J. Phys. Chem. 1984, 88, 3314-3318
3314
Mechanism of the Atmospherlc Oxidation of Sulfur Dioxide. Catalysis by Hydroxyl Radicals James J. Margitan Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91 109 (Received: December 14, 1983)
-
+
A flash photolysis/resonance fluorescence system was used to study the decay of OH due to the reaction OH SO, (+M) HOSO, (+M). In the presence of small amounts of NO (lOI4 ~ m - and ~ ) 0, (1015~ m - ~the ) , decays deviated from the normal semilogarithmic linearity due to reformation of OH. Computer simulations of the decay curves suggest the reactions HOSO, + 0, HO, + SO3 (k,) and H 0 2 + NO OH + NO, are the likely subsequent steps in SO, oxidation. k3 was found to be (4 f 2) X cm3 s-l, indicating an upper limit of 32 kcal/mol for the binding energy of HOS02 relative to OH + SO2. The atmospheric implications of a catalytic oxidation mechanism are discussed briefly.
-
-
Introduction The gas-phase oxidation of SO2 in the earth’s atmosphere is initiated by reaction with hydroxyl radicals: OH
+ SO2 (+M)
-+
HOSO2 (+M)
(1)
Detailed information on the subsequent fate of the HOSOz radicals is sparse, so that, until recently, the overall reaction scheme converting SO2 into H2S04was included in models as
OH
+ SO2
+
H2S04
(2)
resulting in the loss of one O H for every SO, oxidized. On the other hand, if HOS02 reacted with a second O H radical
OH
+ HOS02
-
H20
+ SO3
followed by the reaction of SO3with H 2 0 to form H2S04,then two O H radicals would be lost for every SO2 oxidized. Recently, however, Stockwell and Calved have proposed a catalytic scheme HOSOz H02
+
0 2
+ NO
-
-+
+ SO, NO2 + O H HOz
(3) (4)
-
wherein the OH is regenerated. This mechanism is based on their observation that SO2 did not affect the rate of CO C 0 2 oxidation in their FTIR smog chamber studies of a HONO/NO/ N O z / H 2 0 / C O / S 0 2 mixture. Resolution of the question of O H loss or regeneration in SO2 oxidation has important consequences for both tropospheric and stratospheric chemistry. Loss of OH in SO2 oxidation leads to a highly nonlinear response of acid formation to decreases in SOz emissions in tropospheric pollution models.’5 In the stratosphere, loss of OH would result in a serious depletion of lower stratospheric O H as a result of volcanic injections of SO2,with a consequent lengthening of the SOz H2SO4 conversion time.6 In this work, we have used the flash photolysis/resonance fluorescence technique to follow directly the OH loss via reaction 1. Addition of NO and O2to the reaction cell caused the observed decay plots to deviate significantly from linearity, demonstrating the reformation of OH, and thus supporting the catalytic mechanism of Stockwell and Calverta2
-
(1) J. G. Calvert and W. R. Stockwell in “Acid Precipitation: SO2,NO, and NO2 Oxidation Mechanisms: Atmospheric Considerations”, Ann Arbor Science Publishers, Ann Arbor, MI, 1983. (2) W. R. Stockwell and J. G. Calvert, Atmos. Environ., 17, 2231-5 (1983). (3) H. Rodhe, P. Crutzen, and A. Vanderpol, Tellus, 33, 132-41 (1981). (4) P. J. Sampson, 1982, quoted in ref 2. ( 5 ) NAS report, “Acid Deposition: Atmospheric Processes in Eastern North America”, National Academy of Sciences, Washington, D.C., 1983. (6) S. A. McKeen, S. C. Liu, and C. S . Kiang, J . Geophys. Res., in press.
0022-3654/84/2088-3314$01.50/0
Experimental Section The flash photolysis/resonance fluorescence system used in this study has been described previously in conjunction with the study of the O H H N 0 3 reaction.’ Briefly, small amounts of nitric acid are entrained in part of a helium carrier gas flow-and are, photolyzed at 266 nm to produce OH. The O H is monitored by resonance fluorescence, by using a multichannel analyzer to accumulate the photomultiplier signals resulting from 2000 laser flashes. The data are analyzed as semilogarithmic plots of the fluorescence signal, proportional to [OH], vs. time. The laser was typically operated at -2 mJ/pulse. At this power density, there was no measurable emission from SO,; at higher powers, a complex emission was found with an intensity that depended on (laser p ~ w e r ) ~Approximately . 200 experiments were performed at pressures of 40 and 100 torr of Ar and at temperatures of 250 and 298 K. Reactive species concentrations were as follows: NO, (1.8-34) X IOl3 c m 3 O,, HNO,, (0.7-2.5) X l O I 5 (1.3-43) X lOI4 cm-,; SOz, (0.8-8.5) X 1015 ~ m - ~Initial . OH concentrations were -3 X 10” ~ m - so ~ ,that radical-radical reactions were unimportant.
