown in Figure 2 and thus obtain the second-order rate constant for the reaction at a given temperature. Rate constants obtained at different temperatures are listed in Table 1 for the reaction of OH with both HFC-143a and with HFC-245fa. The data for each reaction were fit to the Arrhenius equation and the resulting parameters are given in Table 2 along with the statistically determined 95% confidence intervals. The measured rate constants are plotted in Figures 3 and 4 with levels of confidence of 95% and the results from previous investigations. Since the statistical uncertainties in the A factor are correlated with the uncertainty of E/R and do not reflect the spread of the experimental data obtained over a limited temperature range, we must consider how to best represent the uncertainty in the rate constants in and about the temperature range of measurement. To begin with, the confidence interval outside of the measurement range is asymptotically bounded by k∆+(T) and k∆-(T):
k∆+(T) ) (A + ∆A+)exp{-(E + ∆E)/RT} k∆-(T) ) (A - ∆A-)exp{-(E - ∆E)/RT} Here ∆E is the statistically determined confidence interval for E; ∆A+ and ∆A- are statistically determined upper and lower
Figure 3. Arrhenius plot of the measured k143a values and the leastsquares fit to our data (solid line) with its 95% confidence intervals (dashed lines).
Figure 4. Arrhenius plot of the measured k245fa values and the leastsquare fit to our data (solid line) with its 95% confidence intervals (dashed lines).
confidence intervals for A factor. These lines intersect at a temperature Tm, which is the data-weighted average temperature of the experiments (i.e., the average value of 1/Ti weighted by the number of data points at each Ti). Over the temperature range of the study, however, the systematic uncertainty associ-
TABLE 2: Summary of All Measurements of k143a and k245faa molecule (HFC) CH3-CF3 (HFC-143a)
CHF2-CH2-CF3 (HFC-245fa)
1012A, cm3 molecule-1 s-1
E/R ( ∆E/R, K
1015kHFC(298), cm3 molecule-1 s-1
3200 ( 500
1.5 ( 1.0 1.71 ( 0.43
2.12 ( 0.65 1.3b 1.2c +0.21 0.95-0.17
2200 ( 200 2043b 2070c 1979 ( 65
+0.089 0.632-0.078
1331 ( 43
1.35 ( 0.25 1.4b 1.2c 1.24 ( 0.09d 6.6 ( 0.7e 7.28 ( 0.50d
69.
}
ref Clyne and Holt10 Martin and Paraskevopoulos9 Talukdar et al.8 Hsu and DeMore11 this work Nelson et al.12 this work
a All the values and uncertainties are those quoted by the authors. b,c Relative rate constant measurements using CH and CHF -CF as reference 4 2 3 compounds respectively. d Error bars at 298 K include estimated systematic errors. To obtain the rate constant uncertainties at any temperature, eqs e -15 4 or 5, given in the text, should be used. A rate constant of (6.12 ( 0.70) × 10 was measured at T ) 294 K. The value reported here for T ) 298 K was calculated by the authors12 using an E/R ) 1600 K.
8910 J. Phys. Chem., Vol. 100, No. 21, 1996
Orkin et al.
