16967
J. Phys. Chem. 1995,99, 16967-16975
A Mechanistic Study of the Reaction of OH with Dimethyl& Sulfide. Direct Observation of Adduct Formation and the Kinetics of the Adduct Reaction with 0 2 A. J. Hynes* and R. B. Stoker Division of Marine and Atmospheric Chemistry, Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Causeway, Miami, Florida 33149
A. J. Pounds?$5T. McKay? J. D. Bradshaw? J. M. Nicovich? and P. H. Winet*”$ Georgia Institute of Technology, Atlanta, Georgia 30332 Received: July 20, 1995@
A pulsed laser photolysis-pulsed laser-induced fluorescence technique has been employed to study the detailed mechanism for the reaction of OH radicals with deuterated dimethyl sulfide [(CD&S, DMS-d6]. Equilibration of pulsed laser-generated OH with a (CD,),S-OH adduct has been directly observed, thus confirming the existence of this controversial weakly bound species. Elementary rate coefficients for adduct formation and decomposition and, therefore, the equilibrium constant for OH (CD3)2S (CD&SOH have been determined as a function of temperature. From the temperature dependence of the equilibrium constant over the relatively narrow temperature range 250-267 K, a 258 K adduct bond strength of 13.0 zk 3.3 kcal mol-’ has been obtained (second law method). Altematively, an entropy change calculated using standard statistical mechanical methods and ab initio theory (for determining the (CD3)zS and (CD&SOH structures) has been employed in conjunction with an experimental value for the equilibrium constant at a single temperature to obtain a 258 K adduct bond strength of 10.1 f 1.1 kcal mol-’ (third law method). Experiments in the presence of 0 2 confirm the previously reported dependence of the OH DMS-d6 rate coefficient on the 0 2 partial pressure and are consistent with the previously proposed four-step mechanism involving hydrogen abstraction, addition of OH to the sulfur atom, and adduct decomposition in competition with an adduct 0 2 reaction [Hynes et al. J . Phys. Chem. 1986, 90, 41481. The rate coefficient for the adduct 0 2 reaction is found to be (8 f 3) x lo-’, cm3 molecule-’ s-l independent of pressure (100-700 Torr of N2) and temperature (250-300 K).
-
+
+
+
Introduction
analogue, reaction 2.5-7
Dimethyl sulfide (DMS) constitutes the largest natural component of the atmospheric sulfur burden. While quantitative rates are difficult to obtain, recent estimates indicate that DMS accounts for about 15% of the total atmospheric sulfur burden and for approximately 40% of sulfur emissions in the Southem Hemisphere.’ The potential role of DMS in global climate change has been a subject of considerable controversy in recent years. DMS, a product of phytoplankton degradation,is thought to be the precursor of the non-sea-salt/methanesulfonateaerosol which is distributed throughout the marine boundary layer. This marine aerosol appears to be the only significant source of cloud condensation nuclei in remote regions, and Charlson et al. have argued that this biologicalkhemical cycle could form the basis of an efficient method of climate regulation.2 In the low NO, environment that characterizes the remote marine boundary layer, reaction with OH appears to be the most significant loss process for DMS. OH
+ CH,SCH, - products
(1)
The kinetics of reaction 1 have been studied extensively by a variety of direct and competitive techniques, and a survey of the literature shows a wide discrepancy between the various studies, most of which were performed in the absence of 02.3%4 In previous work Hynes et al. utilized the pulsed laser photolysis -pulsed laser-induced fluorescence (PLP-PLIF)technique to study the kinetics of reaction 1 and its deuterated
’ Georgia Tech Research Institute.
School of Earth & Atmospheric Sciences. School of Chemistry & Biochemistry. * To whom correspondence should be addressed. Abstract published in Advance ACS Abstracts, November 1, 1995.
8
@
+
OH
+ CD,SCD, - products
(2)
In the absence of oxygen the observed rate coefficient had a positive activation energy, was independent of pressure, and showed a kinetic isotope effect. In the presence of oxygen the observed rate coefficient was dependent on the partial pressure of oxygen and in 1 atm of air or oxygen displayed a dramatic negative temperature dependence below 350 K. These results were consistent with the reaction proceeding via a two-channel mechanism, shown here for reaction 2, involving both hydrogen abstraction and addition channels. Hynes et al. proposed that the thermalized DMS-OH adduct produced by the addition channel could decompose back to reactants or react with oxygen to form unidentified products.
+ OH - CD3SCD2+ HOD CD,SCD, + OH + M CD,S(OH)CD, + M CD,S(OH)CD, + 0, - products CD,SCD,
(2a) (2b) (3)
They were unable to directly observe adduct formation. However, on the basis of the assumed mechanism, they were able to measure the elementary rate coefficients for reactions l a and 2a, obtain estimates for reactions 2b, -2b, and 3 at 261 K, and obtain an estimate of the binding energy of the (CD&SOH adduct. If their interpretation is correct, the relative importance of the addition and abstraction routes, and hence the effective mechanism of DMS oxidation, changes dramatically over the temperature range encountered in the marine boundary layer. A subsequent competitive rate study of reaction 1 by Barnes
0022-3654/95/2099-16967$09.00/0 0 1995 American Chemical Society
Hynes et al.
16968 J. Phys. Chem., Vol. 99, No. 46, 1995 et a1.8 c o n f i i e d the dependence of the observed rate on oxygen partial pressure at room temperature. At atmospheric pressure they observed an 0 2 rate enhancement which was approximately 50% greater than the value reported in the direct study. In a recent study Gu and Turecek9 presented experimental and theoretical evidence which led them to conclude that the adduct does not exist. Sabsequently, McKee’O published results of a theoretical study indicating that the adduct was indeed stable and reported a binding energy of 6 kcal mol-’. Turecek,” however, has recently published another theoretical study which has again concluded that the adduct is not bound. We have reported preliminary results which we believe constitute a direct observation of adduct f ~ r m a t i o n . ’ ~Barone - ~ ~ et alei5have recently presented results which appear to be consistent with our observations. In this paper we present a detailed analysis of our complete set of experimental data. Elementary rates for adduct formation and decomposition and hence the equilibrium constant are determined. Both “second law” and “third law” methods have been employed to determine the adduct binding energy. Experiments in the presence of oxygen c o n f i the previously reported dependence of the observed rate coefficient on oxygen partial p r e s s ~ r e , ~are - ~ consistent with the rate coefficients obtained for adduct formation, and allow the rate coefficient for the reaction of the adduct with 0 2 to be determined.
