J. Phys. Chem. 1984, 88, 2095-2104
2095
R2(meta OH adduct) decays by pure second order; no water splitting from this transient isomer could be observed. This is not in unison with the previous conclusions3 that all OH-adduct isomers are capable of eliminating water. In order to examine the reliability of the optimized parameters, a sensitivity matrix has been evaluated and is presented in Table 111. The elements of the matrix represent the change of the overall O D values in percent, which is produced by increasing k and E values by a factor of 2. It is evident that the parameters kl-k3, k9/, and all t values are very sensitive at least at some wavelengths. On the other hand k4, k7, k8, and k l o are relatively insensitive, demonstrating their small influence on the total absorption in the time range up to 200 p s after pulse end. The sensitivity of the parameters k7 and k , , increases considerably after 200 p s . From Table I11 is also evident that the prompt formation of R3(phenoxyl radical; parameter k 3 ) is very sensitive in the time up to 30 p s at the wavelengths 260 and 405 nm. Hence, its small contribution can be determined with sufficient accuracy.
molecule could be elucidated. More than 90% of the OH radicals form adducts on the phenol ring. It was further stated that ortho-directed transient (R,) decays predominantly by water elimination, resulting in phenoxyl radical, whereas for the meta isomer exclusively second-order decay could be established. A small share of the O H radicals are involved in an H-abstraction reaction from the OH group of the phenol ring, resulting in prompt formation of phenoxyl radical. The O H attack on both ipso sites (Cl- and C,-positions) is in total about 10%; on the alanine moiety it is less probable.
Conclusion The kinetics of the specific-site O H attack on the tyrosine
16-8;
+
Kinetics of the Reaction OH SO2 4- M Dependence in the Falloff Region
-
Acknowledgment. S.S. and N.G. thank Prof. Dr. D. Schulte-Frohlinde, director of Max Planck Institut fur Strahlenchemie, Mulheim/Ruhr, F.R.G., for use of the pulse radiolysis equipment. The financial supp~rtwarded by Bundesministerium fur Wissenschaft und Forschung, Austria, is gratefully appreciated. Thanks are expressed to Dipl. Phys. F. Schworer, F. Reikowski, and K. H. Toepfer for valuable help. Registry No. Tyrosine, 60- 18-4; tyrosine OH-adduct (R]), 89462tyrosine OH-adduct (R2), 89462-15-7; tyrosine phenoxy radical
(R3),16978-66-8; hydroxyl, 3352-57-6.
HOS02 4- M. Temperature and Pressure
P. H. Wine,* R. J. Thompson, A. R. Ravishankara, D. H. Semmes,+ C. A. Gump, A. Torabi, and J. M. Nicovich Molecular Sciences Group, Engineering Experiment Station, Georgia Institute of Technology, Atlanta, Georgia 30332 (Received: July 11, 1983; In Final Form: February 16, 1984)
-
The flash photolysis-resonance fluorescence technique has been employed to study the kinetics of the combination reaction OH + SO2 + M HOSO, + M. A total of 58 bimolecular rate coefficients are reported for varying conditionsof temperature (260-420 K), pressure (13-696 torr), and buffer gas identity (He, Ar, N2,SF6). Complicating side reactions involving SO2 photofragments have been eliminated by filtering the photolysis flash with SOz. The reaction is found to be in the falloff region between third and second order over the entire range of conditions investigated. Falloff parameters are derived from the data by the method of Troe. Under conditions of atmospheric pressure and gas composition, rate coefficients derived from our data are about 30% lower than currently recommended values.
Introduction The kinetics of the reaction O H SO2 M
+
+
-
HOSO2
+M
(1)
have been the subject of intensive investigation in recent years. This interest has been stimulated by the importance of reaction 1 as an initiation step in the atmospheric oxidation of SO?.to sulfate, and its resultant role in the chemistry of acid rain, visibility reduction, and climate modification. Also, because reaction 1 is in the "falloff" region between third and second order over the range of total pressures typically accessible to laboratory studies, it is of interest as a test case for theories of unimolecular decomposition-recombination reaction rates. Reaction 1 has been studied a t pressures below 10 torr in discharge flow systemsl-2and at pressures in the range 10-1000 torr by using flash p h o t o l y ~ i ssteady-state ,~~ photoly~is,~-'~ and pulsed radiolysis' techniques. Despite this large data base, the dependence of kl on pressure and temperature is not well defined. The uncertainty in k , is about f50% at T = 298 K, P = 760 torr of N, and is much larger at lower temperatures and pressures. The poor agreement between the numerous laboratory investiPresent address: Department of Chemistry, California Institute of Technology, Pasadena, CA 91 125.
0022-3654/84/2088-2095$01.50/0
gations of reaction 1 can be largely attributed to experimental difficulties associated with such studies. These include heterogeneous reactions in flow tube and steady-state photolysis experiments and side reactions involving SO2photofragments in flash photolysis studies. In this paper we report the results of a flash photolysis-resonance fluorescence study of reaction 1. Bimolecular rate coefficients have been measured over a wide range of temperature (1) G. W. Harris and R. F. Wayne, J. Chem. Soc., Faraday Trans. J,71, 610 (1975). (2) M. T. Leu, J . Phys. Chem., 86, 4558 (1982). (3) R. Atkinson, R. A. Perry, and J. N. Pitts, Jr., J . Chem. Phys., 65, 306 ( 1976). (4) D. D. Davis, A. R. Ravishankara, and S. Fischer, Geophys. Res. Lett., 6, 113 (1979). (5) G. W. Harris, R. Atkinson, and J. N. Pitts, Jr., Chem. Phys. Lett., 69, 378 (1980). ( 6 ) G. Paraskevopoulos, D. L. Singleton, and R. S. Irwin, Chem. Phys. Lett., 100, 83 (1983). (7) R. A. Cox, Int. J . Chem. Kinet. Symp., 1, 379 (1975). (8) A. W. Castleman, R. E. Davis, H. R. Munkelwitz, I. N. Tang, and W. P. Wood, Int. J . Chem. Kine?. Symp., 1, 629 (1975). (9) A. W. Castleman and I. N. Tang, J . Photochem., 6, 349 (1976). (10) R. A. Cox and D. Sheppard, Nature (London), 284 330 (1980). (11) S . Gordon and W. A. Mulac, In?. J . Chem. Kinet. Symp., 1, 289 (1975).
0 1984 American Chemical Society
2096
Wine et al.
The Journal of Physical Chemistry, Vol. 88, No. 10, 1984
(260-420 K) and pressure (13-696 torr), and for several buffer gases (He, Ar, N,, SF6). Experimental improvements over previous flash photolysis studies include (1) elimination of complications resulting from photolytic production of SO and O(3P) through use of an SO, filter between the flashlamp and the reaction cell and (2) direct measurement of the SO, concentration in the slow flow system by UV photometry.
