The Journal of Physical Chemistty, Vol. 83, No.
Flash Photolysis-Resonance Fluorescence Kinetics
25, 1979 3191
(19) R. F. Hampton, Jr., and D. Gamin, Natl. Bur. Stand., Spec. Pub/., No. 513 (1978). (20) H. Nikl, P. D. Maker, L. P. Breitenbach, and C. M. Savage, Chem. Phys. Lett., 57, 596 (1978); J. V. Michael, D.S. Nava, W. A. Payne, and L. J. Stief, J. Chem. Phys., 70, 1147 (1979). (21) S.W. Benson, "Thermochemical Kinetics", 2nd ed,Wlley, New Y d k , 1976. (22) J. M. Heuss and W. A. Glasson, Environ. Sci. Techno/.,2 , 1109 (1968). (23) W. E. Wilson, Jr., A. Levy, and E. H. McDonald, Envkon. Sci. Techno/., 6, 423 (1972). (24) A. P. Altshuller, J. Air Pollut. Confro/ Assoc., 28, 594 (1978).
(13) J. P. Reilly, J. H. Clark, C. 8. Moore, and G. C. Pimentel, J. Chem. Phys., 69, 4381 (1978). (14) K. Shibuya, T. Ebata, K. Obi, and I. Tanaka, J. Phys. Chem., 81, 2292 (1977). (15) F. Su, J. 0.Calvert, C. R. Lindley, W. M. Uselman, and J. H. Shaw, J. Phys. Chem., 83, 912 (1979). (16) W. M. Uselman, S.2. Levine, W. H. Chan, J. G. Calvert, and J. H. Shaw, "Nitrogenous Air Pollutants", D.Grosjean, Ed., Ann Arbor Science, Ann Arbor, Mich., 1979, Chapter 2, p 17. (17) J. Chao and B. J. Zwdinski, J. phys. Chem. Ref. Data, 7,363 (1978). (18) E. C. A. Horner, D.W. G. Style, and D. Summers, Trans. Faraday SOC.,50, 1201 (1954).
-
Flash Photolysis-Resonance Fluorescence Kinetics Study of the Reaction OH 4- NOp M HNOB 4- M P. H. Wine,*
+
N. M. Kreutter, and A. R. Ravlshankara"
Molecukrr Sciences Group, Engineering Experiment Station, Georgia Institute of Technology, Atlanta, Georgk 30332 (Received July 18, 1979) Publication costs assisted by the National Science Foundation
-
The flash photolysis-resonance fluorescence technique has been employed to study the kinetics of the combination reaction OH + NO2 + M HNOB+ M. A total of 57 bimolecular rate constants are reported for varying conditions of temperature (247-352 K), pressure (14-700 torr), and diluent gas identity (He, Ar, N2,SF6). These new rate data are compared with previous measurements, and their significance to atmospheric chemistry and unimolecular rate theory is discussed.
Introduction The kinetics of the reaction OH + NO2 + M - "03 +M (1) has been the subject of extensive investigation in recent years. This interest has been stimulated by the importance of reaction 1 as a sink for reactive HO, and NO, species in the atmosphere. Also, because reaction 1 is in the "fall-off" region between third- and second-order kinetics over the range of total pressures typically accessible to laboratory studies, it is of considerable interest as a test for theories of unimolecular decomposition-recombination reaction rate^.^-^ Most direct measurements of kl have been carried out in discharge-flow systems at total pressures of less than 10 t ~ r r . ~ Measurements -l~ at higher pressures have been reported by Smith and co-workers13-15 using the flash photolysis-resonance absorption technique and by Atkinson et a1.16 using the flash photolysis-resonance fluorescence technique. Because N2 quenches electronically excited OH very efficiently, the flash photolysisresonance fluorescence study could not obtain data under conditions which are directly applicable to atmospheric chemistry. Therefore, the choice of kl for input into atmospheric models relies heavily on results from a single laboratory.13-15 The present study was undertaken to reduce the uncertainty in kl under atmospheric conditions and also to broaden the available data base for testing unimolecular reaction rate theories. Bimolecular rate constants are reported for a wide range of temperatures (247-352 K), pressures (14-700 torr), and diluent gases (He, Ar, NS, SF6). Of particular interest is the fact that measurements have been carried out using resonance fluorescence detection of OH at nitrogen pressures up to 225 torr. The improvements in OH detection sensitivity which allowed these measurements to be made are discussed. 0022-365417912083-319 1$01.OO/O
Experimental Section The apparatus used in this study has been described previo~sly.~'J~ Hence, we will describe the system briefly and elaborate only on new modifications. An all-Pyrex jacketed reaction cell with an internal volume of -150 cm3was used in all experiments. The cell was maintained at a known constant temperature by circulating either methanol (247-297 K) or ethylene glycol (297-352 K) from a thermostated bath through the outer jacket. OH radicals were produced by the flash photolysis of H 2 0 at wavelengths between the onset of absorption at 185 nm and the Suprasil cutoff at -165 nm. An OH resonance lamp situated perpendicular to the flash lamp excited resonance fluorescence in the 0-4band of the A%+ - X2asystem; this fluorescencewas detected perpendicular to both the flash lamp and resonance lamp by a hotomultiplier fitted with an interference filter (3095- peak transmission, 100-A 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 three l / e times. In order to avoid the accumulation of photolysis or reaction products, all experiments were carried out under "slow-flow" conditions.18 NO2was flowed from a 12-L bulb containing a dilute N02/diluent mixture; in all cases, the fraction of NO2 which existed as N2O4 in the storage bulb was negligible. The water mixture was generated by bubbling diluent gas through distilled water at room temperature and a pressure of 800 torr. The NOP mixture, water mixture, and additional diluent 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 fraction of NO2 in the N02/diluent mixture was checked frequently by simultaneous mea-