Experimental Section The PLP-PLIF apparatus has been described in detail el~ewhere.~ Modifications and a brief review of its operation are given below. Experiments were performed in a Pyrex cell which had an i.d. of 4 cm and a length of 50 cm. Two side arms, 4 cm i.d. and 14 cm long, which terminated in Brewster angle windows were attached to the center of the cell. The photolysis laser passed through these side anns across the direction of gas flow while the probe laser passed along the length of the cell. Fluorescence was detected through a third side arm,4 cm i.d. and 5 cm long, perpendicular to the photolysis and probe beams. The central 25 cm length of the cell was jacketed to permit the flow of heating or cooling fluid from a thermostated bath. A copper-constantan thermocouple with a stainless steel jacket was inserted into the reaction zone through a vacuum seal, allowing measurement of the gas temperature under the precise pressure and flow conditions of the experiment. OH was produced by the pulsed laser photolysis of H202 using the 266 nm-fourth harmonic output from a Nd:YAG laser. Pulsed laser-induced fluorescence using a Nd:YAG-pumped, frequency-doubled,tunable dye laser was used for OH detection; excitation was via the Ql 1 line of the A2X+ - X2rI(1-O) transition at ~ 2 8 nm. 2 All kinetic studies were performed with a line narrowing etalon in the dye laser cavity, giving an estimated line width of 0.1 cm-’ at 280 nm. The laser could be reproducibly scanned on and off the OH line by pressure tuning using NZ gas. Fluorescence in the 0-0 and 1-0 bands was detected by an EM1 9813QB photomultiplier after passing through collection optics and filters to discriminate against Rayleigh scattering and Raman scattering from NZ and/or 0 2 . The photomultiplier output was appropriately terminated and fed to a 100 MHz wave form analyzer to obtain the peak voltage averaged for (typically) 100 laser shots. Kinetic information was obtained by varying the delay between the photolysis and probe lasers using a digital delay generator which had a minimum delay increment of 100 ns. For single-exponential decays the signal was collected for 1520 delays in order to map out an OH decay profile over 3-4
l/e times. For double-exponential decays typically 30-40 delays were sampled. In these cases it was critical to accurately establish the delay time at which the photolysis and probe lasers overlapped and to minimize any drift in this overlap time. The intemal timing systems of the lasers were inadequate to maintain this stability, and we were required to use two delay generators to trigger both the flash lamps and q-switches of the lasers. The use of two delay generators introduced some jitter, and our ability to accurately characterize this was limited both by the relatively large minimum time increment of the generators and by the bandwidth of the signal averager. It was possible to obtain delays with an initial delay time which varied between 0.5 and 2 ps. The minimum time delay at which signal could be collected depended on the amplitude of the noise from the photolysis laser which increased significantly as a function of DMS-d6 concentration. In order to avoid the accumulation of photolysis or reaction products, all experiments were carried out under “slow flow” conditions with the linear flow rate through the reactor varied between 1 and 5 cm s-l. DMS-d6 concentrationswere measured in situ by W photometry using the 228.8 nm line from a Cd lamp, absorption cells of various lengths, and a band-pass filter. Concentrations were calculated using the previously measured absorption cross section of Hynes et aL5 5.16 x cm2. The pure gases and chemicals used in this study had the following stated minimum purities: N2, 99.999%; 0 2 , 99.99%. Air was zero grade, 1 ppm total hydrocarbons. H202 (70%) was obtained from FMC Corp.; it was further concentrated and purified by bubbling buffer gas through the sample for several days before use in experiments. DMS-d6 was obtained from Aldrich and had a stated chemical and isotopic purities of 99+% and 99.9 atom % D. Results and Discussion Kinetic Analysis of the Two-Channel Mechanism. It is instructive to examine the behavior of a kinetic system which is described by a four reaction sequence consisting of (2a, 2b, -2b, 3) together with “global” loss reactions for OH and (CD3)2S-OH. OH
-
loss by diffusion or background reaction
(CD,),S-OH
-
(4)
loss by diffusion or background reaction (5)
Under pseudo-first-order conditions, Le., [DMS-d6] >> [OH], the OH temporal profile is described by the double-exponential expression
where
A I = 0.5[(a2 - 4/3)’12 - a ]
(111)
A2 = -0.5[(a2 - 4/3)’12+ a1
(IV)
a =K
+ k4 +
+ k,,)[CD,SCD,]
(V>
If the concentration of OH is much greater than that of the adduct, i.e., [OH] >> [(CD&S-OH], the steady-state approximation can be applied to the adduct, and the effective rate
J. Phys. Chem., Vol. 99, No. 46, 1995 16969
Reaction of OH with Dimethyl-d6 Sulfide
60000
7 40000 m
3
40 0 i f
20000
3b
Figure 1. Variation of pseudo-first-orderOH decay rate, k‘, with DMSconcentration at 267 K. Curves a-d are calculated using eq I and the elementary rate parameters listed in Table 2. d6
60 [DMS]
90
cm-3
li0
Figure 2. Variation of pseudo-first-order OH decay rate, k’, with DMSconcentration at 258 K. Curves e and f are calculated using eq I and the elementary rate parameters listed in Table 2.
