J. Phys. Chem. 1986, 90,4143-4147
4143
Discharge Flow Measurements of the Rate Constants for the Reactions OH 4- SO, 4He and HOSO, 4- 0, in Relation with the Atmospheric Oxidation of SO, D. Martin, J. L. Jourdain, and G. Le Bras* CNRS Centre de Recherches sur la Chimie de la Combustion et des Hautes Tempgratures, 45071 Orleans Cedex 2, France (Received: October 30, 1985; In Final Form: February 7, 1986)
-
The reactions OH + SO2 + M (M = He, SOz) HOS02 (1) and HOSOz + O2 (2) have been studied by the discharge flow EPR technique at room temperature and at pressures ranging from 1 to 6.4 Torr in a halocarbon-wax-coated reactor. For He and SO2 as the third body the bimolecular rate constant can be expressed as k,(He) = (8.1 f 0.2) X 10-3z[He] + (2.4 f 0.4) X (P= 1-6.4 Torr) and k l ( S 0 2 )= (1.3 f 0.4) X 10-30[S02](P d 0.1 Torr). Units are cubic centimeters per molecular per second. Reaction 2 was studied by adding Ozto the reacting medium and NO for the conversion of HOZ into OH. The value of k2 was found from the computer fitting of the OH profiles with and without added O2 as a function cm3 molecule-'^-^. of reaction time: k2 = (3.5 f 1) X
Introduction The reaction OH SO2 M HOS02 + M (1) is important in tropospheric chemistry since it is the first step in the conversion of SO2into sulfuric acid which contributes to acid deposition. This reaction also initiates the oxidation of SO2 into aerosols in the stratosphere. Reaction 1 has been extensively studied. kl has been measured by using the flash photolysis resonance fluorescence technique'" at pressures ranging from 13 Torr (1 Torr = 133.3 Pa) to 1 atm with various third bodies (He, Ar, Nz, SF,) and at temperatures up to 424 K. Results have shown that the high-pressure second-order limit was not reached at atmospheric pressure. Results of experiments at pressures below 10 Torr carried out by using the discharge flow resonance fluorescence technique have been reported by Harris and Wayne' (P= 1-4 Torr; T = 295 K; M = Ar, N2) and Leu* ( P = 0.9-10 Torr; T = 261-414 K; M = He, Ar, NZ,02,C 0 2 , SO2). There is a discrepancy of a factor of 4 between these two results. Recently Stockwell and Calvert9 have found some evidence for the Occurrence of a reaction between the adduct HOSOzand 02.The reaction proposed is HOS02 O2 SO3 + H 0 2 (2) This result has been confirmed by Margitan5 in a flash photolysis study of the SO2 + OH reaction, in which OH was regenerated in the system through step 2, and H02 + NO O H + NO2when O2 and NO were added. Margitan reported a value for rate constant k2 = (4 f 2) X cm3 molecule-' s-I, using a computer simulation of the reaction mechanism. More recently Schmidt et a1.I0 have also noticed the regeneration of O H from a continuous photolysis study of the OH + SO2 reaction in 1 atm of synthetic air and in the presence of NO. Since only one determination of k2 has been reported to date, it appeared useful to remeasure k2 by using a different technique, the discharge flow. It is worth notice that a direct discharge flow measurement of k2 has been carried out by Howard" while our study was in progress.
+
+
+
--+
-
-
(1) Atkinson, R.; Perry, R. A.; Pitts, J. N., Jr. J . Chem. Phys. 1976, 65, 306. (2) Davis, D. D.; Ravishankara, A. R.; Fisher, A. R. Geophys. Res. Lett. 1979, 6, 113. (3) Harris, G. W.; Atkinson, R.; Pitts, J. N., Jr. Chem. Phys. Lett. 1980, 69, 378. (4) Paraskevopoulos, G.; Singleton, D. L.; Irwin, R. S. Chem. Phys. Lett. 1983, 100, 83. (5) Margitan, J. J. J . Phys. Chem. 1984, 88, 3314. (6) Wine, P. H.; Thompson. R. J.; Ravishankara, A. R.; Semmes, D. H.; Gurnp, C. A.; Torabi, A.; Nicovich, J. M. J . Phys. Chem. 1984, 88, 2095. (7) Harris, G. W.; Wayne, R. P. J. Chem. Soc., Faraday Trans. 1 1975, 71, 610. (8) Leu, M. T. J . Phys. Chem. 1982, 86, 4558. (9) Stockwell, W. R.; Calvert, J. G. Amos. Environ. 1983, 17, 2231. (IO) Schmidt, V.;Zhu, G. Y.; Becker, K. H.; Fink, E. H. Ber. Bumen-Ges. Phys. Chem. 1985,89, 321. (11) Howard, C. J. Communication at the 17th Symposium on Free Radicals, Granby, CO, Aug 18-23, 1985.
