J. Phys. Chem. 1983, 87, 5425-5429
calculation of kinetic isotope effects on H (D) + HZ (Dz) reactions has been reported previously.'~2J1 These calculations, however, deal with the reactions in the gas phase above room temperature. In order to obtain qualitative information on the hydrogen atom reactions in the solid state at 4 K, the rate constants for reactions 3-6 are calculated here by a simple method such as that used in a recent paper.12 The rate constant ( k ) for the tunneling abstraction is given by
k = ( A / R T ) l m G ( W )exp(-W/RT) dW 0
(8)
where G ( W ) is the permeability of the particle with the kinetic energy of W 3and can be obtained exactly for the unsymmetrical Eckart p0tentia1.l~ A is the frequency factor. Since concentrations of H2 and D2 are practically constant during the proceeding of reactions in solid hydrogen, the reactions can be assumed to be pseudo-firstorder reactions. A is taken here as 1014s-', which is roughly equal to a vibrational frequency of a hydrogen molecule. In order to calculate the permeability (G(W))by use of the unsymmetrical Eckart potential, a barrier height and a thickness of potential energy curve for reactions 3-6 must be assumed. The barrier heights for reactions 3-6 are taken here as 7.8,6.0,6.0, and 7.8 kcal/mol, respective1y.l' The barrier heights for the reverse reactions of reactions 4 and 6 are taken as 6.8 kcal/mol.llc Since reaction 6 is endothermic by 1 kcal/mol, the integration in eq 8 was (11) (a) Karplus, M.; Porter, R. N. Discuss. Faraday SOC. 1967,44,164. (b) Weston, R. E. Science 1967,158,332. (c) Suplinskas, R. J. J. Chern. Phys. 1968,49,5046. (d) Quickert, K. A.; Le ROY,D. J. Zbid. 1970,53,
1325. (e) K ~ p p lG. , W.Zbid. 1973,59,3425. (0M a w , H. R.Zbid. 1980, 7.? .-, -917. - .. (12) Aratono, Y.;Tachikawa, E.; Miyazaki, T.; Nagaya, S.;Fujitani, Y.; Fueki, K. J. Phys. Chem. 1983,87, 1201. (13) For a review, see: Caldin, E. F. Chern. Reo. 1969, 69, 135. (14) (a) Eckart, C. Phys. Reo. 1930,35,1303. (b) Johnston, H. S. J. Phys. Chern. 1962, 62,532.
5425
done over a range from 1 kcal/mol to m. The barrier thickness parameter ( a ) is taken as either 0.6 or 0.5 A, where 1 . 7 6 ~is equal to a width of a potential curve at a half-height when the potential function is symmetric. The barrier thickness in the present calculation is the same as that for the H + H2potential curve16 in the gas phase. The calculated rate constants for reactions 3-6 are summarized in Table 11. Tunneling corrections (F), defined by eq 9, are also shown in Table 11. k is the rate r = k/kclassicd k / ( A exp(-V/RT)l (9) constant that takes account of tunneling and is given by eq 8. kchid is the rate constant that is calculated without taking account of tunneling. V is the height of the potential barrier. The large value of the calculated kDtH,/ kH+D ratio is consistent with the experimental ratio (> 3 X loa) in Table I. The large value of the ratio is due to the tunneling plus the fact that reaction 6 is endothermic and reaction 4 is exothermic. Extremely large values of F indicate that the tunneling effect plays an important role in the reactions at 4 K. Since the rate constants for reactions 3-5 are relatively large, it may be possible for these reactions to take place before ESR measurements. Therefore, the tunneling migration may be probable in solid hydrogen at 4 K. The rate constant for the H + Dzreaction, however, is very small and thus Ht atoms in the D2 matrix cannot migrate by a successive tunneling abstraction. It is highly desirable to calculate the rate constants more precisely by use of an exact potential energy surface in solid hydrogen. Acknowledgment. This work was supported in part by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Science, and Culture. Registry No. Dz, 7782-39-0; H2, 1333-74-0; D, 16873-17-9; H, 12385-13-6. (15) Truhlar, D.G.;Horowitz, C. J. J. Chem. Phys., 1978, 68,2466.