d6
20000 y
coefficient for OH loss in the presence of excess DMS-d6 is given by the equation
2 At low DMS-d6 concentrations, and in the absence of oxygen, the equilibrium (2b, -2b) lies well to the left, and the steadystate approximation holds. Although the double-exponential expression describes the OH temporal decay, the “fast” component of the decay is so small that the temporal profiles are well described by single-exponential decays with pseudo-firstorder decay rates, k’. The observed rate coefficient, kobs, is obtained from a linear plot of K us [DMS-d6]. Under these conditions the observed rate coefficient is the hydrogen abstraction rate coefficient, k2a. As the Dh4S-Q concentration increases, the equilibrium (2b, -2b) shifts to the right, and the concentration of the adduct increases until the steady-state approximation no longer holds. Although the steady-state approximation is no longer valid, the OH temporal profiles are described by eq I, and doubleexponential behavior may be observable if the experimental time resolution and signal-to-noise ratio are adequate. If the experimental time resolution is inadequate, then only the slow component of the double-exponential decay will be observed. This slow component can be used to calculate an apparent pseudo-first-order loss rate. However, the rate coefficient calculated from this apparent pseudo-first-order rate will be smaller than h a , and as a consequence, a plot of pseudo-firstorder rate us concentration appears to “roll over” as the DMSd6 concentration is increased. Equation VI1 predicts that an increase in the 0 2 partial pressure at a fixed total pressure will result in the observed rate coefficient increasing as (CD&S-OH is scavenged by 0 2 rather than decomposing back to products. The observed rate coefficient increases until it asymptotically approaches a limiting rate of (k2, k2b). At this 02 concentration dl of the (CD3)2SOH adduct is scavenged, and a further increase in oxygen partial pressure results in no increase in the observed rate coefficient. Observations in the Absence of 0 2 . A plot of the experimentally observed pseudo-first-order OH decay rate us [DMS-d6] at 267 K in 100 Torr of N2 is shown in Figure 1. At low DMS-d6 concentrations we observe a linear dependence of k‘ on [DMS-d6], with k’ “rolling o f f at high [DMS-d6]. Leastmean-squares analysis of data with [DMS-d6] < 1 x 1Ol6
+
..... 0
10 [DMS] / l o L 5 cme3
$0
Figure 3. Variation of pseudo-first-order OH decay rate, k’, with DMSconcentration at 250 K. Curves g-i are calculated using eq I and the elementary rate parameters listed in Table 2. The extrapolation of the linear portion of the curves, calculated from k’ obtained with [DMSd6] < 4 x 1OI5 ~ m - is ~ also , shown. d6
molecules cmV3gives an observed rate coefficient of (1.59 f 0.23) x 10-l2 cm3 molecule-’ s-I (2a error). At the highest DMS-d6 concentration, 1.2 x 10’’ molecules ~ m - the ~ , measured decay rates are approximately 50% of the rate obtained by extrapolation from the linear region. At 267 K we saw no evidence for double-exponential temporal profiles on the time scale of our experiments. Figures 2 and 3 show similar rolloff behavior at 258 and 250 K; however, in this case the deviation from linearity is apparent at lower DMS-d6 concentrations. At these temperatures double-exponential behavior becomes resolvable at high DMS-d6 concentrations. Figure 4 shows a series of OH temporal profiles at 261 K in 100 Torr of N2 and with DMS-d6 concentrations of 2.73 x 10l6, 4.03 x 10l6, and 5.29 x 10l6 molecules ~ m - ~At . the lowest concentration double-exponential behavior is barely observable; however, at the highest concentration the plot of the ln(signa1) us time shows a pronounced deviation from linearity, which is clearly resolvable on the time scale of our experiments. Figure 5 shows a series of double-exponential temporal profiles obtained at 250 K. In this case we were unable to obtain data during the first 2 ps after photolysis. However, the deviation from single-exponential behavior is clearly apparent. Doubleexponential decays were analyzed by a Marquardt, nonlinear least-mean-squares fit to eq I, which takes the relative values of the OH concentration as a function of delay time and fits to values of [OHIO,K, 11, and &.I6 The routine we used minimized
16970 J. Phys. Chem., Vol. 99, No. 46, I995
Hynes et al.
1 E 8E-0 12-
3
-
0
1
’
7
. .
1 .*.‘
i4
A 0’8kiOO0
’
3E-’005’
6E-’005’ TIME (s) ’
‘ BE1005 ’
’
Figure 4. Double-exponential OH temporal profiles. Experimental conditions: 261 K, 100 Torr of N2. The solid lines are the best fits to eq I. The DMS-d6 concentrations and the values of the elementary rate coefficients which were obtained are listed in Table 1. m
’Oh
5
d
1
o~dEiooo~
X
’
‘4.OEL005
8 .OE I005
TIME (s) Figure 5. Double-exponential OH temporal profiles. Experimental conditions: 250 K, 100 Torr of N2. The solid lines are the best fits to eq I. The DMS-d6 concentrations and the values of the elementary
rate coefficients which were obtained are listed in Table 1.
TABLE 1: Elementary Rate Coefficients Obtained from “Best Fits” to Eq I T/K kZau k2ba k-2bb Kcc [DMS-&ld Figure 250 1.66 1.45 2.70 2.76 2.76 5c 1.30 4.98 1.70 2.92 3.77 5b 1.05 5.63 2.02 2.78 4.61 5a 255 1.40 9.40 6.91 1.36 0.94 1.43 4.26 4.03 1.05 1.52 1.40 7.22 5.70 1.27 2.02 1.56 9.31 5.11 1.82 2.75 1.68 8.55 5.26 1.63 3.19 258 1.58 3.69 2.63 1.41 7.05 1.89 4.26 3.08 1.38 8.86 1.71 4.89 3.75 1.30 10.1 261 1.46 5.72 9.01 0.64 2.13 4a 1.63 5.97 7.22 0.83 5.29 4c 0.80 4.03 4b 1.45 4.06 5.09 a
0.b 0.68 RESIDUAL Figure 6. Scatter plot showing the variation of Kc and k z b with x2,the sum of the squares of the residuals of the experimental and fit points. The data are for Figure 5b.
Units are 10-’2 cm3 molecule-’ s-I.