Experimental Section The apparatus used in this study has been described elsewhere;’, a brief review of its operation is given below. A jacketed Pyrex reaction cell with an internal volume of 150 cm3 was used in all experiments. The cell was maintained at a constant temperature by circulating ethylene glycol from a thermostated bath through the outer jacket. A copper-constantan thermocouple with a stainless steel jacket was inserted into the reaction zone through a vacuum seal, thus allowing measurement of the gas temperature under the precise pressure and flow rate conditions of the experiment. O H radicals were produced by flash photolysis of HzOat wavelengths between the onset of absorption at 185 nm and the Suprasil cutoff at 165 nm. An OH resonance lamp situated perpendicular to the flashlamp excited fluorescence in the 0-0 band of the A2Z+-XZII system. Fluorescence was detected perpendicular to both the flashlamp and resonance lamp by a photomultiplier fitted with an interference filter (309.5-nm peak transmission, 10 nm fwhm). Signals were obtained by photon counting and then fed into a signal averager operating in the multichannel scaling mode. For each decay rate measured, sufficient flashes were averaged to obtain a well-defined temporal profile over at least two and usually three l / e times. The flash duration was 50 1 s while measured O H lifetimes ranged from 1 to 40 ms. In order to avoid accumulation of reaction or photolysis products, all experiments were carried out under “slow flow” conditions. SO, was flowed from a 12-L bulb containing a dilute SO,/buffer gas mixture. An H,O/buffer gas mixture was generated by bubbling buffer gas through high-purity water at 298 K and a pressure of 800 torr. The SO,/buffer gas mixture, H,O/buffer gas mixture, and additional buffer gas were premixed before entering the reaction cell. Concentrations of each component in the reaction mixture were determined from measurements of the appropriate mass flow rates and the total pressure. The SO2 concentration in the mixture exiting or, in a few experiments, entering the reactor was directly measured (at 298 K) by UV photometry with either a mercury (185.0 nm) or zinc (213.9 nm) Pen-ray lamp as the monitoring light source and a bandpass filter-photomultiplier-electrometer combination as the detector. Before each run the SO, flow was shut off, the absorption cell and reactor were flushed with diluent gas, and the unattenuated monitoring light intensity, Io, was measured. SO, was then added and the attenuated intensity, I , was monitored continuously during the course of the experiment. After completion of the experiment the reactor and absorption cell were again flushed to measure I , , The measured value for I / I o seldom changed by more than a few percent during the course of the experiment. SOz absorption cross sections at the monitoring wavelengths were measured during the course of the investigation. In both cases the effective cross section, aef,was found to monotonically decrease with decreasing Illo, presumably due to detection of weak ion lines emitted by both the Hg and Zn lamps. Over the range 0.3 < I/Zo < 0.9 where most experimental measurements were made, uefvaried by less than 10% for both the Hg lamp and the Zn lamp; this variation was taken into account in the determination of [SO,]. For Z/Io = 0.6, the measured values for uefwere 4.40 X lo-’* cm2 for the Hg lamp and 3.87 X lo-’* cm2 for the Zn lamp. These cross sections are consistent with a published ~ p e c t r u m although ’~ the highly structured nature of the spectrum
-
makes quantitative comparisons difficult. Measured cross sections were found to be independent of pressure up to 1000 torr of SF6 and are internally consistent as evidenced by the fact that excellent agreement was obtained when a particular bimolecular rate coefficient, k,(P,T,M), was measured with [SO,] determined first by absorption of Hg lamp radiation and then by absorption of Zn lamp radiation. A few experiments were carried out with the 21 3.9-nm Zn line isolated by using a monochromator; under these conditions, the SO, absorption cross section was found to be 4.83 X lo-’* cmz, independent of Z/Io, but the measured rate coefficients were the same as those measured without the monochromator. One important apparatus modification needed for this study was the inclusion of a filter cell between the flashlamp and the reaction cell.14 Pure SO2 was flowed through the filter cell to selectively attenuate those photolysis wavelengths which are most likely to cause SOz fragmentation in the reaction cell. The filter cell was 5 cm in length and was operated at SO, pressures of 0-10 torr. The gases used in this study had the following stated purities: SO2> 99.98%, He > 99.9999%, Ar > 99.9995%, N, > 99.9995%, and SF, > 99.99%. SOzwas stored in a blackened 12-L bulb and degassed repeatedly at 77 K immediately before preparation of SO,/buffer gas mixtures. All other gases were used as supplied. Vacuum distillation of SO2 (200-77 K) had no effect on the observed kinetics.
Results All experiments were carried out under pseudo-first-order conditions with [SO,] in large excess over [OH]. Reaction mixtures consisted of 40-200 mtorr of H 2 0 , 3-1 50 mtorr of SOz, and 13-696 torr of buffer gas. The initial O H concentration, [OHIO,was typically 1 X 10” molecules ~ m - ~ . To study the kinetics of reaction 1, it is desirable to establish experimental conditions where the O H temporal profile is governed entirely by the following processes: HzO ---* O H + H
OH
-
OH
+ SO, + M
P. H. Wine, N. M. Kreutter, and A. R. Ravishankara, J . Phys.
Chem., 83, 3191 (1979), and references therein. (13) D. Golomb, K. Watanabe, and F. F. Marmo, J. Chem. Phys., 36,958 (1962).
HOSOz + M
(1)
loss by diffusion from detector field of view and reaction with background impurities (3)
Then, since [SO,]
>> [OH], simple first-order kinetics are obeyed:
In ([OH]o/[OH],) = (kl[S02]
+ k3)t
k’t
(I)
The bimolecular rate coefficient, kl, which is a function of T, P, and the identity of M, is determined from the slope of a k’vs. [SO,] plot. Observation of O H temporal profiles which are exponential (Le., obey eq I), a linear dependence of k’on [SO,], and invariance of k’to variations in flash intensity, strongly suggRst that reactions 1-3 are the only processes which affect the O H time history (the presence of reactive impurities in the SO2 sample would not be elucidated by the above set of observations if [impurity] >> [OH]). Initial attempts to study reaction 1 were carried out with no filter cell between the flashlamp and the reactor. At the higher SO, concentrations investigated, where [SO,] [H20],nonexponential OH temporal profiles were observed which varied in a complex manner as a function of flash intensity. When O H resonance lamp radiation was blocked from entering the reactor, a time-dependent signal (Le., a luminescence signal) was still observed. When the luminescence signal was subtracted from the signal obtained with the resonance lamp radiation entering the reactor, the residual temporal profile remained nonexponential and dependent upon flash intensity. Some typical data are shown in Figure 1. The above observations suggest that secondary chemistry initiated by flash photolysis of SOz
so, (12)
-
- so +
o(3~)
(4)
(14) P. H. Wine, R. C. Shah, and A. R. Ravishankara, J . Phys. Chem., 84, 2499 (1980).
Kinetics of the Reaction OH
+ SO2 + M
-
HOS02 + M
The Journal of Physical Chemistry, Vol. 88, No. 10, 1984 2097
' 1J
w-'
;(\ I-
I
5
Y
0
E
8
i
0 .
T
A (nm)
Figure 2. Low-resolution absorption spectra for SO2and H 2 0 . The SO2 spectrum is taken from ref 13 and the H20spectrum is taken from ref 20.
c
The dependence of luminescence intensity on Ar pressure and flash intensity is consistent with the radiative recombination mechanism as are the observed decay kinetics, since O(3P) removal is probably dominated by diffusion from the detector field of view and the reaction
--.
O(3P)
1
-
+ SOz + M
SO3
+M
(6)
Furthermore, reaction 5 has been found to be important in the
.I *'
*i
TIME (ms) Figure 1. Typical data obtained in experiments with relatively high [SO,] and an unfiltered flash. Open circles represent total signal, Le., resonance fluorescence luminescence. Closed circles are data obtained with the resonance lamp blocked and, therefore, give the luminescence component. Solid lines are obtained by subtracting the smoothed closed circle data from the open circle data. Experimental conditions are as follows: P = 30 torr; buffer gas = argon; T = 300 K [H20] = 4.3 X 1015cm-'; [SO,] = 2.5 X 10l5 ~ m - flash ~ ; energy = (a) 120 J, (b) 30 J.