Kinetics and Mechanism of the Oxidation of Aquated Sulfur Dioxide by Hydrogen Peroxide at Low pH James V. McArdiet and Michael R. Hoffmann' W. M. Keck Laboratories, Environmental Engineering Science, California Institute of Technology, Pasadena, California 9 I 125 (Recelved: January 21, 1983)
A stopped-flow kinetic study of the oxidation of sulfur dioxide by hydrogen peroxide was performed over the pH range 0.0-4.5. A rate expression of the following form was verified experimentally: d[S(VI)]/dt = klK,1[H2021[S(IV)](k2[H+] + k3[HAl)/((k-l+ k2[H+]+ k3[HA1)(Ka1+ [H+])J.The following kinetic parameters at 15 O C were determined: kl = (2.6 f 0.5) X lo6 M-' s-', k2/k-l = 16 f 4 M-',k z / k 3 = (5 f 1) X lo2 (HA = acetic acid), AH*'= 37 f 2 kJ mol-', and ASI1 = 4 f 4 J K-' mol-'. The reaction proceeds via a nucleophilic displacement of HSOf by Hz02to form a peroxymonosulfurousacid intermediate which undergoes acid-catalyzed rearrangement to form product: S02.Hz0 HS03- + H+ (Kal),H2Oz + HSO, HOOSO; (kl, k-J, HOOSO; H+ H+ + HSO, (k2),HOOS02- + HA HA + HS04- ( k 3 ) . Application of the above rate expression to reactions occurring in hydrometeors is discussed.
+
-
-
The oxidation of sulfur dioxide by oxygen, ozone, nitrogen dioxide, or hydrogen peroxide in aqueous microdroplets or hydrometeors has been suggested as a non-
--
'Current address: Smithkline Beckman Corp., Philadelphia, P A 19101. 0022-3654/83/2087-5425$0 1.50/0
photolytic pathway for the production of sulfuric acid in humid Oxidation by H202may be the (1) Hoffmann, M.R.;Boyce, s. D. "Advances in Environmental Science and Technology"; SChwdz, S. E., Ed.; Wiley: New York, 1983;v01. 12, pp 147-89.
0 1983 American Chemical Society
5426
The Journal of Physical Chemlstty, Vol. 87,
No. 26, 1983
preferred pathway due to favorable kinetics and thermodynamics at low pH. (The Henry's law equilibrium confor H202(g)==H202(1)is 1.65 stant, represented by HHno2, X lo5 M atm-l.) Hydrogen peroxide is generated in the gas phase by the recombination of hydroperoxyl radicals3 and at air-water interfaces due to photoinduced redox proce~ses.~Kok and co-workerss have reported hydrometeor concentrations of H202as high as 50 pM. The kinetics of this reaction have been studied previously by Mader,G Hoffmann and Edwards,' Penkett et al.,B and Martin and D a m s ~ h e n . ~Madera determined that S(1V) oxidation was characterized by a multiterm rate expression over the pH range 8-13. Evidence for specific and general acid catalysis by phosphate, carbonate, and arsenate was presented? Hoffmann and Edwards reported a two-term rate law for the pH range 4-8 and proposed that the reaction occurs via a nucleophilic substitution by H20zon HS03- to form a peroxymonosulfurous acid intermediate, which undergoes rearrangement assisted by H+ or HA, to form HS04-, where HA is a suitable weak acid such as phosphoric, citric, pivalic, acetic, or phthalic acid. Penkett et a1.8 confirmed the two-term rate law reported by Hoffmann and Edwards,' but they reported a hydrogen ion reaction order of 0.7 over the pH range 4-6 as opposed to an order of 1 in the aforementioned study. Results reported by Martin and Damscheng support the mechanism postulated by Hoffmann and Edwards. They found a single-term rate expression with a direct dependence on [H+]from pH 1-3 and a reciprocal dependence on [H+] below pH 1. I t was our intention in undertaking this study to define carefully the dependence of rate on pH. DasguptalO asserts that the data collected over the pH range of 0-13 by the above investigatorseg cannot be interpreted solely in terms of the Hoffmann and Edwards mechanism. He argues in favor of a radical pathway as a partial explanation for a variable pH dependencythrough the neutral domain. With renewed interest in the reaction of H20zand S(1V) due to its potential importance to the production of atmospheric acidity," we have decided to extend our earlier study to a pH domain (0-4) encountered in atmospheric water droplets and aquated urban aerosols. Of particular interest are the exact pH dependency, the role of general acid catalysis at low pH, and the contribution of freeradical pathways.