Units are lo5 s-I. c Units are
lo-” cm3 molecule-’. Units are lor6molecules ~ m - ~ . the sum of the squares of the residuals of the calculated and experimental values of signal us time with no weighting of the experimental points. The rate of background adduct loss, ks, was considered to be negligible compared with k-2b and was ignored. m e best fits are shown as solid lines in Figures 4 and 5. We were able to observe double-exponential behavior in experiments between 261 and 250 K, and the elementary rate coefficients obtained from the analysis of each decay are given in Table 1. There is a considerable degree of scatter in the elementary rate coefficients reported in Table 1. This reflects both the
quality of the data and the problem associated with extracting three rate parameters, two of which are of similar magnitudes, from a single double-exponential decay. The “quality of data” reflects the experimental difficulty associated with the measurement of OH temporal profiles under these conditions. At the highest DMS-d6 concentrations, the initial decay rates were on the order of (1-5) x lo5 s-I, and the amplitude of the background laser scatter from both the photolysis and probe lasers increased significantly as a function of DMS-d6 concentration. This degraded our signal-to-noise ratio for OH detection and made it difficult to record data at short times after the photolysis pulse because the magnitude of the noise spike saturated our detector. In several cases we were unable to obtain data in the first 2 ps after photolysis because of noise from the photolysis laser, and as a consequence, the initial portion of the fast equilibration is less defined. At lower concentrations this noise is less of a problem, but the extent of the equilibration is small as in Figure 4a. In addition, there is a limitation involved in the analysis of these decays which can be illustrated by examining the dependence of the values of k2b and the ratio k2dk-2b, Le., the equilibrium constant, K,, on the sum of the squares of the residuals, which is the quantity minimized by the fitting routine. Figure 6 shows a scatter plot of the variation of k2b with x2 for Figure 5b. The scatter plot shows that x2can be minimized by a fairly broad range of values of k2b, each of which has an associated set of values of the other fit parameters, [OHIO,kza, and k2b. An examination of the variation in Kc with x2 gives a somewhat tighter fit, an indication of the correlation between the values of k2b and k-2b. our fitting routine provided no measure of “goodness of fit”; however, some feel for the uncertainty in the elementary rate constants can be obtained by visual examination of other fits with small x 2 . Figure 7 shows the data from Figure 5b with fluorescence intensity on a linear scale. The figure includes the fit which minimizes x2 and three other fits which have small residuals. Table 3 lists the relevant fit parameters. It is clear that there is a considerable uncertainty in the value of k2b extracted from the fitting procedure. Values of k2b which differ by greater than a factor of 2 give almost equally good fits to the data. However, the correlation between k2b and k-21, indicates that the uncertainty in Kc is considerably smaller than the uncertainty in the individual rate constants. The absence of data in the first 2 ps certainly contributes to this uncertainty, but an analysis of the variation of k2b and K, with x2 for Figure 4c, a less noisy decay with initial data at 0.5 ps, shows a similar uncertainty. It should also be noted that the
x2,
. I Phys. . Chem., Vol. 99, No. 46, 1995 16971
Reaction of OH with Dimethyl-d6 Sulfide
.-i 3
3 d
, 0
0
3 6 0
10
Figure 7. Sensitivity of fitting procedure to the elementary rate constants obtained. The data are from Figure 5b (250 K, [DMS-d6] = 3.77 x 10l6 ~ m - ~ )Curves . a-d are the calculated temporal profiles using the elementary rate coefficients listed in Table 3.
TABLE 2: “Roll-off’ Parameters T/K 267
curve a b C
258 250
d e f g h 1
j
kzaa
k2ba
k-zbb
1.7 1.6 1.7 1.7 1.55 1.6 1.5 1.4 1.5 1.4
6.0 5.0 9.0 6.0 8.0 4.6 4.0 5.0 6.0 5.0
12.35 9.45 14.0 9.5 6 3.4 1.4 2.1 2.1 1.75
Units are cm3 molecule-’ s-’. io-’’ cm3 molecule-’.
K,‘
x2
0.49 0.53 0.64 0.63 1.33 1.35 2.85 2.38 2.85 2.86
6000 2812 2503 2533 216 258 846 933 920 1158
Units are lo5 s-’. Units are
TABLE 3: Curve Fitting Parameters for Figure 7 a b C
d
1.31 1.25 1.38 1.40
4.98 3.5 6.7 7.90
1.745 1.40 2.00 2.60
2.64 2.40 2.90 2.90
2.85 2.50 3.35 3.04
0.0041 0.0050 0.0050 0.0079
Units are cm3 molecule-’ s-’. Units are io5 s-I. Units are arbitrary. Units are lo-’’ cm3 molecule-’.
standard Marquardt method minimizes the quantity
where y(x:a) is calculated from eq 1 and (T is the standard deviation of the experimental pointy. Our signal averager gave no measure of the standard deviation of the individual experimental points, and we used an unweighted fit with u = 1. In effect, this tends to weight the fit toward the initial points in the decay. We attempted to investigate the effect of this by setting a2equal to y and y2. This gives a greater weighting to points at longer times and produced best fits with smaller k2b but a similar K,. This constitutes a further uncertainty in the elementary rates obtained and emphasizes that for such decays it is important to note the criteria used in any minimization procedure. Any variation of k2b with temperature is not discernible over the 10 K temperature range of our measurements given the scatter in the values. We have therefore taken the average of the 14 measurements and report a value of k2b = (6.1 f 3.7) x cm3 molecule-’ s-’ (&2u) in 100 Torr of N2. 4 s we have noted above, the breakdown of the steady-state approximation as the concentration of DMS-d6 increases leads
to deviations from linearity in the k‘ vs [DMS-d6] plot. We can model this “roll-off’ by using eq I to simulate doubleexponential decays and then calculate the apparent pseudo-firstorder decay rate, K , from the slow component of the doubleexponential decay. The “roll-off’ can be modeled by determining k‘ as a function of k2a, k2b, k-2b7 and [DMS-d6]. The data in Figures 1-3 were modeled using this approach by obtaining the values of k2a, k2b, and k-21, which minimized the sum of the squares of the residuals between the experimental and calculated points. This approach does not provide a unique fit to individual values of k2b and k-2b; however, it is sensitive to their ratio and hence to the equilibrium constant for adduct formation. The value of the ratio is also sensitive to the value of k2a, which is constrained by the scatter in the data at low [DMS-d6]. Figure 1 shows roll-off curves calculated using this approach. The best fit to the data, curve c, is obtained with values of kla = 1.7 x IO-’* cm3 molecule-’ s-I, k2b = 9 x cm3 molecule-’ s-I, and k-2b = 1.4 x lo6 s-I, giving an equilibrium constant, K,, of 6.4 x cm3 molecule-’. However, an almost equally good fit with a residual which is 1% higher is obtained with values of k2b and k-2b, which are consistent with values obtained at lower temperature from double-exponential analysis, Le., kza = 1.7 x cm3 molecule-’ s-l, k2b = 6 x cm3 molecule-’ s-’, and k-2b = 9.5 x lo5 SKI. This fit, shown as curve d, gives an equilibrium constant, K,, of 6.3 x cm3 molecule-’. Reasonable fits can be obtained with values of k2a ranging from 1.6 x to 1.7 x cm3 molecule-’ s-I. A qualitative feel for the sensitivity of this procedure can be obtained by examining simulated roll-off curves with values of and k2b fixed at 1.7 x and 6 x cm3 molecule-’ s-I, and k-2b increased to 1.235 x lo6 s-I. This fit, shown as curve a, gives an equilibrium constant which is approximately 25% lower than the values obtained from the “best fits” with = 1.7 x cm3 molecule-‘ s-’ and is clearly incompatible with the experimental data. Note, however, that fits with k2a = 1.6 x cm3 molecule-’ s-’ (such as curve b) give almost as good a fit but with an equilibrium constant, K,, of 5.3 x cm3 molecule-’. Figure 3 shows 250 and 258 K roll-off curves calculated using both “best fits” and the averaged values of k2b and k-21, obtained from analysis of doubleexponential decays. Table 2 gives the results of the roll-off analyses, and it is clear that the observed roll-off at both 250 and 258 K is consistent with the elementary rates obtained from the analysis of double-exponential decays. At 250 K the deviation from linearity sets in at low DMS-d6 concentration, and it is clear that this could easily lead to the calculation of erroneously low values of kza if the onset of “roll-off’ is not recognized. Adduct Reaction with 0 2 . We examined the variation of the observed rate constant, k&s, with oxygen partial pressure at 267, 258, and 250 K. In all cases the total pressure was fixed at 110 Torr with nitrogen constituting the balance of the gas mixtures. For the time scales and concentration ranges we employed, single-exponentialdecays were observed over at least three l/e times. Plots of pseudo-first-order decay rate against concentration were linear. Figure 8 shows the data at 258 K in mixtures containing 0, 2, 10, and 20% 0 2 . It is clear that the observed rate coefficient increases significantly as the oxygen partial pressure is increased. We saw similar behavior at 250 and 267 K. Figure 9 shows the variation in the observed rate coefficient as a function of oxygen partial pressure at 250 and 258 K. We can model this behavior using eq W and our values of k2a, k2b, and k-2b obtained from the analysis of doubleexponential decays. Obviously, the value of k3 obtained depends on the values of kza, k2b, and k-2b which are used. Nevertheless,
16972 J. Pkys. Ckem., Vol. 99, No. 46, 1995 15000
-
/y
I
b,
Hynes et al.