SO2 afterglow and to result in intense emission within the bandpass of our OH detection system.I5 The nonexponential decays observed in the absence of interfering luminescence (Figure 1) imply that OH was being produced and/or removed on a time scale competitive with the time scale for reaction 1. The dependence of the observed temporal profiles on flash intensity indicates that biradical processes were involved. Potential complicating side reactions include the following (thermodynamic data are taken from ref 16 and 17):
+
was influencing the temporal behavior of OH and also leading to a luminescence signal which interfered with OH detection. To characterize the luminescence signal, a series of experiments were carried out where S02/Ar and S 0 2 / A r / H 2 0 mixtures were photolyzed with 1000 torr cm of O2between the flashlamp and the reaction cell, thus eliminating the possibility of H 2 0 photolysis. The observed temporal profiles were nonexponential with the instantaneous decay rate varying from 1000 s-' a t short time to -40 s-l at long time. The limiting short and long time decay rates were independent of flash intensity or Ar pressure but the slow component became significantly more intense relative to the fast component at high Ar pressure and/or high flash intensity. H 2 0 appeared to quench the fast component preferentially. When the region between the flashlamp and reaction cell was evacuated, allowing H OH to be produced, little effect on the luminescence intensity or temporal behavior was observed. The origin of the fast component cannot be deduced with certainty from these observations although emission from SOzexcited by the photoflash is a likely source. The slow component is almost certainly due to the radiative recombination process
-
+
so
+
+
o(~P)
M
-
S02*
SO2
+
+
M
hv
O(3P) + OH
-
SO + OH
H
+ OH
SO3
HOS02
H
+ O2
AH = -17 kcal mol-'
(7)
SO2
AH = -29 kcal mol-'
(8)
-+ - + - + - +
O(3P) + H O S 0 2
H20
OH
+ HOS02 H2 SO3 H + SO3 OH + SOz H
-
-% HOSOZ.
AH = -64 kcal mol-' (9)
SO3
AH = -47 kcal mol-' (10)
AH = -45 kcal mol-'
(1 1)
AH = -19 kcal mol-'
(12a)
AH = -56 kcal mol-'
(12b)
The rate coefficients at 298 K for reactions 7 and 8 have been measured to be 3.3 X lo-'' and 8.4X lo-" cm3 molecule-' s-', r e s p e c t i ~ e l y , ' ~while ~ ' ~ kinetic data for reactions 9-12 are not available. On the basis of comparison with subsequent experiments where the flash was filtered by SO2,it can be concluded that both the high and low flash intensity temporal profiles shown in Figure 1 were affected by reactions 10-12 but only the high flash intensity (15) C. J. Halstead and B. A. Thrush, Proc. R. SOC.London,Ser. A , 295, 363 (1966). (16) S. W. Benson, "Thermochemical Kinetics: Methods for Estimation of Thermochemical Data and Rate Parameters", Wiley, New York, 1968. (17) S. W. Benson, Chern. Rev., 78, 23 (1978). (1 8) W. B. Demore, R. T. Watson, D. M. Golden, R. F. Hampson, M. J. Kurylo, C. J. Howard, M. J. Molina, and A. R. Ravishankara, "Chemical Kinetics and Photochemical Data for Use in Stratospheric Modeling", Jet Propulsion Labs, Pasadena, CA, 1983, publication no. 83-62. (19) J. L. Jourdain, G . LeBras, and J. Combourieu, In?.J . Chem. Kinet., 11, 569 (1979).
2098
The Journal of Physical Chemistry, Vol. 88, No. 10, 1984
TABLE I: Bimolecular Rate Coefficients for the Reaction OH 10-l7[~1, cm'
5
M
260 K
He Ar
29.6
f
1.1
He Ar
11.8
f
0.9
37.0
f
3.0
"6
He Ar
16.7
f
0.9
SF6
60.4
f
3.0
He Ar
23.6 i. 1.6
SF,
160
a
+ Ma
He Ar SF, He Ar SF,
f
f
f
0.27
12.9 f 0.9 4.35 t 0.38 21.8
1.7
6.22 28.6
f
* 0.29 2.2
420 K 2.26 10.7
f
3.53 15.1
f
4.90 24.9
f
f
0.28
0.4 f
0.32
1.1 f 0.41
2.0
14.4 f 1.0 15.8 f 1.3 41.7 ?r 6.8 52.2 f 2.0
43.8
2.4
39.0 c 4.2
21.1 23.4 71.7
1.5 2.1 3.5
13.4 f 0.6 58.3 f 3.3
10.9 t 1.1 49.1 f 5.0
34.0 f 2.0 33.9 f 5.0 100 f 1 0
18.5 f 2.2 74.5 f 8.5
15.8 f 1.5 7 1 . 6 f 8.2
3.1 8.6
54.6 f 4.4 124 f 14
2.79
10.3 c 0.9 12.1 f 0.6 28.9 f 3.0 43.8 f 3.1
75.2 f 4.6 36.5 95.0
5-l
360 K
6.90 f 0.70 7.75 f 0.50 18.1 f 2.0 29.0 f 2.0
N2 80
HOSO,
300 K
N2
40
--f
4.67 f 0.28 4.91 f 0.48 11.3 ?: 1.0 19.2 f 2.0
8.21 c 0.53
'6
N* 20
+ SO, + M
lO"k,, cm3 molecule-'
N2 10
Wine et al.
f f f
9.59 f
f
0.88
7.22 i. 0.45
Errors are 2u and refer to precision only.
temporal profile showed a significant contribution from reactions 7-9. Published absorption spectra for S0,13and H2OZQ are reproduced in Figure 2. Convolution of these spectra with the spectral distribution of the photoflash (assumed wavelength independent over the range 165-220 nm) and the Suprasil transmission curve indicates that the fraction of SO, photolyzed by an unfiltered flash is about a factor of six greater than the fraction of HzOphotolyzed. Hence, in experiments where 1 X 10" OH cm-3 were produced by the photoflash and [HzO] N [SO,], more than lo1, SO, photofragments cm-3 would be produced. Under these conditions, reactions 7 and 8 can consume O H at a rate competitive with consumption via reaction 1; reactions 10-12, if their rate coefficients are sufficiently large, may result in regeneration of O H on a time scale which competes with removal. Because of the SO, absorption cross section is small in the wavelength region 165-180 nm where most HzO photolysis occurs but is quite large in the 190-219-nm region, production of O(3P) and SO could be greatly suppressed by filtering the photoflash with appropriate amounts of SO,. Calculations suggest that with 50 torr cm of SOz in the filter cell, SO, photolysis is reduced by about a factor of 80 while H,O photolysis is reduced by a factor of 2.5. With sufficient SO,in the filter cell, the observed OH kinetics were well behaved. Exponential decays were observed whose time constants were independent of both flash intensity and further increases in filter cell SO, concentration. Linear dependences of k' on [SO,] were observed for all temperatures, pressures, and buffer gases investigated. To ensure that the SO, concentration in the reactor was being properly measured, some rate coefficients were measured first with the absorption cell traversed by the reaction mixture after leaving the reactor and then with the absorption cell traversed by the reaction mixture before entering the reactor. No dependence of k l on absorption cell position was observed. Some typical OH temporal profiles are shown in Figure 3, while typical k'vs. [SO,] plots are shown in Figure 4. Approximately 500 experiments (an experiment is the determination of one pseudo-first-order rate coefficient) were carried (20) J. G. Calvert and J. N. Pitts, Jr., "Photochemistry", Wiley, New York, 1966.