0022-3654/86/2090-4143$01.50/0
In this paper we present the results of a discharge flow study of the OH + SOzreaction at pressures ranging from 1 to 6.4 Torr of He. EPR was used for the detection of OH radicals. The effect of O2on the fate of HOSO, has also been studied, and the rate constant of reaction 2 has been determined.
Experimental Section The discharge flow EPR mass spectrometer apparatus has been previously described.I2 The EPR spectrometer (Varian El 12 cavity E235) was used for the gas-phase detection of OH radicals. The sensitivity of the EPR spectrometer was calibrated from comparison of the OH spectra with those of known concentrations of NO as described by Westenberg.I3 Particular care was taken for the calibration of OH since the sensitivity generally measured from the peak-to-peak height of the signal was modified by the pressure broadening and the additional broadening by SO2 and 02, which were flowed in fairly high concentrations. For example, the sensitivity was reduced by 2 when a concentration of 2 X lOI5 cm-3 of SOz was added to the reactor. The 22 mm i.d. quartz reactor was pumped by means of a 250 m3/h roots pump. The pressure was measured with a 10-Torr MKS baratron, and the flow rates were respectively 26, 10,6.4, and 4.3 m/s a t 1, 2, 4.3, and 6.4 Torr. Linear flow rates and the system pressure could be adjusted either by a valve which changed the pumping efficiency or by varying the diluent gas flow. The quadrupole mass spectrometer (Riber QX200) located at the end of the reactor could be used for purity tests and product analysis. To minimize heterogeneous processes that could occur in the presence of SO2, the quartz reactor was coated with halocarbon wax (Halocarbon Products Corp., Wax 12.00). This coating has been found to be very efficient in reducing the wall reactions of O H with sulfur
+
compound^.^^ OH radicals were generated from the reaction of excess NO2 with H atoms. H atoms were produced by a microwave discharge of H2diluted in He. SO2 (99.9% Air Liquide) was used directly from the cylinder (it had been shown that further purification had no effect on the kinetics). Helium (99.995%) was passed through a liquid nitrogen trap to remove compounds that could produce reactive species in the microwave discharge. NO2 (99.9% ~, Matheson) concentration never exceeded 2.5 X 10l2 ~ m - and it was flowed without purification. NO (99% Air Liquide) was distilled under vacuum to remove NO2. NO2 and SO2 were flowed through axial movable inlets, NO2 through the intermediate one and SO2 through the central one. The extremities of the two inlets were located so that the H NO2 reaction was completed before SO2 was admitted into the reactor. O2was flowed with SOz. NO was introduced either with
+
(12) Jourdain, J. L.; Le Bras, G.; Combourieu, J. J . Phys. Chem. 1981, 85, 655. (13) Westenberg, A. A. Prog. React. Kine?. 1973, 7, 24. (14) Martin, D.; Jourdain, J. L.; Le Bras, G. In[.J . Chem. Kine?. 1985, 17. 1247.
0 1986 American Chemical Society
4144
The Journal of Physical Chemistry, Vol. 90, No. 17, 1986
Martin et al.
TABLE I: Summary of the Experimental Conditions Used for the Study of the OH + SO,
+ M Reactiono k,lIS02,
p, Torr 1 2 4.3 6.4
[He19 i O l 6 cm-'
[SO2109
cm-3
3.25 6.5 14 20.8
0.85-4.31 0.57-5.95 0.34-3.97 0.4-2.6 6
[OHIO, 10" cm-'
cm6 molecule-2 s-l
no. of runs
1.5-2 2-6 7 7-10
1.7 1.35 0.93
14 29 25 12
kIIp02 was determined from the least-squares fitting of the experimental straight line (k,- kW)/[SO2] =f ( [ S 0 2 ] ) .