K
@ 1979 American Chemical Society
3192
The Journal of Physical Chemistry, Vol. 83, No. 25, 1979
Wine, Kreutter, and Ravishankara
the use of focusing optics, the reaction volume defined by the region where the resonance lamp radiation and flash lamp radiation intersected was moderately large (-1.5 cm3). Sensitivity of the Apparatus. To determine the sensitivity of the apparatus, we carried out back to back experiments where the signal/noise per flash was determined under typical experimental conditions (flash energy = 60 J, 130 mtorr of H20, 100 torr of He) and compared with the signal/noise per flash obtained under conditions where a known OH concentration could be produced. The procedure used to generate a known concentration of OH involved replacing the flash lamp with a frequency-quadrupled Nd:YAG laser and adding 3 mtorr of O3 to the reaction mixture. Then OH could be produced by the reaction sequence Flgure 1. Schematic of the reaction cell, flash lamp, resonance lamp, and detector geometries. For clarity the flash lamp and resonance lamp are pictured at 180' to each other whereas in reality they were situated at 90'. BPF, bandpass filter (3095-A peak transmission, 100-A FWHM); F, 7-54 filter; FL, flash lamp; L1, L2, 1.541 focal length Suprasil lenses; L3, 4-in. focal length Suprasil lens; PM, photomultiplier; RC, reaction cell; RCOJ, reaction cell outer jacket; RMI, reaction mixture inlet; RMO, reaction mixture outlet; VH, vacuum housing; W, Suprasil window.
surement of the total pressure (of the mixture) and the NO2 absorption at 365 nm. The measurement was carried out by using a mercury pen-ray lamp as the light source, a 60.5-cm absorption cell, and a bandpass filter-photomultiplier detector. Two strong closely spaced mercury lines were transmitted by the bandpass filter (365.02 and 365.48 nm). The absorption cross section used to determine the NO2 concentration was 5.75 X cm2. This cross section represents an average of our measured value and the literature values at the wavelengths of the two atomic lines;lg we estimate that it is accurate to within i3%. The gases used in this study were obtained from Matheson and had the following stated purities: He 299.9999%, h 199.9995%, N2 299.9995%, SF6 299.99%, NO2 199.5%. Trace quantities of NO in the NOz were converted to NOz by reaction with ultrahigh-purity oxygen. NO2 was then degassed several times at 77 K; each time, the initial fraction to vaporize as the sample was warmed from 77 K was pumped away, thus ensuring complete removal of NO and 02.He, Ar, N2,and SF6 were used as supplied. Because it was desirable to carry out measurements at high N2 pressures where (due to collisional quenching of the fluorescent A22+ state) the OH fluorescence yield is very low, we spent considerable time experimenting with focusing optics and various baffle arrangements in an effort to improve the sensitivity of the apparatus. The arrangement which was adopted is shown in Figure 1. Both the resonance lamp radiation and the flash lamp radiation were weakly focused into the reaction cell. In the case of the resonance lamp, this simultaneously reduced the scattered light background and increased the fluorescence signal. The advantages of focusing the flash lamp radiation were to prevent excitation of long-lived fluorescence from the Pyrex walls of the reaction cell and to allow experiments to be run at lower flash energies where problems associated with deposition of sputtered material on optics were minimized. A third lens was employed to collect the resonance fluorescence and focus it onto the photocathode of the detector. Use of this lens resulted in a large increase in both fluorescence signal and scattered light with a significant improvement in the signal to noise ratio. Despite
O(lD) + H2O
20H