ated with the measurements is greater than the statistical uncertainty. Therefore, we have chosen the following approach to represent the confidence intervals for the rate constants determined in the present work. First, the data are refit around Tm using the modified Arrhenius expression
k(T) ) k(Tm)exp[-(E/R)(1/T - 1/Tm)]
(3)
to yield k(Tm) in the intercept as well as a value for ∆k(Tm). The values of Tm, k(Tm), and ∆k(Tm) thus determined are
k143a(Tm ) 323 K) ) (2.07 ( 0.03) × 10-15 cm3 molecule-1 s-1 k245fa(Tm ) 320 K) ) (9.86 ( 0.14) × 10-15 cm3 molecule-1 s-1 for the reactions with HFC-143a and HFC-245fa, respectively, where ∆ki(Tm) are the levels of confidence of 95%. Of course, the values for E/R and ∆E/R are identical with those determined from the standard Arrhenius fit. The value for ∆k(T)/k(T) at any temperature can then be calculated from
∆ki(T)
)
ki(T)
[ ] ∆k k
+ sys
∆ki(Tm) ki(Tm)
{ |
∆E 1 1 R T Tm
exp
|}
(4)
where [∆k/k]sys is the systematic measurement uncertainty, estimated to be (5% for these studies (independent of temperature). For the purposes of atmospheric modeling, where the region below room temperature is of interest, we can rewrite eq 4 as
∆ki(T) ki(T)
)
[∆kk]
sys
+
∆ki(298) ki(298)
{∆ER|R1 - 2981 |}
exp
(5)
and ∆ki(298)/ki(298) are obtained using eq 4 to be 0.023 and 0.019 for HFC-143a and HFC-245fa, respectively. This equation has the benefit of a common reference temperature for all reaction studies, rather than a different Tm for each, and is identical to that chosen by the NASA Panel for Data Evaluation.7 It also yields results identical with those from eq 4 only for T e 298 K, since Tm > 298 K. Use of eq 5 for T > 298 will lead to a slight overestimation of ∆k(T)/k(T) with respect to that from eq 4. The impurity level in our sample of HFC-245fa appears to be very low based on the Allied Signal Corp. analysis and is unlikely to have contributed to the observed kinetics. Even if an alkene impurity was present at 10 ppm (the limit of our analysis sensitivity), less than a 1% contribution to the measured rate constant would be expected based on typical OH + alkene rate constants.5 Our initial sample of HFC-143a, however, was of lesser purity but the major reactive impurities (CH2F2 and CHF2Cl) were at levels low enough to also result in less than a 1% error in the determination of k143a, despite their higher OH reactivity than CH3CF3.7 There was no difference found in k143a values measured at T ) 298 K when either of the two samples of HFC-143a were used. In addition to the possible influence of reactive impurities, secondary chemistry can also be a source of systematic errors. OH can react with both the radical products of the reaction under study as well as with relatively stable products that can accumulate in the reactor because of the multiflash experimental procedure. In the case of HFC-245fa the following experiments were performed to check both possibilities. At T ) 313 K, the
initial OH concentration was decreased by a factor of approximately 4 by lowering the discharge energy of the xenon flash lamp without changing the flow conditions in the reactor. (The ratio of signals extrapolated to t ) 0 was used to derive the relative initial OH concentrations.) The difference in the rate constants obtained was less than 2%, well within the confidence limits of the measurements. At T ) 370 K, the flash energy was decreased and the total pressure in the reactor reduced to 20 Torr (2.7 kPa) from 100 Torr (13.3 kPa) at the same flow rates (STP) of argon and water. Such a reduction in both the photolyte (water) concentration and the flash energy resulted in a reduction in the initial OH concentration by a factor of approximately 16. The rate constant measured in this experiment was within 1% of the average value obtained at T ) 370 K, again within the confidence limits of the measurements. Similar tests were performed on the HFC-143a reaction system and the rate constants obtained were always statistically indistinguishable. The