+
-
Results and Discussion Hydroxyl radicals generated by the photolysis of nitric acid decay under pseudo-first-order conditions via the reactions
--
OH diffusion loss OH HNO, H 2 0 NO3
+
+
(5) (6)
and, in the presence of added reactants such as SO2 OH
+ SO2 5H O S 0 2
(1)
These decays are analyzed as semilogarithmic plots of the OH fluorescence signal vs. time and yield the first-order rate constants (k‘) as the slopes. The linearity of the decay plots over 1-2 orders of magnitude change in [OH] verifies the absence of complicating secondary reactions. For a series of experiments conducted with a fixed [HN03] and various concentrations of SO,, the resulting k”s can be plotted against [SO,] to give a linear plot whose intercept is k5 k6[”03] and whose slope is kl. Effective bimolecular rate constants, kl, were measured for Ar pressures of 40 and 100 torr at 298 K, and 40 torr at 250 K. Under these conditions, the reaction is in the falloff region between purely third-order and second-order behavior. The measured kl’s are in good agreement (-20% lower) with values calculated by using the NASAs Troe expression with a kOAr= 1.09 X lo-,’ cm6 s-l, taken from Leu.g
+
(7) J. J. Margitan and R. T. Watson, J. Phys. Chem., 86, 3819-24 (1982). (8) W. B. DeMore, M. J. Molina, R. T. Watson, D. M. Golden, R. F. Hampson, M. J. Kurylo, C. J. Howard, and A. R. Ravishankara, JPL 83-62, Jet Propulsion Laboratory, Pasadena, CA, 1983.
0 1984 American Chemical Society
Atmospheric Oxidation of SO2 40 3. 8-.
1
I
I
100
I
15 M A R 83 RUN 11
I
I
I
I
.
k‘ vs [NO]
3.6 3.4 3.2
2 z
g5
..
9
0 e
3.0 2.8
T - Z M K @torr
2.6
mr
2.4 2.02.2-
1.8
-
1 -
n\o
1.2 -
0
1.6
-
0
1.4
0
I
1.0
I
200 -
-
100
I
I
1
0
1.1 x
=
[02]
-2.6~10~~ =6ms =6ms
At At
2
4
3
[NO]
1
ld5
[“Os]
5
ld4d
Figure 3. Plot showing the effect of OH regeneration on the initial OH decay rate. The decay plots are themselves curved so that the “pseudo k’” is an “average”slope over the first 6 ms. The [SO,] = 0 data show the effect due to the OH + NO reaction. The [O,] is large so that reaction 4 is rate limiting in OH formation. I
1
l 1.6 l
1.41 0
1
. 3
2
4
5 6 TIME ImsecJ
0
7
8
[ S O ~ ] = 2.4
1 9 1 0 0
Figure 2. Semilogarithmic OH decay plot demonstrating the reformation of OH by NO and 02.
If NO is added to the A r / H N 0 3 / S 0 2 mixture, the OH decays are slightly enhanced due to reaction 7 but remain linear (Figure OH
+ N O 2H O N O
(7)
1). Addition of O2 to this mixture, however, causes the decay plots to curve (Figure 2), approaching a pseudosteady state at longer times, due to the regeneration of OH, via a process such as HOSOz O2 H 0 2 SO3 (3)
+
H02
+ NO
+ O H + NO2
-+
+
(4)
In the present experiments, only OH was observed-no other intermediates. It is, therefore, not possible to unambiguously identify the reactions which reform OH; reactions 3 and 4 are merely the simplest and most likely candidates consistent with the observed rates of the N O and O2reactions. In the discussion that follows, the data are first analyzed in order to derive k3 and k, as the rate constants of the 0, and NO reactions, respectively, without regard to the exact nature of the H0,-containing species. Evidence in favor of reactions 3 and 4 as written will be discussed ~~~
~~
(9) M. T. Leu, J . Phys. Chew., 86, 4558-62 (1982).