(3) The laser beam was expanded so its cross-sectional area as it traversed the reaction cell was approximately equal to that of the flash lamp radiation. The laser power was measured at the rear of the cell with an EG&G radiometer and corrected for the loss due to reflection by the back window (-10%). Since the absorption cross section for O3 at 266 nm is known,z0we could determine an upper limit for [OH] by assuming an O(lD) yield of 1 from reaction 2 and an OH yield of 2 from reaction 3. Neither of these assumptions is expected to result in overestimation of [OH] by more than 5-10% The assumption that all O(lD) reacts with H 2 0 is also expected to result in negligible error, since reaction 3 proceeds at a near-gaskinetic ratez1 while the rate constant for quenching of O(lD) by He is 11.5 X cm3/(molecules s).~~ The results of the actinometry experiment indicate that, for the reaction mixture employed, 5 X lo9 OH per cm3 could be detected (signal/noise = 1)with an integration time of 1 X s. Extrapolation of this result to other experimental conditions shows that most experiments were carried out with OH concentrations between 5 X 1O'O and 1 X 10" per cm3and that the maximum OH concentration employed in any experiment was 3 X loll per cm3, Kinetic Scheme. The following reactions must be considered in order to properly interpret kinetic data obtained from flash photolysis of H 2 0 / N 0 2mixtures: +
.21g22
hv 165 nm < X > 250 nm'
H + NO2
+
O(lD) + NO
OH + NO
O(3P) + NOz
-
2N0
(5b) (6) (7)
O('D) + HzO ---+ 20H (8) OH(v > 0) + M OH(u = 0) + M (9) OH NOz + M H N 0 3 + M (1) OH NO + M + H N O ~+ M (10) OH loss by diffusion out of field of view of detector (11) All OH production mechanisms except reaction 6 are fast enough to be considered instantaneous on the time scale for OH decay.24 The minimum value of k6/kl en-
-.
+
-
+ +
The Journal of Physical Chemistry, Vol. 83, No. 25, 1979 3193
Flash Photolysis-Resonance Fluorescence Kinetics
I
-:. (C)
"
lo
10
TIME
15
'
i
(FSEC)
Figure 2. Typical OH temporal profiles observed following flash photolysis of H,O/NO,/diluent mixtures. Experimental conditions: T = 297 K; P = 293 torr; diluent = SF,; flash energy = 61 J; [H20] = 4.4X IOl5 molecules/cm3. (A) [NO,] = 0; (B) [NO2] = 1.57 X 1013 molecules/cm3; (C) [NO,] = 3.40 X IOi3molecules/cm3.
countered in our experiments was 5 (under conditions of low temperature and high SF6 concentration). Model calculations showed that even in this extreme case, the OH temporal profile was unaffected by the presence of the relatively slow formation process except during the first 35% of the decay; this initial part of the decay was ignored in the data analysis. Modeling calculations indicated that photochemical conversion of NO2 to NO and/or biradical reactions such as OH OH and OH + O(3P)would not influence the OH decay kinetics under our experimental conditions. To verify this experimentally, factor-of-four variations in the flash energy and the water concentration were carried out for a variety of reaction mixtures and at all three temperatures investigated. Variation of the water concentration by a factor of four at constant flash energy results in a factor of four increase in the initial OH concentration and also an increase in the amount of NO2 converted to NO, the magnitude of which depends upon the importance of reaction 6 relative to reactions 5 and 7 as an NO production mechanism. Variation of the flash energy by a factor of four at constant water concentration results in a factor of four increase in the initial OH concentration and a similar increase in the amount of NO2 photochemically converted to NO. Measured rate constants were found to be independent of variations in both flash energy and water concentration, thus establishing that the prediction of the modeling calculations was correct. Other potential kinetic complications involve buildup (with successive flashes) of reaction products which could react with OH and/or loss of NOz by heterogeneous processes. Experimentally, we found that kl was invariant to large changes in the linear flow rate through the cell (0.3-6 cm/s; flash repetition rate -0.6 Hz), thus establishing that these potential complications were unimportant. All experiments were carried out under pseudo-firstorder conditions with [NO,] >> [OH]. As discussed above, experimental conditions were established where the decay of OH with time followingthe photoflash was due entirely to reactions 1and 11. Therefore, the OH temporal profile was expected to obey first-order kinetics In {[OHlo/[OH],) = (kl[NOz] + k l J t = k't (12) where k l is the bimolecular rate constant for a particular diluent gas at a particular pressure. The linear variation of In [OH] with time predicted by 12 was observed in all
a"0
1
2 tfO2l(1"14 POLEC/CC)
I
3
Figure 3. Typical plots of the pseudo-first-order rate constant vs. [NO,]. Experimental conditions: T = 297 K; diluent = N;, flash energy = 80 J; [H20] = (5-13)X loi5 molecules/cm3. (0) IN2] = 5.4 X (m) [N,] = 16 X (0) [N2] = 29 X loi7, (0) [N2]= 9.5 X ( * ) [N,] = 62 X 10'' molecules/cm3. Solid lines are obtained from linear least-squares analyses. For the sake of clarity data points for [NO,] = 0 are not plotted.