SO, and 0,(for global type kinetics) or a t a fixed position upstream of the EPR cavity (for delayed conversion of HOz into OH as described in the next section). Experiments were carried out under pseudo-first-order conditions. The OH concentration was usually kept lower than 1 X lo1, cm-3 for the determinations made a t 4.3 and 6.4Torr and lower than 6 X 10" cm-3 at 1 and 2 Torr. The SO, concentration was varied between 0.5 X 1015 and (3-4) X loi5~ m - ~The . data were processed on line by a microcomputer. Under our experimental conditions, the correction on k l due to axial diffusion never exceeded 5%. Systematic errors which could occur in flow rate, concentration, or pressure measurements did not exceed 10%. Our results are given with a precision of f 2 u calculated from a least-squares-fitting program.
Results and Discussion Since reaction 1 was studied a t low pressures (P 6 6.4Torr), the effective rate constant represents the addition of several terms. In the reacting medium H e and SOzcan act as third bodies. As already reported by Leu: kIIIHe and kIIf'O2 are respectively the third-order rate constants for He and SO2as the third body, kllW is the second-order rate constant of a assumed bimolecular wall reaction of OH with SO,, and k, is the first-order heterogeneous loss of OH. The pseudo-first-order rate constant was expressed by LeuE as
kl = kIIIHCIHe][SOz]+ kII~02[S02][SOZ]+ k 1 ~ ~ [ S + 0 ~k ,] (a) This formula applies to a pressure range corresponding to a pure third-order regime for the homogeneous OH SO,+ M reaction. This point and the Occurrence of a OH SO,wall reaction will be discussed later. In the case where kII~W[SO2] is not negligible compared to klIIHCIHe],the plot of kl vs. [SO,] can deviate from a straight line to give a branch of a parabola. k, was measured without SO2before and after the kinetic runs, and it was assumed that k, was not dependent on the SO2concentration. No variation of k , could be seen after a prolonged exposure of the halocarbon-wax-coated flow tube to SO,. The range of k, measured was 5-1 5 s-l. Experimental results are reported in Figure 1. The curves represent ( k , - k,) as a function of [SO,] at pressures of 1, 2,4.3, and 6.4Torr in the coated reactor and a t 2.05 Torr in the uncoated reactor. This last curve certainly results from a fast heterogeneous reaction between OH and SO,as already noticed for reactions of OH with sulfides on such a quartz surface.14 In addition, this heterogeneous effect was confirmed by the observation of the OH signal, slowly reaching its initial value when the SO, flow was turned off. Such a phenomenon was not apparent with the halocarbon-wax-coated reactor. Determination of klI~02. kIIto2 was obtained a t pressures of 1, 2, and 4.3 Torr from the slope of the straight line ( k , kw)/[S02] =A[SO,]), the intercept being kIIIHCIHe]+ kIIw.The data obtained a t 6.4Torr were not suitable for the determination of kIIIS02because at this pressure the influence of SO,as the third body becomes small compared to that of He. Such a determination of kIIISo2is valid only if reaction 1 with SO, as the third body is purely third order. As the maximum SO2concentration never exceeded 3.5 X 1015 (-0.1 Torr), this assumption appears to be valid. The straight lines were fitted from a least-squares analysis of the data. Results are reported in Figures 2 and 3 and Table I. The average rate constant derived from these data is k111S02 = (1.33 f 0.4) X cm6 molecule-2 s-l
+
The error is twice the standard deviation.
+
-
Figure 1. Reaction OH + SO2 + M HOSOz + M (1). Plots of the apparent first-order rate constant as a function of SOz concentration obtained at P = 1,2,4.3, and 6.4 Torr using the halocarbon-wax-coated reactor (solid lines) and at 2.05 Torr using the clean quartz reactor (dashed line). The curves were obtained from a weighted least-squares fitting of the experimental data.
lo-'*
c m 3 moleculo-1a-1 )
1
2
I
I
3
4 I
5
6
7 I
Figure 2. Determination of kllp02 from.the plot of (k,- k w ) / [ S 0 2 !as a function of SO2concentration for P = 1 (A)and 2 Torr (0). Straight lines were obtained from least-squares fitting of the experimental data.