- 1
[HN03] = 1.1 x 1015
1.2 1
-I
1
2
[so2] = 0
3
[o,]
4
5
6
--7
d5cm-3
Figure 4. Plot analogous to Figure 3, showing OH regeneration under conditions where [NO] is large and reaction 3 is rate limiting.
later. It is clear that the OH reformation reactions involve the adduct formed in the OH + SO2 + M reaction: that reaction is the major loss of O H in the experiments, so that the OH lost in that step must be regenerated to account for the large amount of OH recycled. Furthermore, no OH production is observed in the absence of SO2. Quantitative estimates for the rate constants k3 and k4 were obtained in two ways. Under conditions of fairly high [O,], and small amounts of NO, the N O reaction 4 is rate determining in the OH formation. If the apparent “average” slopes of these In [OH] vs. t plots are measured over a fixed At interval and plotted against [NO], the apparent OH disappearance rate decreases from a correct, initial value to a lower one due to the increasing rate of O H reformation. In the limit of high [NO] and [O,], the reformation of OH from HOSOz is so rapid that the apparent k’ for OH loss is virtually equal to the rate in the absence of SO2 (Figure 3). Similarly, with relatively large amounts of N O present, and small amounts of 02,the O2 reaction (3) is rate limiting and a similar k’ vs. [02]plot is obtained (Figure 4). These plots show that the concentrations of O2 required to achieve a given level of suppression of the O H decay are about a factor of 30 higher than
3316
The Journal of Physical Chemistry, Vol. 88, No. 15, 1984
TABLE I: Reaction Scheme Used in Computer Simulations reaction k",O cm3 s-l k', s-I note OH SO2 -* HOSO2 1 1 X 100-1500 b HOS02 + O2 H 0 2 SO, 3 4 X lo-" 100-1500 c HO2 + NO OH + NO2 4 8.3 X 100-3000 OH, HOS02, H 0 2 diffusion loss 5 80 b OH + HN03 H20 + NO3 6 1.2 X 100-300 b OH + NO HONO 7 5 X lo-" 10-300 HOSO2 NO loss of HO, 8 2.5 X lo-'* 50-700 c
-
+
Margitan 3.81
15 MAR 83 RUN 13
+
+
+ -t
Nominal value. P,T dependencies were included where known. *Calculationsused actually measured k'. C kvaried to obtain best fit.
3.2
-2 J
8
-
3.0-
KOBS
m734.5 sec-'
[SO2]
=3.42xd5
1.90 x 1014
[NO]
=
[02
-1.48
1
~ H N O , -2.04 ~ x
d5
2.8-
0 2.4 Ln
;2.20
the corresponding NO concentrations-indicating that the NO reaction is about 30 times faster than the O2 reaction. A crude approximation of the magnitude of k3 or k4 can be obtained from these plots and indicates k3 (3-5) X cm3 and k4 1 X lo-" cm3 s-l. The accuracy of this procedure is a factor of 3 at best. A better estimate of k3 and k4 could be obtained from a simulation of the OH decays by using a computer model of reactions 1 and 3-7 (Table I). Rate constants for reactions 1 and 5-7 could be measured independently and were consistent with literature values.8 Diffusion loss of HOS02 and H 0 2 was also included at rates equal to k5. Rates for reactions 3 and 4 were varied to obtain the best agreement of the calculated OH decay curves with those determined experimentally. The experimental data were generally obtained under conditions where either reaction 3 or reaction 4 was rate limiting in the OH reformation. Sets of experiments were performed in which all concentrations were held constant except for that of the ratelimiting species ( N O or 0,) which was varied over approximately 1 order of magnitude. Since the calculated decay curves were sensitive only to the rate-limiting step, the fits had basically only a single, adjustable parameter. For example, the experiment shown in Figure 5 has k 4 [ N O ]>> k 3 [ 0 2 ]so that the O2 reaction is rate limiting. k4 was set initially to the literature value for the H 0 2 N O reaction and k3 was adjusted to obtain the best agreement of calculation with the experimental data. Other experiments from the same set were then examined in which only the [O,] had been changed. After an optimum k , was found which fitted that particular data set (6-10 experiments with [02] varied by a factor of lo), that k3 was used to fit the complementary experiments where k 3 [ 0 2 ]>> k 4 [ N O ] .In these experiments, the decay curves are sensitive only to k4. Those data (as well as other data