results of previous experimental studies of these reactions are listed in Table 2 with those from the present work. The most extensive previous study of the reaction of OH with HFC143a was carried out by Talukdar et al.,8 who used both discharge-flow laser-magnetic-resonance (DF/LMR) and flash photolysis laser induced fluorescence (FP/LIF) techniques. Our analysis of their data obtained using the FP/LIF technique results +0.39 ) × 10-12 cm3 molecule-1 s-1 and E/R ) in A ) (1.01-0.28 (2015 ( 93) K, which agree with our values well within the uncertainty limits. The results obtained by DF/LMR, however, are somewhat higher than ours as well as those obtained in the same laboratory using FP/LIF. The k143a(298 K) value measured by Martin and Paraskevopoulos9 is in agreement with that of Talukdar et al.8 within combined uncertainty limits, but the difference between the central values is actually 27%. The temperature dependence derived by Clyne and Holt10 over the temperature range 333-425 K is very different from that derived by all other investigators. Their data on k143a probably cannot be considered as reliable in so far as their results for other hydrohalocarbons are also in poor agreement with many other studies. A very recent relative rate study,11 published during the course of this work, yielded Arrhenius expressions and values for k143a(298 K) nearly identical with those derived here. We have also recently received information about the only other measurement of the rate constant for OH + HFC-245fa, a DF/ LIF study at T ) 294 K12 in which a rate constant of k245fa ) (6.12 ( 0.70) × 10-15 cm3 molecule-1 s-1 was reported, 9% lower than the value obtained from our Arrhenius expression. Atmospheric Lifetimes. Reactions with hydroxyl radicals in the troposphere are the main removal processes for HFCs. The atmospheric lifetime of an HFC (τHFC) can be estimated from the results of long term field measurements coupled with emission inventories (see ref 13) as well as by atmospheric modeling.14 Following Prather and Spivakovsky14 we use the rate constant calculated for T ) 277 K in a simple scaling procedure with methyl chloroform as a reference to derive estimates of the lifetimes due to reactions with hydroxyl radicals in the troposphere: OH ) τHFC
kMC(277) kHFC(277)
OH τMC
(6)
OH OH are the atmospheric lifetimes of HFC and τMC where τHFC under study and methylchloroform (MC) respectively due to reactions with hydroxyl radicals in the troposphere only. The total atmospheric lifetime of methyl chloroform has been derived from measurements of trends in its concentration in the
Atmospheric Lifetimes of HFC-143a and HFC-245fa atmosphere to be τMC ) 4.8 years.13 A correction for both the ocean loss15 and photolysis in the stratosphere16,17 must be done OH from τMC: to estimate τMC
1 OH τMC
)
1 1 1 - ocean τMC τstr τMC MC
J. Phys. Chem., Vol. 100, No. 21, 1996 8911 of or imply an official endorsement by the Agency. We would like to thank Dr. H. Magid from Allied Signal Corp. for providing us with the very pure sample of HFC-245fa, for his continuing interest in this work, and for helpful discussions about sample purity problems. Appendix
str τMC
ocean τMC
are the characteristic times for MC losses and Here from the atmosphere due to photolysis in the stratosphere (ca. 45 years16,17) and due to ocean removal (ca. 85 years15). OH ) 5.7 years, τOH Such estimations result in τMC 143a ) 51 years, OH and τ245fa ) 7.4 years. Note that eq 6 has been established for substances that are uniformly distributed throughout the troposphere and stratosphere.14 Due to its strong absorption of stratospheric UV radiation, methyl chloroform actually has a nonuniform distribution in the stratosphere (becoming completely photolyzed at altitudes above about 22 km)16,18 in contrast with substances such as HFC-143a and HFC-245fa which have negligible photolytic sinks in the stratosphere. Since the actual loss rate in any region of the atmosphere is concentration dependent, this difference in stratospheric reservoirs can be taken into account by using a modified version of eq 6: OH τHFC )