+
I +
c
+
,5t c
c
-
+
Figure 4. Comparison of our results for OH iNO2 -I-N2 HNO, N2 with those of Anastasi and Smith. ( 0 ,A,E) Our results at T = 247,297,and 352 K (0, A,0)their results at T = 238,296,and 358 K.
experiments. Bimolecular rate constants kl were determined from the slopes of k'vs. [NO2] plots. Some typical experimental OH temporal profiles are shown in Figure 2. In Figure 3, plots of pseudo-first-order rate constant vs. NOz concentration obtained at various N2pressures and a temperature of 297 K are shown.
Results and Discussion A total of 57 bimolecular rate constants have been measured under varying conditions of temperature, pressure, and diluent gas. These rate constants are tabulated in Table I. Tables listing the experimental conditions employed to measure each pseudo-first-orderrate constant are too long to present in this paper but are available as supplementary material. (See paragraph at end of text regarding supplementary material.) Under all experimental conditions employed in this study, reaction 1was found to be in the transition region between third- and second-order kinetics. Direct comparison of our results with previous work is possible in the case of Nz diluent at all three temperatures investigated and Ar diluent at T = 297 K. These comparisons are shown in Figures 4 and 5. In Figure 4, our rate constants at 247,297, and 352 K with N2as the third body are compared with those measured by Anastasi and Smith15at 238,296, and 358 K. The agreement is excel-
3194
The Journal of Physical Chemistry, Vol. 83, No. 25, 1979
TABLE I: Rate Constants for t h e Reaction OH t NO, t M Pressure, and Diluent gasa
Wine, Kreutter, and Ravlshankara -+
HNO,
+ M as a Function of Temperature,
lo1%,cm3/(moleculess )
10-"[MI, molecules/cm3
T = 247 K
T = 297 K
T = 352 K
8.52 i: 1.16 11.0 f 1 . 2 18.2 f 1.5 26.4 i 1.4 18.3 f 1.4 27.5 i: 2.0 26.5 + 2.0 34.9 i 3.3 29.8 i 1.9 38.8 i 4.5 60.9 i 4.8 73.0 f 4.2 64.1 i 4.1 82.8 i: 11.4 1281 8 95.2 i 5.7 81.5 f 6.5
4.61 i 0.64 7.17 i 0.54 9.96 i 0.76 18.3 i 1.0 1 1 . 3 i 0.7 1 6 . 2 i 0.9 15.8 f 1.1 24.1 i 1.6 21.3 i 2.2 24.4 F 1.9 34.5 f 2.2 62.0 i 4.2 42.2 i 2.6 47.6 i: 5.4 1 1 4 i 10 58.7 f 4.1 55.5 * 3.4
2 0 3 i 22 1 0 5 f 11
151 k 1 3 79.4 i 7.2
3.41 i 0.20 4.65 f 0.62 6.81 i 0.49 12.2 i 1 . 2 6.55 f 0.39 10.0 i 0.8 11.5 f 0.9 1 5 . 3 k 1.8 15.4 i 1 . 2 16.5 i 1.1 23.3 i. 1.9 54.3 i 4.2 26.6 i. 1.9 29.4 i 4.0 1OOf 8 41.9 i 2.0 46.5 i 5.0 52.6 i 4.0 135 i 14
M
5.4
He Ar
9.5
SF.5 Ar
N? N* Ar N? He
16 29
62
N?