sets) were consistently fitted very well by using the literature values of the H 0 2 N O rate constant for k4, once again over 1 order of magnitude range in [NO]. The rate constants obtained by this procedure are probably accurate to approximately a factor of 2. The curve fitting was carried out for about 50 individual experiments. For k3,values of (4 f 2) X cm3 s-l gave the best fits at both 298 and 250 K. Although k3 would be expected to vary with temperature, the factor of 2 uncertainty in values obtained by fitting could have masked that variation. The 298 K value of 4 X cm3 s-l is consistent with an Arrhenius expression of 1 X lo-" exp(-lOOO/T) which would predict only a factor of 2 change in k3 from 298 to 250 K. Fitting the OH decays at low 0, concentrations (and high [NO]), where reaction 3 is rate limiting in the OH reformation, showed that somewhat better fits could be obtained if an additional loss of HOS02 was included, which did not lead to recycling of the OH. The high-[02], low-[NO] experiments, however, were best fitted if this loss was small, suggesting a possible reaction HOSO, N O loss of OH (8)
-
-
+
+
-
+
2.0-
-
with ks 2.5 X cm3 s-l. Since the 0 2 / N 0 ratio was typically large, most of the HOS02 reacted with 0, to ultimately regenerate OH. The inclusion of reaction 8 has only a marginal effect on the goodness of the fit, so that its identification is highly uncertain. A reaction such as (8) is consistent with the known tendency for NO to act as a free-radical scavenger. Inclusion of the reaction OH + H 0 2 H 2 0 O2was found to have virtually no effect on the calculated curves so that it was +
+
1.41
*
.
-I
1.21
TIME (msec)
Figure 5. Sample plot showing comparison of experimental data and calculated curves using rate constants from Table I. Reaction 3 is rate limiting in OH regeneration and curves are shown for a factor of 2 variation in k3 in both directions. Experimental data for the first 1.5 ms
fall exactly on the solid line and are omitted for clarity. normally excluded. The absence of radical-radical reactions permitted the calculations to be done without requiring knowledge of the absolute OH concentration. The values derived from the data for k3 (4 X cm3 s-*)and k4 (1 X lo-" cm3 s-l) can be used to identify likely candidates for the O2 and NO reactions. Since the generation of OH upon addition of NO is often used as a detection/monitoring technique for H 0 2 , it is reasonable to consider that known reaction as the NO reaction H02
+ NO
+
OH
+ NO2
(4)
with the agreement between literature values of k4 and those needed for the curve fitting adding credence to that assignment. The H 0 2 N O reaction is not unique, however, since NO R 0 2 rate constants seem to be typically -1 X lo-" cm3 s-l. If the N O reaction here were with some peroxy radical other than HOP, it would then be necessary to postulate a decomposition or subsequent reaction of the R O product into OH. In the absence of any likely candidates for a such a reaction, it seems reasonable to assume that the NO reaction is the H 0 2 NO reaction, as written for reaction 4. Using reaction 4, in conjunction with the requirement that the HOS02adduct is ultimately recycled to give OH, leads to reaction 3 as the logical connecting reaction between HOSOz and H 0 2 .
+
+
+
HOS02 + O2
+
H 0 2 + SO3
(3)
The value observed for k3 (4 X cm3 s-l) is certainly reasonable for such a bimolecular reaction, indicating a maximum barrier of 2 kcal/mol for the H abstraction. The abstraction of a hydroxyl hydrogen atom by O2is known to occur in the reaction CH2OH
+ 02
-
CH2O
+ H02
which is widely used as an H 0 2 source in kinetic The rate constant of 2 X cm3 s-l for that process indicates that the intrinsic barrier to such an abstraction is no more than 1 kcal/mol. The 2 kcal/mol limit derived here for reaction 3 disagrees with Benson's12 estimate of the HOS02enthalpy, since that enthalpy predicts reaction 3 to be -6 kcal/mol endothermic.
-
(10) H.E.Radford, Chem. Phys. Letr., 71,195 (1980). (11)S. P.Sander, M. Peterson, R. T. Watson, and R. Patrick, J . Phys. Chem., 86, 1236-40 (1982). (12)S. W. Benson, Chem. Reo., 78,23-35 (1978).