c),
10000
v)
z
E
0-
A-
4
[DMS]
/lo"
cm-3
Figure 8. Plots of pseudo-first-order OH decay rate versus DMS-& concentration at four oxygen partial pressures (258 K, 110 Torr total pressure). Oxygen partial pressures are (a) 0, (b) 2.2, (c) 10.1, and (d) 20.2 Torr.
(DMSO,, (CD3)2S02), Barnes et ~ 1 noted . ~ the possibility that channel 3c could be significant. However, any dimethyl sulfoxide (DMSO, (CD3)2SO) produced in their system would probably have been rapidly oxidized to DMSO;?since OH reacts with DMSO at close to a gas kinetic rate.i4,i7,'8We have experimental evidence that is consistent with a yield of 0.5 for DMSO from reaction 3.I3-l4 Barnes et al. have now reported the direct observation of DMSO in CW photolysis of H202/ DMS/02 mixtures.I9 We would not have observed channel 3c in our previous direct study or in this work since we monitor OH loss in a pseudofirst-order excess of DMS. If channel 3c is occurring to a significant extent, our measured rates would underestimate the effective rate of DMS removal. This could account for the discrepancy between the direct and competitive studies. A comparison of the rate coefficients for the forward equilibration rate and the observed rate enhancement in oxygen offers the possibility of assessing the significance of OH regeneration. The steady-state analysis, eq VII, indicates that the effective rate, kobs, should increase as a function of oxygen partial pressure, from its value in the absence of oxygen, k2a, and reach a limiting value, ( k ~ , k2b). Since we can directly observe the equilibration process, then in principle we have two independent routes to the determination of k2b. It is important to note that adduct formation is a three-body process which may be in the lowpressure or fall-off regimes. Hence, our determinations of k2b, by the two alternate routes, need to be made at equal pressures, with buffer gases which have equal third body efficiencies. Fortunately in systems in which it is possible to directly measure third body efficiencies, NZ and 0 2 typically have very similar values. However, the assumption of equivalent efficiencies is central to this analysis, and of course, it is not possible to determine this experimentally for oxygen in this system. Consequently, good agreement between equilibration measurements of k2b in N2 and a limiting value of the oxygen rate enhancement in an 0 2 or 0 2 / N 2 mixture at the same pressure indicates that no OH regeneration channels proceed at a significant rate. If the limiting value of the rate enhancement is less than the value of k2b, this is an indication that OH regeneration may be significant. If the limiting value of the rate enhancement is greater than the value of k2b, this is an indication that one or both of the measurements are in error or that we do not fully understand the reaction mechanism. Consequently, these independent measurements represent an opportunity to confirm the internal consistency of the approach and provide additional mechanistic information. Unfortunately, the rather large uncertainty in the value of k2b and the fact that we have not made a clear observation of the limiting rate enhancement makes it difficult to be definitive about the possible magnitude of any OH regeneration process. At 250 K we observe a rate enhancement of approximately 4.5 x 10-l2 cm3 molecule-' s-I when we increase the oxygen partial pressure from 0 to 20 Torr, and we do not appear to have reached the limiting value in the enhancement. This is rather less than our reported value for k2b = (6.1 f 3.7) x cm3 molecule-' s-' but is well within the 2a uncertainty. The agreement between the values is a good indication that our proposed mechanism is correct and that our measurements are intemally consistent. It does not, however, permit us to exclude the possibility of an OH regeneration channel. Adduct Binding Energy. Assuming that our mechanistic interpretation is correct, we can use our values of the elementary rate constants to determine an adduct binding energy. The equilibrium constant, Kp, is related to the forward and reverse rates for adduct formation:
+
a Q Figure 9. Variation of observed rate coefficient, kobs. with oxygen partial pressure at 258 and 250 K and a total pressure of 110 Torr. Curves a-e are calculated using eq VI1 and the elementary rate parameters listed in Table 4.
TABLE 4: Analysis of Variation of kob with Oxygen Concentration 250
a b
258
C
d e
1.45 1.45 1.55 1.55 1.55
5.5 6.0 6.0 5.0 4.3
2 2 4.5 3.5 3.15
2.75 3.0 1.33 1.43 1.37
8 6.5 6.5 7.0 8.4
1.17 1.34 0.07 0.02 0.13
Units are cm3 molecule-' s-I. Units are lo5 s-I. Units are 10-l' cm3 molecule-'. dunits are 10-l3 cm3 molecule-' s-'.
if these values are consistent with the measured kza and K,, then k3 is constrained to a value of (8 f 3) x cm3 molecule-' s-I. Figure 9 shows a series of calculated fits, and the fit parameters are listed in Table 4. Analysis of the 267 K data using the value of Kc obtained from "roll-off' measurements is also consistent with this rate coefficient. As we note below, our analysis assumes that the reaction of the adduct with oxygen does not regenerate the OH radical. Potential exothermic reaction channels for the adduct reaction with molecular oxygen include CD3S(OH)CD3-I- 0,
-
(CD,),SO
+ HO,
+ CD,O, (CD3),S02 + OH CD3SOH
(34 (3b) (3c)
On the basis of their observation of product dimethyl sulfone
J. Phys. Chem., Vol. 99, No. 46, 1995 16973
Reaction of OH with Dimethyl-d6 Sulfide
1000
Kp(RT)= K, = k 2 d k - 2 b From the van’t Hoff relationship, the slope of a plot of In Kp vs T I gives the exothermicity of reaction 2b, the adduct binding energy.