95 140 190
SF.5 Ar He Ar SF.5 Ar
230
a Errors are 20 and include both the precision of the pseudo-first-order rate constant vs. concentration data and the uncertainty in the absolute NO, concentration.
I
1%
t
3@
i
1
c- - #
t 0
'4 1-
- +
t
t
t
'4
4 I
I
I
I , ,
I
P(TORR)
+
+
-
I
1
1
+
Figure 5. Comparison of our results for OH NOp Ar HNO, Ar with those of Atkinson, Perry, and Pitts. (0)Our results at T = 297 K; (0) their results at T = 298 K.
lent. Because the two studies were carried out under very different experimental conditions and, therefore, are not expected to be subject to the same systematic errors, the observed agreement means that the values of kl available for atmospheric modeling must now be considered very reliable. In Figure 5, our rate constants at 297 K with Ar as the third body are compared with those measured by Atkinson et al. at 298 K. The pressure dependences observed in the two studies are nearly identical but our rate constants are consistently 15% higher. Systematic errors in the determination of the NO2 concentration appear to be the most likely explanation for this discrepancy. Photochemical conversion of NO2to NO probably was not a problem in either study, although the experimental conditions employed by Atkinson et ala-low water concentration and photolysis at all wavelengths above the lithium fluoride cutoff (104 nm)-suggest that their resulb are more likely to have been influenced by this problem than are ours. In order to estimate the relative efficiencies (OM) for stabilization of the OH...N02 complex by He, Ar, N2,and SF6and also define the pressure dependence of kl over the broadest possible range, a trial and error procedure was employed where, at each temperature investigated, a set of PM'swere generated which gave the best defined fall-off N
0
+
+
+
Figure 6. Fall-off curve for OH NOp M + HN03 M obtained from all data at T = 297 K. The assumed relatlve efficiencies are PI.le:@A,$N2:&,= 0.45:0.65:1.0:2.6. (0) He diluent; (0)Ar diluent; (0) Np diluent; (*) SF diluent. The dotted lines represent low- and hlghtemperature limlts calculated by Anastasi and Smlth.15 The solid lines represent low- and high-temperature limits calculated by Smith and Goldena4
curve (i.e., PM[M] vs. k1 plot) over the entire range of were found PM[M]. The efficiency ratios PHe:PAr:PNz:PSFs to be 0.35:0.55:1.0:1.7 at 247 K, 0.45:0.65:1.02.6 at 297 K, and 0.45:0.60:1.0:2.9 at 352 K; the estimated uncertainty in these relative efficiencies is f15%. The fall-off curve obtained at 297 K is shown in Figure 6. This curve is constructed from data covering an equivalent N, pressure range of 8-1500 torr. Also shown in Figure 6 are extrapolated high- and low-pressurelimiting rate constants calculated by Anastasi and Smith15using the Kassel integral method of TroeZ5and by Smith and Golden4assuming a Gorin transition state26with hindered fragment rotations. Both calculations used the highpressure data of Anastasi and Smith15(which is in excellent agreement with our data) to evaluate adjustable parameters while the Smith and Golden calculations also used the low-pressuredata of Howard and Evensonloand Anderson, Margitan, and K a ~ f m a n Our . ~ results do not allow us to verify the validity of either low-pressure extrapolation. However, the limiting high-pressure rate constant (k,) of 1.6 X cm3/(moleculess) extrapolated by Anastasi and
The Journal of Physical Chemistty, Vol. 83, No. 25, 1979 3195
Flash Photolysis-Resonance Fluorescence Kinetics
Acknowledgment. We thank A. 0. Langford and R. C. Shah for their assistance in carrying out some of the experiments and M. Lupton for her help in preparing the manuscript. This work was supported by the National Science Foundation through Grant No. ATM-7810092. Supplementary Material Available: Tables I-IV containing kinetic data for the reactions OH + NO2 + M HN03 + M, where M = N2, SF6, Ar, or He (13 pages). Ordering information is available on any current masthead page. References and Notes
-24,8-
-
-25 0-
Y 0
2-25,ZL Y 0 J
---25,4-
.u"
m
Y
3
-
J
-25,5-
-258-
+
+
-
+
Figure 7. Rate constants for OH NOp N2 HNOB N2 which are needed for modeling tropospheric chemistry. The data points (0) are obtained by interpolation of fall-off curves such as that shown in Figure 6. The sol! lines represent "visual approximations'' to the smooth curve which best connects the three data points.