O ' °F--
k
t
t
TIME (ms) Figure 3. Typical data obtained under conditions where the OH temporal profile was unaffected by the presence of SO2 photofragments and the luminescence signal was negligible compared to the resonance fluorescence signal. Experimental conditions are as follows: P = 30 torr; buffer gas = argon; T = 300 K [H20] = 6.3 X 1015cm-), flash energy = 60 J; 40 torr cm of SO, in filter cell; [SO,] in units of 1015cm-3 = (a) 0, (b) 1.48, (c) 2.54; number of flashes averaged = (a) 32, (b) 256, (c) 512. Linear least-squares analyses give the following values for k ' k 2a in units of s-l: (a) 49.0 2 . 5 , (b) 164 i 10, (c) 245 rt 11. Comparison of trace (c) with the data in Figure 1 shows how the presence of SO, in the filter cell affects the temporal behavior of OH.
*
out. A total of 58 bimolecular rate coefficients were measured under varying conditions of temperature, pressure, and buffer gas identity; these rate coefficients are tabulated in Table I. The uncertainties quoted in Table I for individual kl determinations are 26 and represent the precision of the k'vs. [SO,] data only.
Kinetics of the Reaction OH
-
HOSOz
+M
The Journal of Physical Chemistry, Vol. 88, No. 10, 1984 2099
+ SO, + He, 300K
OH 4001
+ SOz + M
'160
TABLE 11: Estimated Vibrational Frequencies for HOSO, mode freq, cm-' mode freq, cm-'
80'
OH stretch SO, asym stretch OH bend SO, sym stretch SO, scis
SO, wag SO stretch SO, rock OH torsion
3550 1400 1330 1120 800
610 500 500 450
TABLE 111: Values for Seffand F , as a Function of T and Fcsc as a Function of Sk - Seffand T FcScat sk - Seff=
L A l - - W
OO
1
CSO,~
2
3
(ioi5 c r n 9
Figure 4. Typical k'vs. [SO,] data. Buffer gas (He) concentrations in units of 10" cm-) are given in the figure.
The absolute accuracy of the results is limited by precision, uncertainties in the determination of the SOz concentration, and possible systematic errors. It is our belief that systematic errors are small compared to other uncertainties. We estimate the absolute accuracy of each reported k,(P,T,M) to be A1 5% except for those experiments at the lowest and highest pressures and for M = N2, where experimental difficulties associated with detection sensitivity and/or concentration measurement make *20% a more reasonable estimate of overall accuracy. Tables listing the experimental conditions employed to measure each pseudo-first-order rate coefficient are too long to present in this paper but are available as supplementary material. (See paragraph at end of text regarding supplementary material.)
Discussion Determination of Falloff Parameters. Under all experimental conditions employed in this study, reaction 1 was found to be in the "falloff" region between third and second order. Troe and c ~ - w o r k e r s have ~ ~ - shown ~ ~ that bimolecular rate coefficient vs. pressure curves (i.e., falloff curves) for addition reactions can be approximated by the three-parameter equation k ( [ M I , T ) = km(qFLH F([M1,T) (11) where FLH is the Lindeman-Hinshelwood factor (111) FLH= K/(1 + K ) and K = kI(M,T)[Ml/ka.(T) (IV) In the above equations, ko(M,T) is the rate coefficient in the low-pressure third-order limit, k,( T) is the rate coefficient in the high-pressure second-order limit, and F( [ M ] , T )is a parameter which characterizes the broadening of the falloff curve due to the energy dependence of the rate coefficient for the decomposition of the energized adduct. F ( [ M ] , T )is the product of strong collision and weak collision broadening factors
F([MI,T) = I;""[MI,T) m [ M I , T )
(V)
Pccan be estimated from structural information about the adduct,2'g22while estimation of PCrequires knowledge of the ef(21) J. Troe, J . Phys. Chem., 83, 114 (1979). . Combust., [Proc.], 17rh, 535 (22) K. Luther and J. Troe, Z ~ r Symp. (1978). ( 2 3 ) J. Troe, Ber. Bunsenges. Phys. Cheni., 87, 161 (1983). (24) R. G. Gilbert, K. Luther, and J. Troe, Ber. Bunrenges. Phys. Chem., 87, 169 (1983).
T, K
SPff
Fp
200 260 300 360 420
0.417 0.797 1.064 1.461 1.841
1.065 1.090 1.105 1.128 1.152
1.0 0.940 0.855 0.823 0.741 0.662
1.5
2.0
2.5
0.844 0.767 0.712 0.627 0.566
0.734 0.652 0.599 0.536 0.476
0.617 0.553 0.509 0.446 0.403
ficiency of energy transfer between the energized adduct and the buffer gas. PC([ M ] , T )is obtained from the empirical relations hi^^^
FC([M1,T)= [F,"c(T)Ix (VI) where Fcs(T) is the value for Fsc( [ M ] , T )at the center of the falloff curve (i.e., the pressure where k o ( M , T ) [ M ]= k,(T)) and log K
Nsc + 6(0.1
x=(l+[
- 0.12
+ 0.6 log F,sC)
12)
(VII)
PC= 0.75 - 1.27 log F,sC(T) 6=+1
if K > 1 , - 1
if K < 1
Values for F,SC have been determined by Luther and Troe22*23 in tabular form as a function of the reduced Kassel integral parameters SKand BK. SKis given by the relationship (VIII) SK = Seff + (Ea- - Eo)/RT where E,, is the Arrhenius activation energy for unimolecular decomposition of the adduct in the high-pressure limit, Eo is the critical energy for unimolecular decomposition of the adduct, and Seffis the effective number of transition-state oscillators. Seff can be estimated from the vibrational partition function of the adduct molecule:
where s = 3N - 6 = the number of internal modes including hindered rotations. The parameter BK is approximated by BK
B'(SK - l ) / ( ~- 1)
(X)
where
+
B ' = [Eo a ( E o ) E , ] / R T
(XI)
In eq XI, a(Eo)is the Whitten-Rabinovitch factor2s and E, is the zero point energy of adduct vibrations. The HO-SO, bond dissociation energy has been estimated by Benson" to be 36 f 3 kcal/mol and this value can be used as a reasonable approximation for Eo.HOSOZvibrational frequencies can be estimated on the basis of known frequencies for H O N 0 2 , SO2,and NO,; a set of estimated frequencies is given in Table 11. Using these frequencies we calculate a(Eo) = 0.917 and E, = 14.67 kcal/mol. The value for Ea, is unknown but, if there is no barrier in the reaction coordinate (as is assumed when applying the Troe equations), the relationship 1 < SK- Seff< 2 is usually ~ b e y e d . When ~ ~ . ~the ~ frequencies in Table I1 are used, Fcs can be evaluated as a function of SK- Seffand T . Calculated values for F,SC and Seffare given in Table 111. (25) P. J. Robinson and K. A. Holbrwk, 'Unimolecular Reactions", Wiley, London, 1972.