7
h “
‘E +
In Kp = (ASIR) - (AHIRT)
ld
v
Values of K, between 261 and 250 K were obtained from the analysis of observed double-exponential OH decays. Kc at 267 K was obtained from the “roll-off’ curve shown in Figure 1. As we discuss above, the equilibrium constant obtained by the latter method is sensitive to the value of kza chosen. Values and 1.7 x cm3 molecule-’ s-’ for kza of 1.6 x give almost equally good fits to the data and lead to equilibrium constants, K,, of 5.3 x and 6.3 x cm3 molecule-’; we have used the average of these two values in our van’t Hoff plot, shown in Figure 10. The data used in the analysis are summarized in Table 5. A least-mean-squares fit to the data in Table 5 gives, for reaction 2b, AH = -13.0 & 3.3 kcal mol-’ and AS = -39 & 12 cal mol-’ K-’ (errors are 2 4 . An alternate approach for obtaining thermochemical parameters is the “third law method” where the entropy change is calculated using standard statistical mechanical methods20 and employed in conjunction with an experimental value for Kp at a single temperature to obtain “n,T. Absolute entropies as a function of temperature were obtained by interpolation from the JANAF thermochemical tablesz1for the OH radical and calculated using the structural information in Table 6 for (CD3)zS and (CD3)zSOH. The structural parameters listed in Table 6 are based on ab initio quantum chemical calculations carried out by McKeez2 using density functional theory at the Becke3LYP/6-3 l+g(d) level. To our knowledge there is no information in the literature on the vibrational spectrum of either molecule. However, a comparison of the calculated frequencies for (CH3)zS with published values shows quite good agreement, particularly for the lower frequencies that make significant contributions to So and C, in the temperature range of this study. For the higher energy modes, the theoretical values are, on average, 5% greater than experiment. The highest uncertainty in calculating the thermochemical parameters lies in the treatment of the internal rotations, i.e., the two CD3 rotational modes in (CD3)zS and (CD3)2SOH and the OH rotation in (CD3)zSOH. The entropy and heat capacity contributions from the internal rotations were approximated by three different methods: (1) The motions were treated as torsional oscillations using the theoretically derived frequencies shown parenthetically in Table 6. (2) The motions were treated as free rotors and the thermochemical contributions calculated by established methods.z3 (3) More realistically, each rotation was treated as having a potential barrier hindering the motion. While the precise height of any given barrier is not known in this case, reasonable values can be assigned based on barrier heights for methyl and hydroxyl group rotations in similar moleculesz3 and the thermochemical contributions calculated as outlined by Lewis and The change in entropy for reaction 2b was calculated using the different methods of assessing the contributions from the internal rotations with an average value of As258 K = -27.4 & 3.2 cal mol-’ K-’ reached. The error bar reflects the range of values resulting from the limits discussed above. Using this value for the entropy change in conjunction with Kp(258) = 340 atm-’ calculated from the second law expression derived above leads to the result fi&n,258 K = -10.1 f 1.1 kcal mol-’. Here the error represents both the uncertainty in AS7 discussed above and an estimated factor of 1.6 uncertainty in K, at 258 K. The adduct binding energy has been corrected to the reference
1
Figure 10. van’t Hoff plot for reaction 2: (0),This work; the solid line, a least-mean-squares fit to the data (Table 5 ) gives AH = -13.0 f 3.3 kcal mol-’ and AS = -39 k 12 cal mol-’ K-’ (errors are 2 4 . The dashed line is extrapolated from the AH and AS presented by Barone et al.I5 ( 0 )Obtained from reanalysis of 1986 “roll-off’ data of Hynes et al.5
TABLE 5: Values of K , Used in van’t Hoff Analysis
250 255 25 8 26 1 267
2.82 & 0.14 1.43 & 0.54 1.36 0.09 0.76 0.17 0.58
**
827 412 381 214 159
temperatures, 298 and 0 K, using tabulated heat capacity data for OH2’ and calculated heat capacities for (CD3)2S and (CD3)2S-OH. The latter calculations were carried out with the internal rotations treated as torsional modes. As seen in Table 7, the corrections to 298 and 0 K are small, and the error bar has been increased to account for use of the approximation. The values of U f , T for the adduct listed in Table 7 were calculated from M r x n , T , Mf,.r(OH), and AHf,.r(DMS-d6). The latter of these quantities was derived from the heat of formation of ( C H ~ ) Zcorrected S ~ ~ for the difference in zero-point energies. Because of the uncertainty in the fundamental frequencies in (CD3)2S, the error bars for M f , T values are somewhat larger than for AHrxn,~. Comparison with Previous Experimental Results. (i) Kinetic Studies of the DMS/OH/O2 System. Results of early competitive rate studies of reaction 1 have been discussed previ0usly.4.~ These studies used a variety of NO,-based OH production schemes, and it is now accepted that such approaches give erroneously high rate constants in studies of sulfide reactions. Two previous studies have examined the 0 2 dependence of the observed rate coefficient. The 1986 study of Hynes et looked at kobs for reactions 1 and 2 as a function of air pressure at room temperature; Le., the oxygen partial pressure was fixed and total pressure varied. Subsequently, Barnes et al.8 examined the variation of k&s as a function of oxygen partial pressure at a fixed total pressure of 760 Torr, again at room temperature. In both studies an increase in kobS was reported; however, the observed enhancement was considerably greater in the work of Barnes et al. In addition, Hynes et al. reported a dramatic enhancement in kobs as the temperature was reduced, based on measurements in air or 0 2 at 700 Torr. This work provides a further confiiation of the “ 0 2 enhancement” in the apparent rate constant. In the absence of oxygen, Hynes et al. saw a “roll-off’ in the pseudo-first-order rate at 261 K. They used an estimated k z b to model the “roll-off’ and obtain a value for k-2b and hence an estimate of the equilibrium constant. This procedure gave k z b = 1.13 x lo-” cm3 molecule-’ s-’ and values of k-2b of 2.5 x lo6 or 3.6 x lo6 s-I depending on the
16974 J. Phys. Chem., Vol. 99, No. 46, 1995
Hynes et al.