Methods All kinetic measurements were made on a Durrum-Dionex Model D-110 stopped-flow spectrophotometer. Absorbance output was digitized with a Gould Biomation Model 2805 wave form analyzer equipped with a variable input sensitivity and variable sampling interval. One hundred data points were collected for each kinetic determination. At least six kinetic determinations were made (2) Jacob, D. J.; Hoffmann, M . E. J. Geophys. Res. 1983,88,6611-21. (3) Chaimedes,W. L.;Davis, D. D. J . Geophys. Res. 1982,87,4863-77. ( 4 ) Zika, R. G.; Saltzman, E.; Chaimedes, W. L.; Davis, D. D. J. Geophys. Res. 1982,87, 5015-7. (5) (a) Kok, G.L.; Darnall, K. R.; Winer, A. M.; Pitts, J. N., Jr.; Gay, B. W. Enuiron. Sci. Technol. 1978,12,1077-SO. (b) Kok, G. L. Atmos. Enuiron. 1980, 14, 653-6. (c) Richards, L. W.; Anderson, J. A.; Blumenthal. D. L.: McDonald. J. A. Zbid. 1983.17, 911-14. (6) Mader, P.M.J. Am'. Chem. SOC.1958,80, 2634-9. (7)Hoffmann, M. R.; Edwards, J. 0.J.Phys. Chem. 1975, 79,2096-8. (8)Penkett, S. A.; Jones, B. M. R.; Brice, K. A,; Eggleton, A. E. J. Atmos. Enuiron. 1979, 13, 123-37. (9) Martin, L.R.; Damschen, D. E. Atmos. Enuiron. 1981,15,1615-21. (10) Dasgupta, P. K. Atmos. Enuiron. 1980,14,620-1. (11) Waldman, J. M.;Munger, J. W.; Jacob, D. J.; Flagan, R. C.; Morgan, J. J.; Hoffmann, M. R. Science 1982,218,677-9.
McArdle and Hoffmann I
I
I
05
IO
1.5
I
I
I
I
20
25
30
3.5
I50
125
100
B
75
2c
50
25
0
0
PH Figure 1. Dependence of kob4 on pH for the oxidation of S(IV) by hydrogen peroxide at 15 ' C . The solid line represents the leastsquares fit to the data.
for each value of kobsd. Above pH 1.8, an average of 12 determinations was made for each value of kOw Data were reduced by a DEC MINC-23 computer and were permanently stored on magnetic disks. Constant temperature was maintained at 15 "C with a Haake FK2 constanttemperature water bath. Water was circulated to the optical cuvette and reactant syringes by a 1/3 hp Oberdorfer pump. A Beckman Altex 071 pH meter was used to determine [H+] in buffered solutions. In unbuffered solutions, hydrogen ion concentrations were calculated by dilution of standardized HC1 solution. Water used to prepare reagent solutions was obtained from a Milli-Q water purification system (Millipore) and had a resistivity of 18 MQ-cm. Ionic strength ( p = 1.0 M) was maintained with sodium chloride, and all reagents were analytical grade. EDTA was used (10 pM) to inhibit trace-metal catalysis. The extent of reaction was monitored at 280 nm (the absorbance maximum for S02(aq))for reactions at pH 51.8 (the pKa1of S02(aq))and at 220 nm for unbuffered reactions at pH >1.8. Loss of H202and S(1V) contributes to the decrease in absorbance at 220 nm. The reaction at pH 0.5 was followed at both 220 and 280 nm to determine if kobsdvalues are dependent upon the wavelength of observation. The concentration of S(1V) was determined directly by weight of Na2S03 dissolved in a volumetric flask. The concentration of Hz02in approximately 30% stock solution was determined periodically according to the method given by Wilson and Wilson.12 In unbuffered M solution, the total S(IV) concentration was 6 X M in order to except at pH 3.4 where it was 5 X maintain an eightfold excess of hydrogen ion concentration, and the hydrogen peroxide concentration was at least 7 times the S(1V) concentration. In acetate-buffered solution, S(1V) was maintained in at least 10-fold excess over H202. The H202concentration was 1 X 10" M, and the reaction was followed at 260 nm. In formate buffers, H202 was maintained in at least sevenfold excess over S(1V). M, and the reacSulfur(1V) concentration was 2.4 X tion was followed at 220 nm. In solutions buffered by either trichloroacetic acid or bisulfate, the S(1V) concenM, the H202concentration was 4.24 tration was 6 X X M, and the reaction was followed at 280 nm. (12) Wilson, C. L.;Wilson, D. W., Eds. "Comprehensive Analytical Chemistry";Elsevier: New York, 1960; Vol. lB, p 278.