Determination of kIIIHe.klIIHecan be determined from eq a, as done by Leu,6 if it is assumed that the pressure range of the study corresponds to the third-order regime. However, from the data of Leus and from their own results, Wine et a1.6 noticed that reaction 1 with helium as the third body would be in the falloff region even at the low pressures (10 Torr) used in the discharge flow studies. If this assumption is correct, the determination of kIIIHC in a pure third-order regime would be in error. Even if the assumption of Wine et aL6 is valid, expression a can be used to determine the bimolecular rate constant of reaction 1 in the presence of helium. In that case kIIIHe[He]is replaced by kIIHe in expression a. kIIHehas been obtained by plotting A = ( k , - kW)/[SO21kIIIS02[S02] as a function of helium pressure (Figure 4). For each helium pressure (1, 2, 4.3,and 6.4Torr) the value reported
The Journal of Physical Chemistry, Vol. 90, No. 17, 1986 4145
Discharge Flow Measurements of Rate Constants
respectively kIIIHC, kIItoz, and kIIw. From 80 experimental data the following values were derived: kIIIHC = (8.3 f 0.2) X kIIfoz = (1.28 f 0.09) X and kIIW= (2.4 f 0.4) X 10-15; precision is twice the standard deviation. It has to be mentioned that the system could not be solved with only the two unknown parameters A and B, considering the C equal to zero. It can be observed that these results are in excellent agreement with those obtained by using the graphical method. Therefore, for helium as the third body in the pressure range 1-6.4 Torr, the bimolecular rate constant kl is linearly dependent on the helium concentration and can be expressed as the following mean value:
.. e
.
* A
-2
e
A
t1
*
*
*:
* A
A .
A
. .: A
I
A
A
A
i
A
kl(He) = (8.1 f 0.2) X 10-32[He]
+ (2.4 f 0.4) X cm3 molecule-’ s-l
I so, I ( 1 0 ’ ~cm-3 )
A
Figure 3. Determination of k I I ~ o from z the plot of ( k , - &,)/[SO2] as a function of SO2 concentration for P = 4.3 (A) and 6.4 Torr ( 0 ) .
Straight lines were obtained from least-squares fitting of the experimental data. Results at 6.4 Torr were not suitable for the determination of kIIIm because the influence of SO2as a third body becomes negligible compared to that of helium.
Two interpretations of the intercept value can be discussed. the According to Leu,* this intercept value corresponds to kIIW, rate constant of a bimolecular wall reaction between OH and SO2, and then (8.1 f 0.2) X is the third-order rate constant for the OH SO2 He reaction. However, in a recent work, Wine et a1.6 have made an extensive study of the OH SO2reaction by the flash photolysis method in the pressure range 15-500 Torr, using various diluents (He, Ar, N,, SF6). They used their experimental data and Troe’s theory of addition reactions to calculate the falloff parameters for this reaction. With helium as the third body they calculated a low-pressure-limit third-order rate constant kIIIHe= 1.49 X a t 300 K. By comparing with the assumed third-order value obtained by Leus (kIIIHC = 8.45 X Wine et al. concluded that the pressure range 0.9-10 Torr of Leu’s study corresponded to the falloff region and not to the third-order one. In that case, the value of the nonzero intercept would only show that the OH SO2 H e reaction is still in the falloff regime below 10 Torr. Then the coefficient 8 X in the expression and the rate constant of reaction of k,(He) would not be kIIIHC, 1 should be expressed in its bimolecular form from the above complete formula. Wine et al. used their falloff parameters to reproduce Leu’s experiments, and they found that between 1 and 10 Torr the results could be fitted by a straight line with a slope and an intercept of 1.5 X These results were of 8.81 X in excellent agreement with those reported by Leu.a Our value for the slope is also in very good agreement with both