The Journal of Physical Chemistry, Vol. 88, No. 15. 1984 3317
Atmospheric Oxidation of SOz The 4 kcal/mol discrepancy is virtually within the f 3 kcal/mol uncertainty of his estimate, however, and indicates that the formation of HOSOz from OH SO2 is no more than 32 kcal/mol exothermic. Since the overall exothermicity of the process
+
(OH
+ SO, + 0, + NO)
---
(OH
+ NO2 + SO3)
is only -37.3 kcal/mol, Benson’s estimate that the HOSO, formation was 36 kcal/mol exothermic would impose severe limitations on any subsequent O2and N O reactions (Le., they must both be virtually thermoneutral). The CODATAI3 thermodynamic data yield 53 kcal/mol for the OH-S02 bond strength, which can not be reconciled with the observations and mechanism of this study. There are three other possible routes for the HOSO, O2 reaction which can be rejected: (I) Stockwell and Calvert, proposed and rejected the hypothesis that reaction 3 might actually be a reaction of O2with HOS02*, the O H SOz adduct which had not yet been deactivated by collisions. The initial deactivation rate for quenching of the very excited HOS02* (32 kcal/mol) by Ar is much faster than, and certainly dominates, any reaction with 02.However, the less excited HOS02* resulting from multiple, stepwise deactivation and containing only 4-6 kcal/mol internal energy may be much less efficiently deactivated so that reaction with 0,could compete with quenching by the much more abundant Ar. It seems unlikely, however, that the O2reaction could compete with quenching by SO2 (or H N 0 3 ) , which is present in amounts roughly equal to the O2concentrations. It might be possible to resolve the question experimentally by performing experiments with high pressures (1 atm) of a good quencher such as SF6. In the absence of reliable data, the hypothesis that the 0, reaction involves a slightly excited (4-6 kcal/mol) HOS02* adduct cannot be completely ruled out but does seem unlikely in view of the large amounts of SO2present. (11) The possible association reaction of HOSOz with O2to lead to HOSO2.0,
+
+
HOSO,
+ 0,
-
HOS02.02
-
(9)
is postulated to be exothermic12by 16 kcal/mol. Although the HOSO2.O2 adduct would probably react rapidly with NO
HOS02.02
+ NO
--*
HOSO2O
+ NO
(10)
the resulting HOS03 radical is expected to be stable by -39 kcal/mol, with respect to dissociation to O H SO3,so that OH reformation would not occur via this reaction sequence. (111) Friend et al.I4 proposed the hydration of HOS02 and then reaction with O2
+
HOSO,
+ HZO
HOSOyH20
+0 2
-
HOSO,.H,O
-+
H2SO4
+ HO,
as a probably exothermic process leading to odd hydrogen regeneration. This mechanism could explain the Stockwell and Calvert results, but fails here since the present experiments are done in a water-free environment. The rejection of these alternative mechanisms leaves reactions 3 + 4 as the most likely route to OH regeneration, with the additional indication that the H0-S02 binding energy is probably about 32 kcal/mol, rather than the 36 kcal/mol estimated by Benson.12 Although more complex reaction schemes should also be able to fit the data, the present mechanism has the desirable feature of containing only one “speculative” reaction, (3). Verification of this scheme would require the detection of either HOSO, or H 0 2 (and their kinetic behavior), neither of which could be done here. In view of this fundamental uncertainty in the kinetic scheme, no attempt was made to refine the accuracy of the rate constant extraction process to better than the ap(13) 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, 327-496 (1982). (14) J. P. Friend, R. A. Barnes, and R. M. Vasta, J. Phys. Chem., 84, 2423-36 (1980).