2100 The Journal of Physical Chemistry, Vol. 88, No. 10, 1984
The weak collision broadening factor, Pc([M],T), is given by the empirical expressionz4 ~ P"[MI,T) = [ F C W C ~ ~ M 1 ~ ~ l (XII) where y =
(1+ [
log + NWc - d(l0g K
Nwc = 0.7 + 0.3SK c
+ C)
12)
(XIII)
+ 0.25 log PC
Wine et al. TABLE IV: Calculated Values for Z L ~Keq, , and kosc T, K
M
ZLJ(M,T)
Keq(r)
koSC(R.I,r)
200 260
N, N, Ar SF, N, He Ar SI', N, AI SP, N, A; SP,
4.13 4.35 3.80 4.34 4.49 6.08 3.90 4.44 4.67 4.05 4.57 4.83 4.20 4.72
3.64 X 6.70 x 10-5
7.60 4.58 4.01 4.56 3.64 4.94 3.18 3.60 2.71 2.35 2.65 2.05 1.78 2.00
300
360
= 0.085SK - 0.17 log Pc d = -0.2 - 0.12 log 0,
420
In the above equations, Fcwcis the weak collision broadening factor at the center of the falloff curve and @, is the collision efficiency Pc
= ko/koBC
kGC= kO,dsc/Kq
(XVI)
where kO,dscis the strong collision rate coefficient for HOSOz dissociation. kO,dsccan be calculated from the relationshipz6 kO,dsc = ZLJ[ P (EO)RT/
Q ~ i deXp(-EO/R
T )FEFanhFrotFcor
(XVII) where ZLJis the Lennard-Jones collision frequency, p(Eo) is the density of states at the critical energy Eo, FE, Fanh,and Fro,are correction terms for the energy dependence of the density of states, anharmonicity, and rotation, respectively, and F, is a correction term to account for coupling between different types of degrees of freedom. F,, is not calculable and is generally set equal to unity. p(Eo) is calculated from the Whitten-Rabinovitch appr~ximation.~' F E is given by
while Fanh is given by
where m is the difference in number of oscillators in the reactant and product molecules (assumed to be Morse oscillators). For = 1.38. Values for F E as a function reaction 1, m = 5 and Fanh of Tare given in Table 111. If we assume no barrier for association, the relevant expression for Fro,is
RT(S
+ Y2)g
R m + Y2Ng - 1) + Eo + a(Eo)E,
(XX)
g = 2.15(E0/RT)'/'
The Lennard-Jones collision frequency is given by Z L j = 8.09 X cm3 molecule-' s-'((T/1000 K) (20 g mol-'/pM)]l/z (aM/5 A)2fiMz,2 (XXI) where the collision integral is approximated by f i ~ ' ' =~ [0.697 + 0.5185 log ( k T / t ~ ) ] - l
(XxII)
(26) J. Troe, J. Chem. Phys., 66, 4758 (1977). (27) G. Z. Whitten and B. S. Rabinovitch, J . Chem. Phys., 38, 2466 (1963).
2.31 X lo4 5.57 X 10'
Assumed Lennard-Jones Parameters
(XIV)
where k p is the low-pressure limiting strong collision rate coeffi~ient.~ To~ a~ ~good ~ approximation, Fcwc is given by the expressionZZ F c W C = P214 (XV) The low-pressure limiting strong collision rate coefficient is calculated from the relationship
0.849
M
NZ
He
Ar
SF,
10l6oM,cm2
4.50 202
3.91 71
4.37 239
5.23 326
E&,
a Units are for Keq, and
K
cm3 molecule-' s-' for Z L J , molecule cm-3 cm6 molecule'2 s-' for k,SC.
In the above equations, pM, uM,and eM are the reduced mass, Lennard-Jones collision diameter, and Lennard-Jones well depth for collisions of HOSO, with the bath gas M. Values for uMand eM were estimated based on known values for polar moleculesz8 and mass transport proper tie^.^^^^^ To obtain the equilibrium constant, we calculated entropies ( S O ) and specific heats (Cpo) for OH and SOz for the temperature ranges of interest using tabulated spectroscopic data and found them to be in excellent agreement with Benson's tabulated valuesi6 at both 300 and 500 K. For similar calculations on HOS02, the vibrational frequencies given in Table I1 were used along with estimated structural parameters (for the calculation of rotational constants). The overall calculation is not very sensitive to the exact geometry assumed for HOSO,. Calculated values for ZLj, Kq,and kgSCare given in Table IV as are the assumed Lennard-Jones parameters. It should be noted that absolute values for Kq (and, therefore, k p ) are very sensitive to the input thermodynamic data and are uncertain by about a factor of two. However, the calculated ratios kgSc(M,Tl)/kosc(M,Tz)should be quite accurate. Since F," is independent of M, eq XIV-XVII allow us to obtain an expression which relates Fc and ko values for different bath gases at temperature T:
The temperature dependence of Pc is given by the relationship (XXIV) where (AE)is the average net energy removed per collision. Since ( A E ) can be taken to be temperature independent, knowledge of @, for a certain buffer gas at one temperature allows calculation of @, for that particular buffer gas at all temperatures. We have determined the parameters ko(M,T), k,(T), and Fcwc([M],T) by nonlinear least-squares curve fitting of our data to eq 11, subject to the constraints that k,(T) must be the same for all buffer gases and that eq XIV, XV, and XXII must be obeyed. Calculated values for kOSC(M,T) and ZLJ(M,T) (Table IV) were used to apply eq XIV and XXII. Initially, SK- Seff was treated as an adjustable parameteq. We found that the data were best fit with SK- Serf 2.5. Based on these results we decided to fix SK- Serfat a value of 2.0; this choice is within the "normal" ~
~~~~
~~~
(28) F. M. Mourits and F. H. A. Rummens, Can. J . Chem., 55, 3007 (1977). (29) R. A. Svehla, NASA Technical Report R-132, Cleveland, OH, 1962. (30) H. Hippler, J. Troe, and H. J. Wendelken, J. Chem. Phys., 78, 6709 (1983).
Kinetics of the Reaction O H
+ SOz + M
-
HOS02 + M
The Journal of Physical Chemistry, Vol. 88, No. 10, 1984 2101
TABLE V: Falloff Parameters Derived by Fitting the Experimental Data to Eq I1 under the Assumption That SK - Seff= 2.0 (See Text)‘ 1Oi2k,, cm3 iO”k,, cm6 molecule-’ s-l Fc( 5 Fc scF,wc) molecule-’ s-’ Pc T, K
M
A
B
C
A
B
C
C
A
B
C
260
AI SF,
0.0591 0.307
0.0590 0.331
0.0600 0.330
0.439 0.553
0.439 0.559
0.439 0.558
2.37 14.0
2.37 15.1
2.40 15.1
1.59
1.53
1.38
300
He Ar N, SF,
0.0296 0.0481 0.142 0.281
0.0304 0.0515 0.147 0.301
0.0319 0.0523 0.153 0.300
0.366 0.392 0.456 0.501
0.367 0.395 0.458 0.506
0.370 0.397 0.461 0.506
1.46 1.53 5.16 10.1
1.50 1.64 5.36 10.8
1.56 1.66 5.57 10.8
1.35
1.27
1.38
360
Ar SF,
0.0357 0.283
0.0431 0.264
0.0438 0.264
0.336 0.449
0.345 0.445
0.346 0.445
0.840 7.50
1.02 7.02
1.03 7.00
1.19
1.15
1.38
420
Ar
0.0374
0.0369
0.0375
0.300
0.300
0.300
0.667
0.658
0.668
1.36
1.58
1.38
A
B
5.54 4.71 4.69 0.234 0.398 0.389 0.388 0.235 0.277 SI;, a A: Results constrained to obey eq XIV, XV, and XXIII. B: Same as A but with the added constraint that eq XXIV must by obeyed. C: Same as B but with the added constraint that k , be independent of’ T.