Smith seems somewhat low in light of our results. We measured a rate constant of 1.51 X cm3/(molecules s) at the highest SF6 pressure studied (586 torr), and this value was -30% higher than that obtained at a factor of 2 lower SF6pressure. Thus it appears that k , is considerably larger than 1.6 X 10-l' cm3/(molecules s). For modeling tropospheric chemistry, rate constants for reaction 1at high N2pressures are needed. Fall-off curves such as that shown in Figure 6 allow us to determine k , at equivalent N2 pressures up to 1 atm by interpolation. The uncertainty in the rate constants obtained in this manner is limited primarily by the uncertainty in the relative efficiencies for stabilization of the activated complex by N2 and SF6 (-15%). Rate constants for reaction 1 over the pressure range 450-760 torr of N2 and the temperature range 247-352 K are obtainable from the curves shown in Figure 7. At 297 K and 760 torr of N2 we obtain kl = 1.1X cm3/(molecules s) which is in excellent agreement with the value recommended by Hampson and G a r ~ i n . ~ ~
(1) P. J. Crutzen, "Physics and Chemistry of the Upper Atmosphere", B. M. McLormac, Ed., D. Reldel, Dordrecht, Netherlands, 1973, pp 110-32. (2) J. Troe, "Physical Chemistry: An Advanced Treatise", Vol. VIB, W. Jost, Ed., Academic Press, New York, 1975, pp 835-929. (3) W. Tsang, Int. J. Chem. Kinet., 5, 947 (1973). (4) G. P. Smlth and D. M. Golden, Int. J. Chem. Kinet., 10, 489 (1978). (5) W. E. Wilson and J. T. O'Donovan, J. Chem. Phys., 47, 5455 (1967). (6) M. F. R. Mulcahy and R. H. Smith, J. Chem. Phys., 54, 5215 (1971). (7) A. A. Westenbsrg and N. deHaas, J. Chem. phys., 57, 5375 (1972). (8) J. G. Anderson and F. Kaufman, Chem. Phys. Lett., 18,375 (1972). (9) J. G. Anderson, J. J. Margitan, and F. Kaufman, J . Chem. Phys., 80, 3310 (1974). (10) C. J. Howard and K. M. Evenson, J. Chem. Phys., 81, 1943 (1974). (11) G. W. Harris and R. P. Wayne, J . Chem. Soc., Faraday Trans. 1, 71. 610 (1975). (12) K. Erler, D. Fidd, R. Zellner, and I. W. M. Smlth, Ber. Bunsenges. Phys. Chem., 81, 22 (1977). (13) C. Morlev and I. W. M. Smith, J . Chem. Soc., F8f8daY Trans. 2 , 88, 1016 (1972). (14) C. Anastasi, P. P. Bemand, and I. W. M. Smith, Chem. Phys. Lett., 37, 370 (1976). (15) C. Anastasi and I. W. M. Smith, J . Chem. Soc., Faraday Trans. 2 , 72, 459 (1976). (16) R. Atklnson, R. A. Perry, and J. N. Pltts, Jr., J. Chem. Phys., 85, 306 (1976). (17) D. D. Davis, S. Fischer, and R. Schiff, J. Chem. Phys., 81, 2213 (1974). (18) A. R. Ravishankara, P. H. Wine, and A. 0. Langford, Chem. Phys. Lett., 83, 479 (1979). (19) A. M. Bass, A. E. Ledford, Jr., and A. H. Laufer, J . Res. Natl. Bur. Stand., Sect. A, 80, 143 (1976). (20) R. D. Hudson, Ed. Natl. Stand. Ref. Data Ser., Nafl. Bur. Stand., No. 38 (1971). (21) S.T. Amimoto, A. P. Force, and J. R. Wiesenfeld, paper presented at the 177th National Meeting of the Amerlcan Chemlcal Soclety, Honolulu, Hawaii, 1979. (22) G. Paraskevopoulos and R. J. Cvetanovic, Chem. Phys. Left., 9, 603 (1971). (23) R. F. Heiner, 111, D. Humin, and J. R. Wlesenfekl, Chem. Phys. Lett., 18, 530 (1972). (24) R. F. Hampson, Jr., and D. Garvin, Eds., Natl. Bur. Stand. ( U . S . ) , Spec. Pub/., No. 513 (1977). (25) J. Troe, Ber. Bunsenges. Phys. Chem., 78, 478 (1974). (26) W. Forst, "Theory of Unimolecular Reactions", Academic Press, New York, 1973.