kMC(277)
1 -1
kHFC(277) (τMC)
-
str -1 (τMC )
-
ocean -1 (τMC )
χHFC (7) χMC
Here
The change in the concentration of an active species from its initial distribution in a pulse generated system can be described by the diffusion equation
∂[R]/∂t ) D∇2[R] - (τ0-1 + kA[A])[R]
(8)
where D is the diffusion coefficient of the species being monitored in the gas mixture. Acceptance of eq 1 as a solution of eq 8 implies that change in the concentration of monitored species due to diffusion can be adequately described by the exponentially decaying term alone, i.e., [R](t) ∝ exp{-t/τdiff}. Unfortunately, this assumption is not generally correct. An instantaneous point source of active species in an infinite volume is probably the simplest mathematical model with which to illustrate an FP/RF experiment. In this case, the diffusion equation
∂[R]/∂t ) D∇2[R]
(9)
has an analytical solution:20
[R](r,t) ) [M/8(πDt)3/2] exp{-r2/4Dt} ηi(h) ∞ dh χi ) ∫h)0F(h) ηi(h)0)
/∫
∞
h)0
F(h) dh
(i ) MC, HFC), F(h) is the altitude profile of air density,19 and ηi(h) are the volume mixing ratios for MC and the substance under estimation respectively. Of course, χi ) 1 for substances which have no sinks in the stratosphere. We estimated χMC ) 0.94 based on measurements of vertical distribution of methylchloroform ηMC(h).16,18 Consideration of the nonuniform distribution of MC over the atmosphere thus results in corrected estimated lifetimes of 53.3 and 7.7 years for HFC-143a and HFC-245fa, respectively. Nevertheless, these values are still somewhat conservative estimates since there is an additional sink for both species due to reactions with OH in the stratosphere which has not been taken into account in equations 6 and 7. However, because of the nature of both the vertical temperature19 and hydroxyl concentration7 profiles, this additional loss takes place mainly above about 25 km. Thus, it is negligible for strongly absorbing substances like MC (less than 1%) but can be as high as 10% for uniformly distributed gases, resulting in slight decreases in the overall atmospheric lifetimes of the latter. In the case of HFCs 143a and 245fa, this additional lifetime reduction offsets the slight lifetime increase obtained using eq 7. In conclusion, then, HFCs 143a and 245fa absorb UV radiation in neither the troposphere nor the stratosphere5 and have no significant oceanic or rainout loss (due to their low OH are water solubility5). Therefore, the original values of τHFC probably reasonably good estimates for the total atmospheric lifetimes: τ143a) 51 years and τ245fa ) 7.4 years. Acknowledgment. This work was funded by the National Aeronautics and Space Administration and the U.S. Environmental Protection Agency. Although the paper has undergone an EPA policy review, it does not necessarily reflect the views
where r is a radial coordinate and M ) ∫V[R](r) dV is the total amount of the diffusing species. Moreover, in an actual experiment the resonance fluorescence signal does not reflect the species concentration at a single point in the reactor. Rather, it reflects a distribution averaged over a detection volume defined by the overlap of three (mutually perpendicular) angular apertures. These apertures correspond to the flash lamp, the resonance lamp, and the detection optics, respectively. The photolysis and analysis light also vary across the viewing region in an unknown manner. Consequently, it is impractical (if not impossible) to attempt to formulate an exact mathematical description of the temporal behavior of the RF signal due to diffusion of the monitored radicals out of their initial distribution. It is, however, clearly not a simple exponential decay. Nevertheless, data from FP/RF experiments can be treated to derive correctly the rate constant in the following manner. Let Idiff(t) be the RF signal obtained in the absence of added reactant and let τ0-1 ) 0, i.e., the signal decay is due to diffusion only. Under such conditions