the experimental value of Leus and the calculated one of Wine et a1.6 About the intercept, the value calculated by Wine et aL6 (1.5 X and our own value (2.4 X lO-I5) are not different enough to draw conclusions about the possible occurrence of the OH + SO2wall reaction in our work. To summarize, the value that we obtained for kl(He) agrees with the experimental work of Leua and with the theoretical determination of Wine et a1.,6 leading us to confirm that the pressure range 1-6.4 Torr would correspond to the falloff regime for this reaction. Product Analysis. In this study, a low-energy electron impact source was used for ionization. All attempts to detect reaction products by mass spectrometry were unsuccessful. No reaction product could be detected a t m / e 81 (HOSOZ+), m / e 98 (H2S04+),and m / e 80 (SO3+)(in the presence of Oz). Such a lack of results concerning the coventional mass spectrometric analysis of reaction products was also reported by Leu.s Kinetics of SO, OH in the Presence of 0,and NO. The works of Stockwell and Calvertg and Margitad have led these authors to propose the following mechanism for the reaction of OH with SO2 in the presence of 0,and NO:
+
+
+
Figure 4. Determination of kIIIHefrom the plot of ( k l - k , ) / [ S 0 2 ] kIIIS0~[S02] as a function of helium concentration. Each point is the average of the values obtained with [SO,] = (1-4) X 1Ol5cm-), and the corresponding error is indicated. Dashed line represents a similar plot from the results obtained by Leu.*
in Figure 4 is the average of the data obtained from Figure 1 for . kIIISOz,its average value of 1.3 [SO,] = (1-4) X 1015~ m - ~For X was taken. Error bars represent the standard deviation of the data. It was shown that knHewas not very sensitive to kIIIm when this rate constant was modified in the range of the experimental values ((0.93-1.7) X The plots of A vs. helium pressure could be fitted by a straight line. The slope was (7.8 f 0.2) X and the intercept (2.3 f 0.2) X l@I5. kIItoz and were also calculated simultaneously by a leastassumed kIIIHC squares computer fitting of the overall experimental data by using the following equation: ki = A[He], B[S021i C (b)
+
+
A, B, and C are constant parameters to be calculated. ki, [He],, , helium and [S021i are respectively (kl(i)- k , ( i ) ) / [ S 0 2 ] ithe concentration, and the SOz concentration for the ith experiment. The mathematical treatment of eq b has been described by Draper and Smitht5and already applied to a similar system, for example, by Howard.16 If we identify eq b to eq a, A, B, and C would be (15) Draper,N. R.; Smith, H.Applied Regression Analysis; Wiley: New York, 1966. (16) Howard, C. J . J. Chem. Phys. 1977, 67, 5258.
+
+
+
OH
+ SO2
HOS02 HO2
-
+ NO
+
HOS02
H 0 2 + SO3
.-+
OH + NO2
(1) (2) (3)
Margitad also suggested that an additional reaction could occur in his experiments: HOS02
+ NO
-
products
(4)
By monitoring the OH decay in the presence or in the absence
4146
The Journal of Physical Chemistry, Vol. 90, No. 17, 1986
TABLE II: Chemical System Used for the Computer Fitting of the Experimental Data rate constant,
reaction
---
OH + SO2 + M HOSO2 (1) HOSOl + Oz H02 + SO, (2) HOSOZ+ NO products (4) HOS02 + OH products ( 5 ) HOS02 + wall products ( 6 ) H02 + NO -+ NO2 + OH (3) HO2 + HO2 H202 + 0 2 ( 7 ) HO2 + OH H2O + 0 2 (8) OH + OH H2O + 0 (9) OH + wall products (10) OH + NO2 + M HNO, (11) OH + NO + M HONO (12) +
+
--
+
-
+
cm3m~lecule-~s-I
Martin et al.
c5
IOHl x
10"
(cfi3)
a see text see text see text see text 8.3 X 1.7 X 7 x lo-" 1.9 X 5-15 s-" 1.7 x 10-13 4.5 x 10-14
" k , was calculated for each SO2 and He concentration: k , = 1.33 X 10-30[S0,]+ 7.8 X 10-3z[He]+ 2.3 X b k l ois the first-order loss rate of OH on the reactor wall measured in the absence of SO,. The rate constants of the other reactions were taken from ref 17.