OH
x
-
+ SO, + Ar
0
17
range 1 < SK- Seff< 2 and is close to the values obtained by allowing SK- Serfto be an independent variable. The results obtained with SK- Sefffixed at 2.0 and the above constraints applied are given in section A of Table V. A small negative activation energy for k , is suggested although a temperatureindependent k , would be within the overall uncertainties of the calculation. The temperature dependences of (?,(Ar) and (?,(SF,) are not consistent with eq XXIV. Hence, an additional set of calculations was performed with the added constraint that eq XXIV be obeyed; the results are summarized in section B of Table V. Comparison of sections A and B of Table V shows only small differences in k,(M,T) and k , ( T ) values for T I 360 K but significant differences in the 420 K values. The higher value for k,(420 K) obtained with the temperature dependence of (?, constrained supports the contention that k , is temperature independent. The results shown in section C of Table V were obtained with p, values constrained to obey eq XXIV and k , constrained to be temperature independent. Because the falloff parameters in section C of Table V were obtained subject to the largest number of constraints, these parameters yield the poorest fit to the experimental data (of the three sets). Even these most constrained fits reproduce the data reasonably well considering the combined uncertainties of the measurements and the calculations. Falloff curves calculated from the parameters in Table V, sections A and C, are compared with experimental rate coefficients in Figures 5-7. Systematic errors in the low- and high-pressure limiting rate coefficients in Table V may result not only from errors in the experiments but also from the fact that neither SK- Sennor Eo is well-known. To examine the potential magnitude of uncer-
19
log CArl (molecules per
log [ M I (molecules Der cm3)
~i~~~~ 5. Falloff for M = H~ and N2 at 3oo K. solid lines are lines are calculated from the parameters in Table v, section c. calculated from the parameters in Table V, section A. The low-pressure limiting rate coefficknts, k,[M], and high-pressure limiting rate coefficients, k,, are also shown.
ia
20
Cm3)
Figure 6. Falloff curves for M = Ar at T = 260, 300 and 360 K. Solid lines are calculated from the parameters in Table V, section C. Dotted lines are calculated from the parameters in Table section A. 3‘
-141
17
. / . . ..,,
I
I
I
18
19
20
log [MI (molecules per cm3)
Figure 7. Falloff curves for M = SF, at T = 260, 300, 360, 420 K, and M = Ar at T = 420 K. Solid lines are calculated from the parameters in Table V, section C. Dotted lines are calculated from the parameters in Table V, section A.
tainties in derived ko and k , values, we performed additional calculations where the 260 and 420 K data were fit by using SK - Seffvalues of 1.5 and 2.5 with E, fixed at 36 kcal/mol, and by fixed at 2.0. The using Eo = 32 and 40 kcal/mol with SK- Seff results of these “sensitivity analyses”, which are summarized in and Table VI, lead us to conclude that uncertainties in SK- Seff E , lead to no more than 3~25%uncertainties in ko and k,. Furthermore, the ratio k o / k , is very insensitive to the choice of SK- Seffand Eo, since both ko and k , increase with increasing SK- S,ffand/or Eo. It is worth noting that the principal effect
2102
The Journal of Physical Chemistry, Vol. 88, No. 10, 1984
TABLE VI: Sensitivity of the Derived Falloff Parameters t o the Choice of SK - Seffand Eoa S K - Seff = 2.0
E o = 36 S K - Seff = SK - Seff =
T, K 260
hl parameter Ar
pc FP
420
Ar
Pc F C
k0 k, sF6
PC F C
k0 k,
E , = 32 E , = 40
1.5
2.5
0.0516 0.431 2.07 1.46 0.257 0.539 11.7 1.46
0.0686 0.448 2.75 1.73 0.371 0.567 16.9 1.73
0.117 0.485 2.16 1.52 0.598 0.609 12.5 1.52
0.0313 0.400 2.60 1.64 0.166 0.505 15.7 1.64
0.0327 0.295 0.583 1.24 0.228 0.387 4.57 1.24
0.0434 0.307 0.774 1.46 0.340 0.409 6.81 1.46
0.0763 0.335 0.620 1.25 0.565 0.443 5.16 1.25
0.0196 0.272 0.716 1.46 0.144 0.360 5.93 1.46
a F , f FcscFcwc. Units for k , are cm6 molecule-' s-' ; units f o r k , are lo-'* em3 molecule-' s - ' ; units for E o are kcalimol.
of varying Eo is to change the calculated value of kgSC. Hence P,, which is derived by comparing a best fit ko with a calculated kGC, is very sensitive to the choice of E,. The @,(SF,) values in Table VI are unusually high when Eo is taken to be 32 kcal/mol and unusually low when Eo is taken to be 40 kcal/mol. Of course, calculated ko% are very sensitive not only to the choice of Eo but also to the choice of entropies and enthalpies used in calculating Kq. For this reason, one cannot assume that the correct value for Eo is the one which leads to the most reasonable values for PC.
The results in Table V indicate that in the high-pressure limit the activation energy for reaction 1 is less than or equal to zero. This finding seems to preclude the possibility that a significant barrier exists in the OH-SO2 reaction coordinate. Since SO, is not a free radical, the possibility that such a barrier exists should be considered. Application of the Troe formalism is only appropriate when the association process occurs on a purely attractive potential energy surface. Comparison with Previous Investigations. Bimolecular rate coefficients determined in this investigation are compared with those reported by other investigators in Table VII. Our results tend to be somewhat lower than those reported in most other studies. In the experiments of Atkinson et al.3 and Harris et al.,5 O H was produced by unfiltered flash photolysis of H 2 0 at wavelengths longer than 104 (LiF window) and 125 nm (CaF window), respectively. In the wavelength region between 104 nm and the Suprasil cutoff at 165 nm, SO, absorbs considerably more strongly than H20.13320Hence, we would expect the complications encountered in our experiments to have been even more severe in the experiments of Atkinson et al. and Harris et al. These authors report the observation of a long-lived chemiluminescence signal, the effect of which they minimized by working only at relatively high pressures, low SO2 concentrations, and limiting their measurements to conditions where OH decays were exponential for at least two half-lives. It is quite likely, however, that reactions of O H with SOz photofragments (Le., 0 and SO) contributed significantly to their observed temporal profiles. Davis et aL4in their study of reaction 1 also produced O H by unfiltered flash photolysis of H,O; the photolysis wavelength cutoff in their experiments was 165 Two disturbing aspects of Davis et al.'s study are the fact that these authors do not report observation of chemiluminescence and that all their experiments were carried out with such low SO2concentrations that the rate of loss of O H
Wine et al. TABLE VII: Summary of Reported Bimolecular Rate Coefficients Coefficients for the Reaction OH + SO, + M -+ HOSO, + M at Total Pressures Greater Than 10 torr T, K
M
10-''[?], cm-
1oi4kbi,cm3 molecule-' s''
ref
260
Ar 5.0-160 FP-RF* this work 8.2 1-5 4.6 SF, 5.0-160 . 29.6-124 6.5-324 297 N, 9.0-109 SSPc 8,9 297 air 246 72 SSPd 10 297 N' 17.8-245 23-95 FP-RAb 6 SF6 32.4 50 29 8 Ar 8.20-2 10 13.5-65.5 FP-RF 3 298 He 16.2-1 62 9.2-26.7 FP-RF 4 Ar 7.8-37.1 6.48-162 3.24-6.48 14.1-21.6 N, 29 8 Ar 211 64.9 FP-RF 5 SI;, 31.8-208 57.0-161 5.0-160 300 He 4.67-34.0 FP-RF this work 5.0-160 AI 4.91-33.9 5 .O-40 11.3-4 1.7 N' SI', 5.0-160 19.2-100 300 air 245 87 SSPC 7 177 32.2 354 Ar FP-RF 5 36.1, 103 SF, 27.3, 178 5.0-160 360 Ar 2.79-18.5 FP-RFb this work 5.0-160 SF, 12.9-74.5 420 Ar 2.26-15.8 5 .O-160 FP-RFb this work 5 .O-160 SF, 10.7-71.6 424 Ar 92.0, 149 16.2, 19.8 FP-RF 5 SF6 22.8-148 25.4-76.1 435 H, 0 169 179 PR-RA 11 a FP = flash photolysis, SSP = steady-state photolysis, PR = pulsed radiolysis, RF = resonance fluorescence, RA = resonance absorption. Photoflash filtered with SO,. Referenced to the reaction OH - CO -+ products. Data corrected to take into account pressure dependence of reference reaction. Referenced to k = 8.0 X cm3 molecule" s-l for the reaction OH + C,H, -+products.