The Journal of Physical Chernjstty, Vol. 87, No. 26, 1983
Oxidation of Aquated Sulfur Dioxide
5427
TABLE I : Kinetic Data for t h e Oxidation of S(1V) by Hydrogen Peroxide in the Absence of Buffer at 1 5 PH 0.00 0.10 0.40 0.50 0.70 1.00 1.20 1.40 1.60 1.80 2.20 2.60 3.00 3.40 a [H,O,] = 4.24 X at pH 3.40 [S(IV)] =
kobsd,
s-'
kcalcdr s-'
15.6 i: 0.3 23.8 i 0.4 39.6 i 0.6 48.8i 1.3 78.1 f 2.6 119.6 f 1.0 137.0 f 4.0 139.4 f 7.7 137.4f 2.8 128.0 f 10.0 69.4 f 2.9 32.7 % 3.4 10.4 i 0.4 5.2 i 0.4 M. [S(IV)] = 6 X 5X M.
18.6 22.9 41.6 50.0 70.0 104.2 123.6 134.1 132.2 118.5 74.6 37.2 16.4 6.8
M except
Results For oxidation of S(1V) by H202under pseudo-first-order conditions with hydrogen peroxide in excess, plots of In (A, - A,) vs. t were linear (1.2 1 0.99) for between 50% and 90% of the reaction. The linearity of the assumed firstorder relationships establishes the fact that the rate of reaction is first order in S(1V). A study of the dependence of rate on the concentration of hydrogen peroxide was done at pE1 0.4. A plot of kobsdvs. hydrogen peroxide concentration up to 1.70 mM yields a straight line (1.2 = 0.99) with a slope of (9.43 f 0.20) X lo4 M-l s-l and an intercept of -0.1 f 1.2 s-l. Thus, the rate of reaction is also first order in hydrogen peroxide. The dependence of kobsd on pH in the absence of a buffer is shown by the experimental points in Figure 1 and is listed in Table I. The pH dependence at low pH may be investigated further by plotting kobd vs. the reciprocal of the proton concentration. Such a plot for the pH range 0.0-0.7 yields a straight line (r2 = 0.96) with a slope of 15.4 f 0.3 M s-l and an intercept of 1.5 f 0.5 s-I. The data from pH 2.6 to 3.4 also yield a reasonable straight line (r2 = 0.96) when kobsd is plotted against the proton concentration (slope = (10.0 f 0.8) X lo3 M-l s-l and intercept = 0.7 & 0.7). Thus, the rate becomes inversely first-order dependent on hydrogen ion at low pH, and it becomes directly first-order dependent on hydrogen ion at higher pH. Data for pH 0.5 were collected at two wavelengths. At 280 nm with [H202]= 4.24 X lo4 M and [s(Iv)] = 6 X M, kobsdwas found to be 48.7 f 1.2 s-l, and at 220 nm with the same reagent concentrations kobsd was found to be 49.0 f 1.6 s-l. Earlier investigations showed that the oxidation of S(IV) by hydrogen peroxide is sensitive to general acid catalys k e 8 In acetate buffer of pH 4.45 with S(1V) present in excess, plots of In (A,- A,) vs. t were linear for about 90% of the reaction and established that the rate of reaction is first order in hydrogen peroxide. A plot of kobsdv8. the concentration of S(1V) up to 49.5 mM with the acetic acid concentration equal to 30.0 mM is linear (r2= 0.99) with a slope of (1.51 f 0.09) X lo3 M-l s-l and an intercept of -0.2 f 1.2. This plot establishes a first-brder dependence on S(1V). Figure 2 demonstrates that two pathways are operating in the oxidation of S(1V) by hydrogen peroxide in the presence of acetic acid. One pathway has a firstorder dependence on acetic acid, and the rate of the other pathway is independent of acetic acid. The data in Figure 2 at 15 "C yield a slope of (2.98 f 0.18) X lo4M-2 s-l and an intercept of (6.0 f 0.9) X lo2 M-l s-l with r2 = 0.99. The dependence of kobsdon formic acid at pH 3.40 is listed in Table 11. A linear dependence of kobsd on formic acid was not observed. The dependence of kobsd on either
-r m I
0 X
[HAc]x
IO'
(MI
Figure 2. Dependence of k,,/[S(IV)] on the concentration of acetic acid for the oxidation of S(IV) by H,Op at pH 4.45; [S(IV)] = 10.0 and 20.0 mM for each point: (a) 6, (b) 15, (c) 21, (d) 30 'C.
TABLE 11: Kinetic Data for the Oxidation of S(1V) b y Hydrogen Peroxide in t h e Presence of Buffers a t 15 'C [HA], M kb 1.0 X lo-' 20.2 f 1.6 5.0 x 41.7 i 3.4 1.5 x lo-' 73.2 f 8.5 2.0 X lo-, 14.9 f 0.3 5.0 X lo-' 14.5 f 0.2 5.0 X lo-' 17.3 i 0.6 1.0 X lo-' 16.0 i 0.8 5.0 x 16.2 i 0.7 5.0 X lo-, 16.9 f 0.7 5.0 x lo-' 17.9 f 0.4 1.0 X lo-' 18.7 i 0.8 2.0 X 1O-I 18.1 i 0.7 a = trichloroacetic acid. Quantities reported are k&sd (s-l) for formic acid and kobsd[H+](M s-') for C1,AcOH and HSO;. The quantity kobsd[H+]is reported in the latter two cases to compensate for the slightly varying values of pH according to eq 10. PH 3.40 3.40 3.40 0.71 0.72 0.64 0.62 0.65 0.69 0.69 0.65 0.64 C1,AcOH
HAa
formic formic formic C1,AcOH C1,AcOH C1,AcOH C1,AcOH HS0,HS0,HS0,HSO; HS0,-
trichloroacetic acid or bisulfate at pH -0.7 also is listed in Table 11. The pH of individual solutions varied slightly so a correction is made by comparing kobsd[H+] to [HA]. Inspection of the data in Table 11 shows the kobsd[H+] varies by a factor of 1.3 for a general acid concentration that varies by a factor of 400 in the case of bisulfate. Therefore, kobsdappears to be independent of either trichloroacetic acid or bisulfate at pH -0.7. The above kinetic information is consistent with the following mechanism: fast
S02(aq)e H++ HS03-
(&)
(1)
(3)
(4)
This mechanism is similar t o the mechanism originally postulated by Hoffmann and Edwards' and is consistent with the absence of dithionate as a pr0duct.I According to this mechanism the rate of appearance of product is given by v = d[HzS04]/dt = k2[H+][O2SOOH-] + k3[HA][OzSOOH-] (5) From steady-state considerations the concentration of the
5420
The Journal of Physical Chemistty, Vol. 87, No. 26, 1983
peroxymonosulfurous acid intermediate, HOOSO;, may be obtained. [HOOSOz-] = kiIHzOz1[HSO3-I/(k-i + kz[H+l + k,[HAI) (6) The concentration of HS03- may be expressed as a function of total S(1V).