of 0, by the flash photolysis method, Margitan could determine from computer simulation a rate constant for reaction 2 and give an estimation for reaction 4. These rate constants were found and 2.5 X lo-', at room temto be respectively (4 f 2) X perature. In the present discharge flow work, the effect of 0, and NO on the OH SO, reaction was studied by performing two kinds of experiments: (1) 0, and NO were flowed together with SO, through the movable internal tube, which generated a chemical system similar to that used by Margitan; (2) 0, was flowed with SO, through the internal tube, but NO was introduced into the reactor through a side tube located upstream from the EPR cavity. The purpose of these experiments was to monitor by EPR the absolute concentration of OH as a function of reaction time with and without added 0, in the presence of NO. In the sequence of reactions 2 and 3 leading to the conversion of HOz into OH, a significant and measurable decrease in the OH consumption should be observed in the presence of 0,. The experimental OH decay curves had to be fitted by a computer program to get the rate constants of reactions 2 and 4. In the global SO2 NO + 0, introduction experiments, considering the k2 and k4 rate constants reported by Margitad if one wants only one variable parameter in the calculations, 0, and NO must be carefully adjusted so that, for example, k 2 [ 0 , ] >> k4[NO]for k2 fitting and k 4 [ N O ]>> k 2 [ 0 2 ] for k4 fitting. Under the conditions where NO was introduced separately, only reaction 2 occurred in the main reaction zone since NO coming NO, reaction was in too low concentration to from the H interfere. In that case HOz was converted into OH just upstream from the EPR analysis part of the reactor. The dimensions of the EPR cavity led us to introduce NO 5 ms before the analysis zone was entered. This last design was found to be very efficient for the computer fitting of k,. With both systems, the first step of the experiment consisted in recording the OH decay profile as a function of reaction time in the presence of NO but without 0,; the experiment was then repeated with 02,so that the two OH profiles could be easily compared under similar conditions of pressure and SOz concentrations. Most of the experiments were carried out for a total pressure of 2 Torr. This pressure was a good compromise giving a high enough reaction rate for OH + SO, and a good sensitivity for the EPR analysis of OH radicals (1 X lo9 cm-3 for S I N = 1). The chemical system used for the calculations is reported in Table 11. The experiments were carried out with SO, concenand 0, concentrations trations ranging from (1 to 3.5) X lOI5 from 3.5 X loi4 to 1.5 X I O l 5 cm4. NO concentrations were usually lower than 1 X loi4~ m - and ~ , OH initial concentrations
+
+
+
W. B.; Margitan, J . J.; Molina, M. J.; Watson, R. T.; Golden, D. M.; Hampson, R. F.; Kurylo, M. J.; Howard. C. J.; Ravishankara, (17) De More,
A. R. Chemical Kinetics and Photochemical Data for Use in Stratospheric Modeling; Jet Propulsion Laboratory: Pasadena, CA, July 1985; No. 85-37.
I
I 5
10
Figure 5. Example of the experimental decay curves of OH as a function of reaction time obtained at 2 Torr in the SO2 + OH and SO2 OH + O2 reacting systems with introduction of NO 5 ms before analysis (solid lines) and corresponding computer-calculated decay curves of OH (dashed lines) for k2 = (2-4) X lo-" with k, = 5 X lo-',, k , = 50 s-l, and klo = 7 s? (see Table 11).
+
never exceeded 6 X 10" ~ m - ~For . a better fit between experiments and calculations the mixing zone of the reactants was taken into account in the calculations. In the computer simulations of experiments where NO was flowed separately, it was found that the HOSO, NO reaction had very little influence on the OH profile in the presence of 0, (reaction 4 was initially given the rate constant value of 2.5 X reported by Margitad). In addition, the possible influence of the reaction
+
HOSO,
+ OH
-
products
(5)
was checked by giving to it a rate constant of 5 X which can be considered as a reasonable upper limit for such a reaction. Even with such a high rate constant, this reaction was found to be negligible due to the low OH and HOSO2 concentrations in the reactor (a maximum variation of 2% of the OH concentration was obtained from the calculations). Then, HOSOz reactions with NO and OH being negligible, a first series of simulations was carried out by assuming that the only reaction of HOSOz was HOSO, + 0, ( 2 ) . Agreement between experimental and calculated decay curves of OH was obtained with kz = (1-2) X for the lowest 0, concentrations used ([02]mi,, = 3.5 X lOI4 ~ m - and ~ ) with kz = (3-4) X for the highest one ([Oz]max= 1.5 X 10" cm3). When 0, concentrations were low, the calculated concentration of OH was too high compared to the experimental one if k2 values higher than 2X were taken, while correct agreement was obtained with k2 = (3-4) X when high 0, concentrations were used. This result appeared to be significant enough to consider the Occurrence of a missing reaction of HOSO2 that did not produce