TABLE 6: Structural Parameters Used in the Evaluation of Absolute Entropies and Heat Capacities for (CD3)zS and (CD&S-OH vibrational frequencies," cm-I
(CDihS
(CD3)2S-OH
2330, 2330, 2319, 2314, 2184, 2182, 1093, 1089, 1082, 1075, 1068, 1049,850,767,726,701, 696,634,227, (133, 126)
3705, 2353, 2352, 2340, 2339,2194, 2193, 1086, 1079, 1077, 1070, 1060, 1042,853,763,730,712,696, 655,636,264,235,228, 166, (144, 128,88)
389,510 6.6
2,281,000 6.6 1.o Vo(CD3) = 1.9
moments of inertia
ABC," amu' A6 Zr(CD3),bamu I,(OH),b amu A2 barriers to internal
2
Vo(CD3) = 1.9
rotation,bkcal mol-[ Vo(0H) = 1.0
Vibrational freauencies and geometries oDtimized at the Becke3LYP16-3l+g(d) 1evel.l' Moments of inertia and barriers typical of internal rotations for CD3 aAd OH substikent groups.i8
TABLE 7: Thermochemical Results for the (CD3)fi-OH Adduct As Derived Using the Third Law Method" TIK adduct bond strength 298 -16.3 f 2.1 10.1 f 1.2 258 -16.0 f 2.0 10.1 1.1 0 -12.1 f 2.2 9.4 f 1.3 Thermochemical parameters are given in units of kcal mol-I.
*
+
value of kza chosen. They reported k-2b = 3.5 x lo6 s-I, which gave an equilibrium constant, K,, of 3.2 x cm3molecule-'. Rearialysis of this roll-off data by minimizing x2 gives Kc = 5.5 x cm3 molecule-', which is still somewhat lower than the value which would be obtained from these results, K = 9.0 x cm3 molecule-'. The value for AH, the adduct binding energy, is in good agreement with the previous estimate. Our value of k3 is much lower than the value (4.2 f 2.2) x cm3 molecule-' s-' reported by Hynes et This could be indicative of a pressure dependence in k3. Reanalysis of the kobs data reported by Hynes et al. using Kc from this work and assuming k2b 1.1 x lo-'' cm3 molecule-' s-' gives values of k3 which are in excellent agreement with the value obtained here. This suggests that the value of k3 is both pressure- and temperature-independent over the range 100-700 Torr of N?; and 300-250 K. Barone et al.I5have recently presented a value of k3 % 1 x cm3 molecule-' s-' independent of pressure and temperature over the ranges 30-200 Torr and 227-258 K, which is in excellent agreement with the value reported here. Barone et al. have also reported observation of equilibration between 217 and 241 K and obtain values of AH = -10.2 kcal mol-' and AS = -28.5 cal mol-'. The values of Kp extrapolated from these values are shown in our van't Hoff plot and are in reasonable agreement with our work. There have been two recent direct measurements of the OH DMS rate coefficient in the absence of 0 2 using low- and high-pressure discharge flow technique^;^.^^ these two studies are consistent with the work of Hynes et and support a room temperature rate coefficient of approximately 5 x cm3 molecule-' s-l and a small positive activation energy. Stickel et aLZ7have recently reported yields of HOD from the reaction of OD with DMS at low pressure in nitrogen.
+
al.596
OD -I- CH3SCH,
-
CH3SCH24- HOD
ized by gas phase electron transfer with Xe. The neutrals were then reionized by collisions with oxygen and mass analyzed. They used both protonated DMSO and DMSO-& and were unable to detect reionized (CH&SOH or its deuterium analogue. They concluded that the adducts must have a unimolecular dissociation rate which is faster than 1.3 x lo6 s-'. ( i i i ) Computational Studies. Three computational studies of the OH DMS addition reaction have now been reported. Gu and Turecekg carried out ab initio molecular orbital calculations at the (MP4/6-31G*) level using GAUSSIAN 86 and were unable to find a bound equilibrium structure for (CH3)zSOH; they concluded that the "adduct" is a transition state rather than an intermediate. McKee,'O however, has shown that the level of theory used in the Gu and Turecek calculations is inadequate to describe the structure of the DMSOH adduct. He finds, using GAUSSIAN 92, that the adduct is indeed bound, but with an adduct binding energy of 6 kcal mol-', which is somewhat smaller than our experimental value. Turecek" has subsequently reported a further study, again using GAUSSIAN 92, which ignores the findings reported by McKee and again claims that the adduct is not bound. Does the Reaction of DMS with OH Proceed via a TwoChannel Mechanism? As with any mechanistic study of this kind, it should be noted that reported observations cannot "prove" but rather can only indicate consistency with a hypothesized mechanism. It is also necessary to consider whether any plausible altemative mechanism exists which could also explain the observations. It is now clear that the apparent rate coefficients for the reaction of both DMS and DMS-d6 with OH are dependent on the partial pressure of 0 2 . At the initial radical concentrations used in our studies, [OHIinitial = (1 - 10) x IO" ~ m - complications ~, from self-reaction or reaction of OH with the products of reaction 2 could contribute only a fraction of the observed OH decay rates, even if such reactions proceeded at gas kinetic rates. Photolysis of DMS is negligible at these wavelengths. All reported experimental observations with the exception of the work of Gu and Turecek9 are totally consistent with a two-channel reaction mechanism involving both hydrogen abstraction and reversible adduct f ~ r m a t i o n . ' ~ Clearly, our observations of stable adduct formation are inconsistent with the conclusions of Gu and Turecek that the adduct is not bound. They noted that the neutralization process they used to prepare the adduct can lead to the formation of highly energized neutrals and that relatively stable species can be subject to fast dissociation. In the absence of some means to characterize energy disposal into the neturalized species, it would appear that this technique is unsuitable for the study of weakly bound intermediates. In addition, this work and the later study by Turecek appear to completely misunderstand the basic hypothesis of the two-channel mechanism. They incorrectly cite the work of Hynes et aL5 as suggesting that competitive
(6)
They find yields of 0.84 f 0.15 at 298 K and 0.87 & 0.13 at 348 K, thus confirming that hydrogen transfer is the dominant channel in the absence of 0 2 . (ii) Mass Spectrometric Studies. The experimental study of Gu and Turecekg utilized a neutralization-reionization mass spectrometry technique and involved the use of chemical ionization of DMSO to generate the cation of the dimethylhydroxysulfuranyl radical, (CH3)2SfOH, which was then neutral-
J. Phys. Chem., Vol. 99, No. 46, 1995 16975
Reaction of OH with Dimethyl-d6 Sulfide attack at sulfur by OH is thought to produce an adduct which dissociates further to products. They do not address the experimental observations, reported by Hynes et al. and confirmed in the competitive study of Barnes et al., that the effective rate of the reaction with DMS is dependent on oxygen pressure. This, of course, indicates that the adduct does not dissociate to products. It dissociates back to reactants or reacts with oxygen; hence the observed oxygen dependence of the rate coefficient. It is easy to demonstrate that the increase in kobs measured in direct studies is inconsistent with any secondary chemistry complications. We are unaware of any mechanism which can explain this kind of oxygen-specific rate enhancement, other than reversible adduct formation in competition with adduct reaction with 0 2 . McKee'O has reexamined the stability of the DMS-OH adduct using a higher level of ab initio calculation than that used by Gu and Turecekg or Turecek." He finds that the adduct is stable and has a binding energy of 6 kcal mol-'. This is rather less than our experimental value, but in view of the rather large uncertainty and the difficulty in the calculations, the agreement is not unreasonable. We conclude that the two-channel mechanism offers the only reasonable explanation of the observations obtained in both the direct and competitive rate studies of DMS oxidation. Although quantitative discrepancies between the experimental studies exist, and a satisfactory description of the electronic structure of the adduct remains elusive, this mechanism offers the only reasonable approach to modeling the atmospheric degradation of DMS.