by diffusion from the detector field of view was probably as large as or even larger than the rate of loss due to reaction with OH. Use of low SO, concentrations helps to reduce complications from chemiluminescence and side reactions involving SO2 photofragments but also significantly reduces the accuracy of the rate coefficient determination. Paraskevopoulos et a1.,6 in their flash photolysis study, produced O H by the following reaction sequence
+ N2 OH + H
N 2 0 -k O(lD) O(lD)
+ H2
-
(14)
These authors filtered their photoflash with 2.5 torr cm of SO, to reduce complications from photofragment side reactions and, since they monitored OH by resonance absorption, background chemiluminescence did not interfere with O H detection. Reaction 14 produces vibrationally excited OH which, if relaxation into the (detected) ground vibrational level occurred in competition with reaction 1, could result in measurement of erroneously low values of k l . However, since our results agree very well with those of Paraskevopoulos et al., we conclude that this potential problem did not influence their results. Our extrapolated value of 8.0 X cm3 molecule-' s-l for k , (760 torr, 300 K, N,) is in reasonably good agreement with the competitive kinetics results of Cox,' Cox and Sheppard,Io and Castleman and Tang9 although quantitative comparison with two of these s t ~ d i e sis~difficult ~'~ since the rate coefficient for the O H CO reference reaction at 760 torr of N2is still somewhat uncertain. The rate coefficients from ref 8 and 9 in Table VI1 were derived from the following expression for the O H CO N2pressure dependence at 298 K?
+
+
k(OH+CO+N,) = (31) G. Herzberg, "Molecular Spectra and Molecular Structure", Van Nostrand-Reinhold, New York: 1950, Vol. I, 2nd ed; 1945, Vol. 11. (32) S. Fischer, private communication.
exptl techniquea
+
6.15 X 4.1
+ 5.65 X 10-l6P + 9.2 X 10-4P
(33) G. Paraskevopoulos and R. S. Irwin, J . Chem. Phys., 80,259 (1984).
Kinetics of the Reaction OH
+ SO2 + M
-
HOS02
+M
The Journal of Physical Chemistry, Vol. 88, No. 10, 1984 2103
TABLE VIII: Falloff Parameters Derived by Fitting the Experimental Data t o Eq XXV under the Assumption That SK - Seff= 2.0' 0.0565 0.340
0.438 0.556
2.27 15.5
1.49
SI;, 300
He Ar N, SF,
0.0301 0.0493 0.160 0.309
0.367 0.393 0.463 0.508
1.49 1.57 5.80 11.1
1.18
360
Ar SF,
0.0412 0.272
0.343 0.447
0.971 7.22
1.04
420
Ar SF,
0.0352 0.242
0.298 0.390
0.628 4.84
1.29
260
Ar
'The results are constrained t o obey eq XIV, XV, XVIII, and XXIV. Units for k , are cm6 molecule-* s-' ;units f o r k , are l o - ' * cm3 molecule-' s-l. where k is in units of cm3 molecule-' s-' and P is in units of torr. The results of discharge flow studies at pressures less than 1 0 torr are not reported in Table VI1 because bimolecular rate coefficients measured in these studies may contain contributions from wall reactions and reaction 1 with two or three different third bodies including the reactant SO2. Both discharge flow studies',2 obtained a linear kl vs. [MI dependence, from which it was concluded that reaction 1 was in the low-pressure third-order limit. However, the falloff curves calculated with our best-fit parameters (Table V) suggest that, in the pressure regime of the discharge flow studies, reaction 1 is not in the strictly third-order regime. The discharge flow study of Leu2 is one of the two most extensive to date, the other being the present study. Under the assumption that reaction 1 is third order under his experimental conditions, Leu reports 298 K values for ko(He), ko(Ar), and ko(N2)of 8.45 X 1.09 X and 2.54 X cm6 molecule-2 s-', respectively. These values are somewhat lower than our extrapolated ko values at 300 K (Table V). In Figure 8 we have reproduced the number of data points and [MI for each data point from Leu's experiments and plotted kl vs. [MI using rate coefficients calculated from the falloff parameters in Table V, section A. The solid lines are obtained from linear least-squares analyses of these data while the dashed lines represent ko[M]. It is interesting to note that even with no experimental scatter in the plotted data, it is difficult to observe a deviation from linearity. Only the nonzero intercepts provide an indication that the low-pressure limit has not been reached. The least-squares slopes give "apparent" third-order rate coefficients in units of cm6 molecule-2 s-' of 8.81 X for He, 1.06 X for Ar, and 3.16 X for N,. These results agree extremely well with Leu's results. Harris and Wayne' have studied reaction 1 in a discharge flow system at 298 K and total pressures of 1-4 torr. They obtain apparent thirdcm6 molecule-2 s-' for M order rate coefficients of 4.5 X
2-
0
1
2
[MI (10" molecules per cm3)
Figure 8. Reproduction of the low-pressure experiments of Leu (ref 2) for M = He, Ar, and N, at 298 K. Each small circle represents one data point. Number of data points and [MI for each data point is the same as in Leu's experiments. Rate coefficients are calculated from the 300 K falloff parameters given in Table V, section A. Solid lines are obtained from linear least-squares analysis and yield the apparent third-order rate coefficients given in the figure (units are cm6 molecule-2 S-]). Dashed lines represent the low-pressure limiting rate coefficients k,[M] obtained from ko values taken from Table V, section A. The number inside each data point represents the number of experiments carried out by Leu at that concentration and the weighting factor used in the least-squares analysis.
= Ar and 7.2 X cm6 molecule-' s-I for M = N2. These rate coefficients are much too large to be consistent with either our data or Leu's data. Application to Atmospheric Chemistry. For purposes of atmospheric modeling, the following approximate form of eq I1 is employed to describe the temperature and pressure dependence
TABLE IX: Recommended Falloff Parameters for Use in Atmospheric Modeling A. Recommended P a r a m e t e d NASA panel18 CODATA this work (constant F,) this work (T dependent F,)
Fc
k , (300 K)
n
k,(300 K )
0.6 0.55 0.525 exp(-T/3 88)
3.0 i. 1.5 3.0 ?r 1.5 4.5 1.0 5.8 k 1.3
3.4 k 1.5 2.9 1.0 3.9 i: 1.0 2.6 f 0.8
2.0 f 1.5 2.5 i: 1.3 1.26 k 0.30 1.26 ~t0.30
*
*
M
O f 1.0 0 0.7 0.7
f ?