(7) WS03-3 = [S(IV)IKa1/Wa1 + [H+Il Substitution of eq 7 into eq 6 and then eq 6 into eq 5 yields
kJH-41) (8) This rate law applies to the entire pH range in this study. In the absence of buffer and with hydrogen peroxide in excess, kobsd is given by kobsd = klk~Kal[H+I [H~Ozl/((k-,+ kz[H+I)(Ka1+ [H+l)) (9)
Equation 9 also applies to the entire pH range studied. Estimates of the various parameters in eq 9 may be obtained by considering behavior at the extremes of pH. At low pH, [H+] >> Kal. (The value of Kal at 15 "C is 1.82 X M.13 See discussion below.) The observed inverse first-order dependence on hydrogen ion at low pH requires that kz[H+] >> k-'. Equation 9 reduces to kobd =
~IK~I[H@zI/[H+I
(10)
from pH 0.0 to -0.7 with kl = (2.06 f 0.05) X lo6 M-l s-'. A temperature-dependence study at pH 0.40 gave AH*' = 37 f 2 kJ mol-' and ASS1= 4 f 4 J K-' mol-' (or 8.8 kcal mol-' and 1.0 cal K-l mol-', respectively) for the forward reaction of eq 2. The temperature dependence of Kal is given by Deveze and Rumpf.13 At higher pH, the firstorder dependence on hydrogen ion requires that k-l >> kz[H+]. A t pH 2.6, Kal = 7.25[H+]. Thus, at pH values above 2.6, eq 9 reduces to kobsd kobsd
( k ~ h / k - [H+1 J [HzOZI
(11)
kZK[H+][HZOZl
(12)
with It& N 2.4 X lo7 M-z s-' and kz/k-l 12 M-'. At pH 4.45 in the presence of acetic acid and with S(1V) present in excess, the rate expression is kobsd
= ki[S(IV)l(kz[H+l + h[HA])/(k-,
+ &[HA])
McArdle and Hoffmann
wts(i) = a(i)-Z (16) The values of kobad were calculated according to eq 9 and the trial parameters were those found in the high- and low-pH regions as described above. Values of the parameters obtained after least-squares refinement are kl = (2.6 f 0.5) X lo6 M-' s-' and k z / k - l = 16 f 4 M-'. The solid line in Figure 1 is a plot of kobsd using these values for the parameters. Calculated values of pseudo-first-order rate constants ( k d d ) are compared to the experimental values in Table I. Discussion The mechanism presented herein is essentially the same as previously postulated for the pH range 4-8.7 However, the present mechanism assumes that the formation of HS03- from SOz(aq)is fast compared to other steps in the mechanism. Unfortunately, there is no agreement in the literature on the rate of formation of HS03-. Reported rate constants vary by 10 orders of magnitude from 2.18 X (20 OC)14 to 1.06 X lo3 (20 "C) s-'.16 The absence of first-order rate-limiting behavior in this study means that, according to our mechanism, the rate of formation of HSOc must be greater than 160 s-l (the largest kobsd measured). This value is consistent with some reports in the literature1"" but inconsistent with others.14 However, the rate reported by Wang and Himmelblau14has been criticized for being too 10w.l~ A more recent study by Roberts16establishes a lower specific rate of 320 s-l. Thus, it is likely that the formation of HS03- is fast compared to other steps in the mechanism. There is a similar disagreement over values for Kal,but the values have a smaller range. Huss and Eckertlg critically reviewed reported values of Kal and reevaluated Kal at 25 "C by independent conductometric and spectrophotometric methods. The value determined by either method agrees well with the earlier temperature-dependent study of Deveze and Rumpf.13 Because the temperature-dependent data are needed in this work, the values of Deveze and Rumpf13have been used. The thermodynamic acid-dissociation constant was given for dilute solutions. However, the present data were collected at an ionic strength of 1.0 M. Clarkez0has discussed the importance of ionic strength effects in the kinetics of aqueous sulfur dioxide. To account for ionic strength effects, a correction of the acid-dissociation constant reported by Deveze and Rumpf13 was made according to the Davies approximation:
(13)
The linear dependence of rate on acetic acid shown in Figure 2 indicates that kl>> k3[HA] for concentrations of acetic acid up to 0.18 M. A pseudo-second-order constant may be calculated by dividing eq 13 by the S(1V) concentration. kobsd/[S(IV)] = klkz[H+l/k-l
+ klk3[HA]/k-l
(14)
At 15 OC,k& = (3.0 f 0.2) X 104 M-2 s-', k& = (1.7 f 0.3) X lo7 M-2 s-', kZ/k3 = (5 f 1) X lo2, and k - l / k 3 44 M. The parameters obtained in the absence of buffer were further refined by using nonlinear least-squares analysis in which the function minimized is a. n
=
i=l
[(hobad - kcalcd)ds(i)12
(15)
where (13) Deveze, D.; Rumpf, P. C. R. Hebd. Seances Acad. Sci. 1964,258, 6135-8.