Acknowledgment. This research was supported by the Georgia Tech Research Institute through intemal grant E-8904047, the Office of Naval Research through grants NO00149410105 and NO00149510242 to the University of Miami, and the National Science Foundation through grants ATM-9104807 and ATM-9412237 to Georgia Tech. We thank M. L. McKee for calculating DMS-d6 and (CD&S-OH frequencies and structural parameters and S. B. Barone, A. A. Turnipseed, and A. R. Ravishankara for a preprint of ref 15. References and Notes (1) Bates, T. S.; Lamb, B. K.; Guenther, A.; Dignon, J.; Stoiber, R. E. J . Atmos. Chem. 1992, 14, 315. (2) Charlson, R. J.; Lovelock, J. E.; Andreae, M. 0.;Warren, S. G. Nature 1987, 326, 655. (3) Abbatt, J. P. D.; Fenter, F. F.; Anderson, J. G. J . Phys. Chem. 1992, 96, 1780.
(4) Atkinson, R. J . Phys. Chem. Ref. Data 1989 (Monograph 1). (5) Hynes, A. J.; Wine, P. H.; Semmes, D. H. J. Phys. Chem. 1986, 90, 4148. (6) Hynes, A. J.; Wine, P. H. In The Chemistry of Acid Rain: Sources and Atmospheric Processes; American Chemical Society Symposium Series No. 349; Johnson, R. W., Gordon, G. E., Eds.; American Chemical Society: Washington, DC, 1987; Chapter 11, p 133. (7) Hynes, A. J.; Wine, P. H. In Biogenic Sulfur in the Environment; American Chemical Society Symposium Series No. 393; Saltzman, E. S., Cooper, W. J., Eds.; Chapter 25, p 424. (8) Barnes, I.; Bastian, V.; Becker, K. H. Int. J . Chem. Kinet. 1988, 20, 415. (9) Gu, M.; Turecek, F. J . Am. Chem. SOC. 1992, 114, 7146. (10) McKee, M. L. J . Phys. Chem. 1993, 97, 10971. (11) Turecek, F. J . Phys. Chem. 1994, 98, 3701. (12) Hynes, A. J.; Pounds, A. J.; McKay, T.; Bradshaw, J. D.; Wine, P. H. Detailed Mechanistic Studies Of The OH Initiated Oxidation Of Biogenic Sulfur Compounds Under Atmospheric Conditions. 12th International Symposium on Gas Kinetics, Reading, UK, July 1992. (13) Hynes, A. J.; Stickel, R. E.; Pounds, A. J.; Zhao, Z.; McKay, T.; Bradshaw, J. D.; Wine, P. H. In Proceedings of the International Symposium on Dimethylsulphide. Oceans, Atmosphere and Climate; Restelli, G., Angeletti, G., Eds.; Kluwer Academic Publishers: Dordrecht, 1993. (14) Hynes, A. J. Reaction mechanisms in atmospheric chemistry: Kinetic studies of hydroxyl radical reactions. Spectroscopy in Environmental Science; Clark, R. J. H., Hester, R. E., Eds.; John Wiley & Sons: New York, 1995. (15) Barone, S. B.; Tumipseed, A. A,; Ravishankara, A. R. Faraday Discuss. 1995, 100, submitted. (16) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in Fortran: The Art of Science Computing; Cambridge University Press: New York, 1992. (17) Barnes, I.; Bastian, V.; Becker, K. H.; Martin, D. Fourier Transform IR Studies of the Reactions of Dimethyl Sulfoxide with OH, NO3, and C1 Radicals. ACS Symp. Ser. 1989, No. 393, 476. (18) Hynes, A. J.; Wine, P. H. J . Atmos. Chem., in press. (19) Barnes, I.; Becker, K. H.; Patroescu, I. Geophys. Res. Lett. 1994, 21, 2389. (20) See, for example: Knox, J. H. Molecular Thermodynamics; WileyInterscience: London, 1971. (21) Chase, M. W., Jr.; Davies, C. A,; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. J . Phys. Chem. Ref. Data 1985.14 (Suppl. 1). (22) McKee, M. L. Private communication. (23) Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley-Interscience: New York, 1976. (24) Lewis, G. N.; Randall, M. Thermodynamics, 2nd ed.; McGrawHill: New York, 1961; revised by K. S. Pitzer and L. Brewer. (25) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J . Phys. Chem. Ref. Data 1988, 17 (Suppl. 1). (26) Hsu, Y. C.; Chen, D. S.; Lee, Y. P. Int. J . Chem. Kinet. 1987, 19, 1073. (27) Stickel, R. E.; Zhao, Z.; Wine, P. H. Chem. Phys. Lett. 1993,222, 312. JP952047Q