OH. This missing reaction would have a low effect for high 0, concentrations and would compete with reaction 2 for low 0, concentrations, leading to a lowering of the OH regeneration through reactions 2 and 3. A second series of calculations was then performed in which a rate constant ranging from 0 to 100 s-' was assigned to the missing reaction. Under these conditions, a good fit was obtained between experimental and calculated profiles on OH in the whole range of 0, concentrations with k, = (3.5 f 1) X and 50 s-I for the missing reaction. An example of the computer simulation is given in Figure 5. Thus these results support the existence of a side reaction of HOSO, in our system. This reaction, which appeared to be first order, could be identified as a wall reaction of HOSO,: HOSO,
+ wall
-
products
(6)
When NO was flowed together with SO, and 0,. the reaction HOSO, + NO (4) had to be taken into account provided it occurs with a sufficient rate. Calculations carried out with k4 = 2.5 X lo-', have shown that no correct agreement could be obtained
The Journal of Physical Chemistry, Vol. 90, No. 17, 1986 4147
Discharge Flow Measurements of Rate Constants
obtained by the flash photolysis method. The procedure used by Margitan was similar to that of the present work except that in his experiments O2and NO were always introduced together with SO2 while in our experiments NO could be also introduced downstream from the main reaction zone. To get a best fit between experimental and calculated decay curves of OH, the reaction H O S 0 2 NO (4)was proposed in addition to the rewas derived for action HOS02 O2 (2). A value of 2.5 X k4. In contrast, in our computations this value was found to be too high, and only an upper limit of 5 X lO-I3 could be attributed to k4. If the H O S 0 2 NO reaction really occurs in the SO2 OH O2 NO system, this difference in the k4 values from works done respectively at 50-100 and 2 Torr could mean that k4 is pressure-dependent and therefore would be an addition reaction. But this assumption remains very speculative due to the indirect determination of k4 in both studies. The last point dealing with the comparison between flash photolysis and discharge flow results concerns the wall reaction of HOS02, which is negligible in the flash photolysis experiments. However, the wall recombination reaction of HOS02 suggested in our study could be kept at a low level compared to reaction 2 by increasing the O2concentration (the rate ratio for reactions HOS02 wall (6) and HOS02 + O2 (2) could be lowered to 0.1). Data concerning the direct determination of k2 have been recently reported by Howard.” In this work, k2 was also obtained from a discharge flow experiment by using laser magnetic resonance detection of H02 and chemical ionization of HOS02. The value obtained at room temperature ( k 2 = (4.4X 0.9) X l0-l3) and our value are in good agreement. In addition, the simultaneous detection of H 0 2 and HOS02 allowed a direct measurement of a lower limit of 70% for the step H O S 0 2 + O2 H 0 2 + SO3 (2).
+
+ +
Figure 6. Example of the experimental decay curves of OH as a function of reaction time (solid lines) obtained at P = 2 Torr in the SO2 + OH NO and SO2 OH NO O2reacting systems (global introduction of reactants) and corresponding computer-calculated curves (dashed on the lines) showing the effect of k4 (k4 = (0, 0.5, 1 , and 2) X OH profile in the presence of O2with k2 = 3.5 X k6 = 50 s-’, and k l o = 14 s-I (see Table 11).
+
+
+
+
between experiments and calculations of O H decay curves using for k2 and k6 the values we previously obtained (k2= 3.5 X and k6 = 50 s-l). To get a correct agreement, it was found that a maximum value of 5 X lo-” had to be attributed to k4. An example of the computer simulation is reported in Figure 6. A total of 22 experiments with and without added O2have been computer-simulated, under global and delayed introduction of NO. The best fit between experiments and calculations was obtained with the following rate constants:
-+ -+ + -
HOS02 + O2
HOS02
HOSO2
H02
NO
wall
SO3
k2 = ( 3 . 5 f 1)
products products
k4 I 5
X
k6 = 50
S-’
The error on k2 represents an estimate of the sensitivity of the reacting system to the fitting procedure. The present computer determination of k2 is in good agreement His k2 value was with that of Margitan5 ( k 2= (4f 2 ) X also obtained by computer-fitting of his experimental results
+
+
+
-
Conclusion The present discharge flow study brings additional data at low pressure concerning the OH SO2 addition reaction and the H O S 0 2 O2reaction. In particular, the determination of the rate constant of the reaction HOS02 O2 H 0 2 + SO3 (k2 = (3.5 f 1) X lO-I3) confirms the important role of this reaction in the atmospheric oxidation of SO2. The catalytic mechanism including reactions 1-3 leads to a more linear response of H2S04 concentration changes with changes of SO2 concentration.
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X
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Registry No. OH, 3352-57-6; SO2, 7446-09-5; He, 7440-59-7; HOS02, 15181-46-1; 0 2 , 7782-44-7.