log 7 = -A$
(+ ~
1
""
p'/Z
-0.2~)
(17)
where A = (1.82 X 106)(eT)-3/2(e = dielectric constant). Application of eq 17 yields values of kl = 1.3 X lo6 M-l s-', AH*'= 8.8 f 0.5 kcal mol-', and AS* = -1 f 1 cal K-l mol-'. By comparison to these parameters reported in the Results section, it is seen that corrections for ionic strength effects are not large. A near-zero activation entropy is expected for a reaction between a singly charged ion and a neutral moleculez1as (14) Wang,J. C.; Himmelblau, D. M. AIChE J. 1964, 10, 574-80. (15) Betta, R. H.; Voss, R. H. Can. J. Chem. 1970,48, 2035-41. (16) (a) Roberts, D. L. Ph.D. Thesis, California Institute of Technology, 1979, Pasadena, CA, pp 26,162. (b) Roberts, D. L.; Friedlander, S. K. AZChE J. 1980,26,593-610. (17) Eigen, M.; Kustin, K.; Maass, G. 2.Phys. Chem. 1961,30,130-6. (18) Beilke, S.; Lamb, D. AZChE J. 1975, 21, 402-4. (19) Huss, A., Jr.; Eckert, C. A. J. Phys. Chem. 1977, 81, 2268-70. (20) Clarke, A. G.Atmos. Enuiron. 1981, 15, 1591-5.
Oxidation of Aquated Sulfur Dioxide
The Journal of Physical Chemistty, Vol. 87, No. 26, 1983
in the forward reaction of eq 2. A possible structure for the transition-state complex is the following:
5429
where G A and a are constants. The absence of a linear dependence of rate on the concentration of formic acid may be due to the failure of the inequality k1>> k3[HA]. If, at higher concentrations of HA, kl N k3[H 1, then the behavior predicted is firstorder linear dep ndence of rate on HA at very low concentrations of HA and no dependence of rate on HA at very high concentrations of HA. The independence of the observed rate on HA at pH 0.7 simply reflects the fact that at high proton concentration k2[H+]>> k3[HA]. The rate of aqueous-phase oxidation of S(1V) from pH 1 to 5 in an open atmosphere can be calculated by substituting eq 19 and 20 into eq 8. The symbol P represents W2021 =F"z~zH~z~z (19)
t
bThe activated complex retains the same charge as the sum of the charges of the reactants; therefore, the degree of solvent ordering, which is largely responsible for the entropy of a system, is not expected to change. If the transition state does resemble the structure suggested above, then it is easy to see that HS03- should be a much more reactive species than S032-because water is a more effective leaving group than hydroxide. The structure of SOz(aq)is not known with certainty, but the existence of HzS03in solution has never been demonstrated. Hydrated but uncombined SO2 is the principal if not exclusive form of sulfur dioxide in solution,16 and the transition-state complex pictured above would be difficult to attain from SOz(aq) in acidic solution. Very negative values of AS* for reactions between an ion and a neutral molecule have been attributed to bond formation between substrate and nucelophile before departure of the leaving group.21 Since AS*is near zero, a mechanism of the latter type is unlikely in the present case. Activation parameters reported by Penkett et for this reaction have little meaning because they simply reflect the temperature dependence of kobsd. Other arguments supporting the peroxymonosulfurous acid intermediate have been presented previ~usly.