0.7 0.7
B. Rate Coefficients Calculated from above Parameters*
300 K 100 torr NASA panel CODAT panel this workC
200 K 760 torr
100 torr
760 torr
4.09 10.7 9.73 15.9 4.18 11.4 9.35 18.1 3.55 8.03 9.67 13.9 ' Units for k , are cm6 molecule-2 s'l ;units for k , are cm3 molecule-' s-'. Units are cm3 molecule-' s-l. Rate coefficients are the average of those obtained from the two sets of parameters given above. Rate coefficients calculated from the two different sets of parameters agree to within 1%over the entire range o f atmospheric temperature and pressure.
J . Phys. Chem. 1984, 88, 2104-2109
2104
of the bimolecular rate constant for addition reaction^:'^^^^ k ( [ M ] , T )= k-(T) FLH([Ml,T) F C ( [ M ] , T ) ~( x x v ) where
z=
[l
+ (log K)2]-’
(XXVI)
and F,([Ml,T) = F,Sc(T)FcwC([M1,T)
(XXVII)
In applying eq XXV to atmospheric reactions, M is taken to be N 2 or air (0, is typically indistinguishable from N 2 as a third body). The temperature dependence of ko and k , are described by the relationships ko(T) = ko(300 K)(T/300)+‘
(XXVIII)
k , ( T ) = k(300 K)(T/300)-”
(XXIX)
Both the NASA18 and CODATA34panels currently recommend expressions in which F, is assumed to be constant over the temperature range 200-300 K. However, the next CODATA compilation will give Fc(T) in the following form:35 F,(T) = exp(-T/constant)
( X W
Employing procedures identical with those described above but using eq XXV instead of eq 11, we obtain the falloff parameters given in Table VIII; these parameters were determined by using the set of constraints employed to obtain the results in section B of Table V. The k , values at 260, 300, and 360 K are best fit by taking m = 1.1. However, if the k,(420 K) value is included, the data are best fit by taking m = 0.3. We have assigned a half-weighting to the 420 K result and, from a linear least-squares analysis of the log T vs. log k , data, obtain the expression k,( T ) (34) D. L. Baulch, R. A. Cox, P. J. Crutzen, R. F. Hampson, Jr., J. A. Kerr, J. Troe, and R. T. Watson, J . Phys. Chem. Ref. Data, 11, 327 (1982). (35) J. Troe, private communcation.
= 1.26 X 10-’2(T/300)4,7cm3 molecule-1 s-I; the uncertainty in the parameter rn is estimated to be f100%. Using the falloff parameters for N2 at 300 K (Table VIII) in conjunction with eq XIV, XV, and XXIV, we have calculated F,([N,],T) and k0(N2,T) over the temperature range 200-300 K. Least-squares analyses of the results give the following “best fit” expressions: F,([N,],T) = exp(-T/388) and k,(N,,T) = 5.76 X 10-31(T/300)-257cm6 molecule-2 s-’. At 250 K, the center of the atmospheric temperature regime, we obtain Fc([N2],250K) = 0.525. Using this value over the entire 200-300K range and adjusting k,(N,,T) to give the same bimolecular rate coefficients as were obtained when the temperature dependence of F, was taken into account, we obtain ko(N2,T,constantF,) = 4.49 T/300)-3.85. Our suggested falloff parameters for use in atmospheric modeling are summarized and compared with currently parameters in Table IX. Rate coefficients calculated from our parameters are lower than currently recommended values, particularly at high pressure (Le,, 760 torr). It should be emphasized that the parameters in Table IX do not represent best estimates for ko and k,. They are simply parameters which facilitate computation of kl(P,T) for use in atmospheric modeling. Acknowledgment. We thank Dr. G. Paraskevopoulos for communicating to us his results on the OH SO, N2 and OH CO N2 reactions prior to publication. A.R.R. thanks Professor J. Troe for his hospitality during A.R.R.’s stay at Professor Troe’s laboratory and for helpful discussions concerning the falloff curve calculations. This work was supported by the National Science Foundation through Grants ATM-80-10940 and ATM82- 17232. The strong collision calculations were supported by the Deutsch Forschungsgemeinschaft (SFB 93 “Photochemie mit Lasern”). Registry No. OH,3352-57-6; SO2, 7446-09-5.
+
+
+
+
Supplementary Material Available: Table containing the experimental conditions employed to measure each pseudofirst-order rate coefficient (20 pages). Ordering information is available on any current masthead page.
CHF(%‘A’) Radical Kinetics. 2. Reaction with 0 and N Atoms Graham Hancock,* Graham W. Ketley, and Alexander J. MacRobert Physical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ U.K. (Received: July 27, 1983)
Ground-state CHF radicals, formed in the gas phase by infrared multiple photon dissociation and detected by laser-induced fluorescence, react with ground-state 0 and N atoms with bimolecular rate constants of (1.5 f 0.2) X cm3molecule-’ s-I and (2.5 A 0.5) X 10-l’ cm3 molecule-’ s-l, respectively, at 295 K. In the 0 + CHF reaction, vacuum-UV emission is observed and attributed to the CO(A’II) state, which is formed by energy transfer in collisions between 0 atoms and a precursor state produced directly by the 0 + CHF reaction. The identity of this state is thought to be either CO(a311)or CO(X’P), both in high vibrational levels. In the N + CHF reaction, luminescence from CN(B2Zf) is observed, with kinetics indicating that it is formed by energy transfer in collisions between N atoms and a precursor state of CN formed directly by N + CHF, with the identity of the precursor either metastable CN a 4Z+or, less favorably, the X2Z+ and A211istates.
Introduction In recent years a number of triatomic carbene radicals (of the form CXY, where X and Y are hydrogen or halogen atoms) have been shown to undergo laser-induced fluorescence (LIF) in the gas phase, and this sensitive and highly selective detection technique has been used to investigate the kinetic behavior of several of these species. Three methods of radical formation have been used in these studies, namely flow discharge techniques,l excimer (1) Meunier, H.; Purdy, J. R.; Thrush, B. A. J . Chem. SOC.,Faraday Trans. 2 1980, 76, 1304.
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laser photolysis,2 and infrared laser-induced multiple photon dissociation (MPD).3-6 The combination of MPD production and LIF detection methods has proved to be a particularly useful (2) Tiee, J. J.; Wampler, F. B.; Rice Jr., W. W. Chem. Phys. Lett. 1980, 73, 519. ( 3 ) Bialkowski, S.E.; Guillory, W. A. J. Phys. Chem. 1982, 86, 2007. (4) Ashfold, M. N. R.; Hancock, G.; Ketley, G. W.; Minshull-Beech, J. P. J . Photochem. 1980, 12, 15. (5) Ashfold, M.N. R.; Fullstone, M. A,; Hancock, G.; Ketley, G. W. Chem. Phys. 1981, 55, 245. (6) Hancock, G.; Ketley, G. W. J. Chem. SOC.,Faraday Trans. 2 1982, 78. 1283.
0 1984 American Chemical Society