proximate factor of 2 obtained in the calculated-experimental comparison. Other experimental studies of the H O , / S O 2 / N 0 / 0 ~ system have yielded results in agreement with the HO, catalytic chain seen here. In studies of the photolysis of H O N O in SOJO, mixtures, Coxl5 found that the SO2 suppressed the level of N O and increased NO,, which he ascribed to a mechanism such as reactions 9 10. He, among others, had also separately verified the oxidation of SO, to SO3 (or HzSO4) in these systems. Leu’ in a low-pressure discharge flow study of the kinetics of the O H + SO, M reaction found that, with M = 02,the O H decay plots showed curvature indicative of O H reformation, possibly involving NO. Because of the potential for heterogeneous reactions, those results could not be extrapolated to the atmospheric mechanism. Stockwell and Calvert2 have reported that the rate of CO oxidation is unaffected in a simulated smog atmosphere even when sufficient SOz is added to reduce the O H concentration by a factor of 2 (assuming O H SOz results in an O H loss). Their study serves as an important complement to this one, in that the present study directly observed OH regeneration in a relatively simple chemical environment, whereas their study was more indirect, but utilized conditions typical of the atmosphere. Their observation that the CO oxidation rate was independent of added SO, also included a report that the production rate codd be fitted by a linear function (their eq 15). An examination of their Figure 2 indicates that that observation may be incorrect: although the data seem to scatter about a straight line, the points from any given experiment show a great degree of curvature, which varies somewhat from run to run but always has the same general shape. The scatter from one experiment to another is probably due to uncertainties in the concentration determination; the consistency (Le., nonrandomness) of shape rules out such uncertainties as an explanation of the curvature, which is probably due to the fact that their eq 15 represents an incomplete mechanism, omitting, for example, radical-radical reactions. Curvature in their data of Figure 2 does not impugn the reliability of their conclusion that SO, does not affect the C O oxidation rate: the curvature and scatter of the points in their Figure 2 are clearly independent of SO,,. An OH-catalytic oxidation of SO, has important impacts on both tropospheric and stratospheric chemistry. The assumption that SO, oxidation consumes O H has led to the prediction that changes in SO2 emissions would result in less than linear changes in H2S04produced in the atmospheric plume downwind of SO, emission source^,^'^ largely because loss of HO, decreases H202 production and thus lessens SO2oxidation by H 2 0 2in aerosol^.^-^ The catalytic oxidation route leads to H2S04 changes that are nearly linear with changes in S02.495 In the stratosphere, the O H SO, reaction normally has little impact on the HO, concentrations. Under conditions of high [SO,], however, it can be a significant loss of odd hydrogen if a noncatalytic route is assumed. In particular, the recent El Chichon eruption is believed to have injected about 2-13.5 Mt of SO, into the If the O H + SO, reaction consumes OH, this injection of SO, dramatically lowers the calculated O H abundances by about 1 order of magnitude at 20 km and correspondingly increases the lifetime of SO, with respect to conversion to H2S04 from 1-2 months to 1 yr.6 The observation that the El Chichon SO2was converted to H2S04with a 1-month lifetime” is consistent with the HO, catalytic mechanism indicated by this work and Stockwell and Calvert, but is not conclusive since the eruptions could have perturbed the ambient OH level via massive injections of HzO. McKeen et ale6discuss additional potential stratospheric perturbations which could result from various sce-
+
+
+
+
-
(15) R.A.Cox, J. Photochem. 3,291-304 (1974175);Int. J . Chem. Kinet. Symp., 1, 379-98 (1975). (16) A. J. Krueger, Science, 220, 1377-9 (1983). (17) D.F.Heath, B. M. Schlesinger,and H. Park, EOS Trans. AGU, 64, 197 (1983) (abstract). (18) W. F. J. Evans, and J. B. Kerr, Geophys. Res. Lett., 10, 1049-51 (1983).
3318
J. Phys. Chem. 1984,88, 3318-3325
narios for the SO2 impact on OH.
followed, probably, by reaction of SO3 with H 2 0 to form H2S0,. The value derived for k3 (4 X cm3 s-’) is reasonable for the reaction as written and further indicates that the binding energy of H O S 0 2 is no greater than 32 kcal/mol, with respect to O H
Conclusion The direct observation of OH reformation following the reaction of O H with SO2 in the presence of trace amounts of O2and N O suggests that the atmospheric oxidation of SO2 proceeds via an HO, catalytic mechanism:
+ SO2 (+M) H O S 0 2 + O2 HO2 + NO
OH
-
+
+
HOS02 (+M)
H 0 2 + SO3
OH
+ NO2
+ soz.
Acknowledgment. The research described in this paper was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Helpful discussions with W. B. DeMore, S. P. Sander, J. G. Calvert, and S. C. Liu were appreciated.
(1)
(3)
(4)
Registry No. SO2, 7446-09-5.