~ Further support for the postulated mechanism of eq 1-4 comes from agreement of the value of k2K in unbuffered solution at pH 2.6-3.4 (2.4 X lo7 M-2 s-l ) and the value of the same parameter from the intercept of the data in Figure 2 (1.7 X lo7 M-2 s-l ). The absence of a contribution by a free-radical pathway to the mechanism was ascertained at pH 0.50 by making kinetic determinations in the presence of the free-radical M concentration. scavenger mannitol, present in 4 X The average value of kobsd obtained in the presence of mannitol is 48.4 f 1.0 s-l with [H202]= 4.24 X lo4 M and M. In the absence of mannitol, k,bsd [S(IV)] = 6 X was determined to be 48.8 f 1.3 s-l with the same reagent concentrations. Mannitol has been used as a free-radical scavenger in the autooxidation of SO:-.22 The dependence of rate on acetic acid was noted earlier by Penketta8 The value of k2/k3 reported herein is about one-sixth that of the earlier value, however, and no obvious reason exists to explain this discrepancy. A similar analysis of the data of Hoffmann and Edwards7yields k z / K 3 = 2.5 X lo5 for the reaction carried out in the presence of H2P0,. For at least these two acids, therefore, k3 varies qualitatively with KHA as predicted by the Bronsted equation (eq 18):23
k, = GAKHAa
(18)
(21) Moore, J. W.; Pearson, R. G. "Kinetics and Mechanism",3rd ed.; Wiley: New York, 1981, pp 26&72. (22) Backstrom, H. L. J. J. Am. Chem. SOC.1927,49, 1460-72.
[S(IV)l = Psop~soz([H'l+ Kal)/[H+l
(20)
partial pressure. Assuming the absence of any appreciable concentration of a general a d 2 and evaluating the rate constants yields v =
(7.6 x 105 M-I s-1)pHpOzHH~O~pSOpHS02 1.0 16 M-l[H+]
+
(21)
The rate law given here agrees with that of Martin and Damschengand the predictions of atmospheric reactivity rate also agree well. At 15 "C, HH20z = 1.65 X lo5 M atm-l (ref 9), Hsop= 1.67 M atm-' (ref 24), and assuming pH 3.0, P H ~=oPSO ~ = 1 ppb, the rate of appearance of S(V1) is df h-l. As is obvious from eq 21 there is little 7.4 X dependence of rate on pH from 2 to 5. According to the treatment of S ~ h w a r t and z ~ ~Schwartz and Freiberg,26the aqueous-phase reaction is not limited by mass transport until the atmospheric concentration of either reagent reaches about 100 ppb. This conclusion is independent of pH. The rate-limiting concentration of either reagent is far above estimates for typical atmospheric conditions, and thus it appears that under all but the most extreme conditions eq 21 will correctly predict the aqueous-phase rate of oxidation of SO2 by H20z. The absence of masstransport limitation in the present reaction directly contradicts an earlier concl~sion.~ In preliminary investigations, the presence of either iron(I1) or formaldehydein the reaction mixtures described above has been found to alter markedly the reaction kinetics. These effects are now being studied in detail and will be the subject of forthcoming reports. Acknowledgment. We are grateful to the US. Environmental Protection Agency (R808086-1)for providing financial support for this research and to the Sloan Foundation Fund administered by Caltech which provided the necessary instrumentation. Registry No. SOz, 7446-09-5; HzOz, 7722-84-1; HzSO,, 766493-9; HSO,, 14996-02-2; HOOSO,, 87712-70-7; sulfate, 14808-79-8, (23) Edwards, J. 0. "Inorganic Reaction Mechanisms"; Benjamin: New York, 1964; p 18. (24) Rabe, A. E.; Harris, J. F. J. Chem. Eng. Data 1963, 8, 333-6. (25) Schwartz, S.E. In "Acid Precipitation: SO2, NO, NOpOxidation Mechanisms"; Calvert, J. G., Ed.; Ann Arbor Science: Ann Arbor, MI, in press. (26) Schwartz, S.E.; Freiberg, J. E. Atmos. Enuiron. 1981, 1 5 , l.129-44.