Idiff(t) ) ∫V[R]diff(xi,t) Φ(xi) dV where xi are space coordinates, Φ(xi) is the spatial apparatus sensitivity function, and [R]diff(xi,t) is a solution for eq 9 with the initial conditions of the real experiment. In this case, [R](xi,t) ) [R]diff(xi,t) exp{-(τ0-1 + kA[A])t} is a solution of eq 8 as well. If IA(t) is the signal in the presence of the reactant (A) being studied, it can be described as
IA(t) ) ∫V[R](xi,t) Φ(xi) dV )
∫V[R]diff(xi,t)exp{-(τ0-1 + k[A])t} Φ(xi) dV ) exp{-(τ0-1 + k[A])t}∫V[R]diff(xi,t) Φ(xi) dV ) Idiff(t) exp{-(τ0-1 + kA[A])t}
8912 J. Phys. Chem., Vol. 100, No. 21, 1996 Thus, IA(t) ) I0(t) exp{-kA[A]t}, where I0(t) ) Idiff(t)exp{-t/ τ0} is the signal in the absence of added reactant A. Rearranging and differentiating, we obtain eq 2, which has been used for our data analysis. Note that the situation of a pulsed experiment as discussed above may be contrasted with that of flow experiments where analysis of the steady-state radical distribution in the reactor makes it possible to estimate the influence of the diffusion transfer and to use it quantitatively for kinetics purposes.21-23 There is no steady-state solution for the flash experiment! Rate constants must be extracted from the signal decay on the same or shorter time scale as diffusion from the unknown initial distribution. References and Notes (1) Kurylo, M. J.; Cornett, K. D.; Murphy, J. L. J. Geophys. Res. 1982, 87, 3081. (2) Wallington, T. J.; Neuman, D. M.; Kurylo, M. J. Int. J. Chem. Kinet. 1987, 19, 725. (3) Liu, R.; Huie, R. E.; Kurylo, M. J. J. Phys. Chem. 1990, 94, 3247. (4) Zhang, Z.; Padmaja, S.; Saini, R. D.; Huie, R. E.; Kurylo, M. J. J. Phys. Chem. 1994, 98, 4312-15. (5) Orkin, V. L.; Huie, R. E.; Kurylo, M. J., manuscript in preparation. (6) Braun, W.; Lenzi, M. Discuss. Faraday Soc. 1967, 44, 252-62. (7) DeMore, W. B.; Sander, S. P.; Golden, D. M.; Hampson, R. F.; Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R.; Kolb, C. E.; Molina, M. J. JPL Publication 94-26, 1994. (8) Talukdar, R.; Mellouki, A.; Gierczak, T.; Burkholder, J. B.; McKeen, S. A.; Ravishankara, A. R. J. Phys. Chem. 1991, 95, 5815-21. (9) Martin, J.-P.; Paraskevopoulos, G. Can. J. Chem. 1983, 61, 86165.
Orkin et al. (10) Clyne, M. A. A.; Holt, P. M. J. Chem. Soc., Faraday Trans. 2 1979, 75, 582-591. (11) Hsu, K.-J.; DeMore, W. B. J. Phys. Chem. 1995, 99, 1235-1244. (12) Nelson, D. D.; Zahniser, M. S.; Kolb, C. E.; Magid, H. J. Phys. Chem. 1995, 99, 16301-06. (13) Prinn, R. G.; Weiss, R. F.; Miller, B. R.; Huang, J.; Alyea, F. N.; Cunnold, D. M.; Fraser, P. J.; Hartley, D. E.; Simmonds, P. G. Science 1995, 269, 187-192. (14) Prather, M.; Spivakovsky, C. M. J. Geophys. Res. 1990, 95, 18,723-729. (15) Butler, J. H.; Elkins, J. W.; Thompson, T. M.; Ball, B. D.; Swanson, T. H.; Koropalov, V. J. Geophys. Res. 1991, 96, 22,347-55. (16) Kaye, J. A.; Penkett, S. A.; Ormond, F. M. NASA Reference Publication 1339, 1994. (17) Proceedings of the Workshop on the Atmospheric Degradation of HCFCs and HFCs, Boulder, CO, 1993. (18) Atmospheric Ozone 1985, World Meteorological Organization, Global Ozone Research and Monitoring ProjectsReport No. 16, 1985; Vol. II. (19) U.S. Standard Atmosphere, NOAA, NASA, USAF, Washington, DC, 1976. (20) Crank, J. The Mathematics of Diffusion; Oxford U.P.: London, 1956. (21) Walker, R. E. Phys. Fluids 1961, 4, 1211. (22) Brown, R. L. J. Res. Natl. Bur. Stand. U.S.A. 1978, 83, 1-8. (23) Orkin, V. L.; Khamaganov, V. G.; Larin, I. K. Int. J. Chem. Kinet. 1993, 25, 67-78. (24) Certain commercial equipment, instruments, or materials are identified in this article in order to adequately specify the experimental procedure. Such identification does not imply recognition or endorsement by the National Institute of Standards and Technology, nor does it imply that the material or equipment identified are necessarily the best available for the purpose.
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