Reactive Differential Cross Sections in the Rotating Llnear Model. Reactions of Fluorine Atoms with Hydrogen Molecules and Their Isotoplc Variants Edward F. Hayes Division of Chemistry, National Science Foundation, Washington, D.C. 20550
and Robert B. Walker* Theoretical Division, T-12, M S 5569, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (Received: December 28, 1983)
-
+
-
Angular distributions are predicted for the reactions F H2(u=0) H + HF(v’=2), F + HD(v=O) D + HF(v’=2), and F + D2(v=0) D + DF(u’=3) by solving the quantum-dynamical equations for the rotating linear model with corrections for bending zero-point energy (the BCRLM approximation). For each of these reactions, time delays, deflection functions, opacity functions, and resonance parameters are reported. The resonance contributionsto the angular distributionsare predicted to be relatively small for each of the title reactions. The resonance lifetimes in all cases are found to be greater than 4 times the vibrational period of the reactant diatomic molecule. However, the angular velocities, lifetimes, and amplitudes of the resonance states are not collectively large enough to produce discernible effects in the angular distributions. Shifts in the peaks of the angular distributions from backward to sideways scattering as the collision energy is increased appear to be due primarily to direct (Le., nonresonance) scattering.
Introduction The objective of this paper is to provide some additional insight into the factors that determine the angular distributions for the reactions F + H~(v=O) H HF(v’=2) F + HD(v=O) D + HF(v’=2) F D2(v=0) D DF(v’=3)
+
-
butions, time delays, quantum deflection functions, and opacity functions for each of these title reactions. Although our calculated results are only an approximation to the true multidimensional scattering, the RLM and BCRLM make it possible to analyze both the resonance and nonresonance contributions to these reactions in greater detail than has been possible to date. The hope is that these approximate results will contain most of the important features of more accurate theoretical methods. If this is the case, our predictions of the state-to-state angular distributions for these reactions should be valuable in guiding future experimental and theoretical investigations.
-- + -+
Recent theoreticaP and experimentalSstudies of the state-testate H HF(v’=2) have suggested that reaction F H2(v=0) quantum-dynamical resonances may be responsible for the shift in the center-of-mass angular distribution from backward peaking to sideward peaking as the relative translational energy is increased from 0.087 to 0.137 eV. In this paper the rotating linear model (RLM) approximation and the RLM with bending correction (BCRLM)6 are used to obtain detailed scattering information, including angular distri-
+
+
11. Theoretical Approach Expressions for the RLM differential scattering cross section were presented by Connor and Child.’ We repeat here only their final result for the differentiarcross section
(1) (a) M. J. Redmon and R. E. Wyatt, Chem. Phys. Lett., 63,209 (1979); (b) R. E. Wyatt in ‘Horizons in Quantum Chemistry”, K. Fakui and B. Pullman, Eds., Reidel, Dordrecht, 1980, p 63; (c) R. E. Wyatt, J. F. McNutt, and M. J. Redmon, Ber. Bunsenges. Phys. Chem., 86,437 (1982); (d) R. E. Wyatt and M. J. Redmon, Chem. Phys. Lett., 96, 284 (1983). (2) M. Baer, J. Jellinek, and D. J. Kouri, J . Chem. Phys., 78, 2962 (1983). (3) E. E. Hayes and R. B. Walker, J . Phys. Chem., 86, 85 (1981). (4) (a) S. H. Suck, Chem. Phys. Lett., 77, 390 (1981); (b) S. H. Suck and R. W. Emmons, Phys. Rev. A 24, 129 (1981); (c) R. W. Emmons and S. H. Suck, Ibid.,25, 178 (1982). (5) R. K. Sparks, C. C. Hayden, K. Shobatake, D. M. Neumark, and Y . T. Lee in “Horizons in Quantum Chemistry”, K. Fukui and B. Pullman, Eds., Reidel, Dordrecht, 1980, p 91. (6) (a) R. B. Walker and E. F. Hayes, J . Phys. Chem., 87, 1255 (1983); (b) R. R. Walker and E. F. Hayes, ibid.,88, 1194 (1984).
0022-3654/84/2088-33 18$01.50/0 , , I
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where v and v’label the initial and final vibrational states, k , is the initial translational wavenumber, E is the total scattering energy, S;,(E) is an element of the scattering matrix at total angular momentum (partial wave) 1, and Z(8) is the angular distribution. The expressions for the differential cross section are unchanged when the bending correction is added to the RLM potential. (7) J. N. L. Connor and M. S. Child, Mol. Phys., 18, 653 (1970).
0 1984 American Chemical Societv -
