A [h

with k = 7.5 ± 1.16 x 107 M~2 s_1 and K = 13 M"1 at 298 K.

Noting that H202 is a very weak electrolyte, that [H+][HSOj ] = //so2^si/?so2, and that, for pH > 2, 1 + A"[H+] ~ 1, one concludes that the rate of this reaction is practically pH independent over the pH range of atmospheric interest. For a H202(g) mixing ratio of 1 ppb the rate is roughly 300pMlr1 (ppb S02r' (700% S02(g) h"1 (gwater/m3 air)"1). The near pH independence can also be viewed that the pH dependences of the S(IV) solubility and of the reaction rate constant cancel each other. The reaction is very fast and indeed both field measurements (Daum et al. 1984) and theoretical studies (Pandis and Seinfeld 1989b) have suggested that, as a result, H202(g) and S02(g) rarely coexist in

FIGURE 7.17 Second-order rate constant for oxidation of S(IV) by hydrogen peroxide defined according to d[S(VI)]/df = fc[H202(aq)] [S(IV] as a function of solution pH at 298K. The solid curve corresponds to the rate expression (7.84). Dashed lines are arbitrarily placed to encompass most of the experimental data shown.

Mader,1958 Hoffmann &

Edwards, 1975 Penkett et al., 1979 Martin & Damschen, 1981 Cocks et al., 1982 Kunen et al., 1983 (22°C) McArdle & Hoffmann, 1983 McArdle & Hoffmann (15°C) Lee et al., 1986 (22°C)

FIGURE 7.17 Second-order rate constant for oxidation of S(IV) by hydrogen peroxide defined according to d[S(VI)]/df = fc[H202(aq)] [S(IV] as a function of solution pH at 298K. The solid curve corresponds to the rate expression (7.84). Dashed lines are arbitrarily placed to encompass most of the experimental data shown.

clouds and fogs. The species with the lowest concentration before cloud or fog formation is the limiting reactant and is rapidly depleted inside the cloud or fog layer.

The reaction proceeds via a nucleophilic displacement by hydrogen peroxide on bisulfite as the principal reactive S(IV) species (McArdle and Hoffmann 1983)

and then the peroxymonosulfurous acid, S0200H , reacts with a proton to produce sulfuric acid:

The latter reaction becomes faster as the medium becomes more acidic.

7.5.3 Oxidation of S(IV) by Organic Peroxides

Organic peroxides have also been proposed as potential aqueous-phase S(IV) oxidants (Graedel and Goldberg 1983; Lind and Lazrus 1983; Hoffmann and Calvert 1985; Lind et al. 1987).

Methylhydroxyperoxide, CH3OOH, reacts with HSOj according to

with a reaction rate given in the atmospheric relevant pH range 2.9-5.8 by

where klxl = 1.7 ± 0.3 x 107 M-2 s_1 at 18°C and the activation energy is 31.6 kJmol_1 (Hoffmann and Calvert 1985; Lind et al. 1987). Because of the inverse dependence of [HSO3 ] on [H+] the overall rate is pH independent (Figure 7.18).

FIGURE 7.18 Reaction rates for the oxidation of S(IV) by CH3OOH and CH3C(0)00H as a function of pH for mixing ratios [S02(g)] = 1 ppb, [CH3OOH(g)] = 1 ppb, and [CH3C(0)00H(g)] = 0.01 ppb.

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The corresponding reaction involving peroxyacetic acid is

with a rate law for pH 2.9-5.8 given by

where ka = 601M"1 s"1 and kb = 3.64 ± 0.4 x 107 M 2 s"1 at 18°C (Hoffmann and Calvert 1985; Lind et al. 1987). The overall rate of the reaction increases with increasing pH (Figure 7.18).

The Henry's law constants of methylhydroperoxide and peroxyacetic acid are more than two orders of magnitude lower than that of hydrogen peroxide (Table 7.1). Typical mixing ratios are on the order of 1 ppb for CH3OOH and 0.01 ppb for CH3C(0)00H. Applying Henry's law, the corresponding equilibrium aqueous-phase concentrations are 0.2 pM and 5 nM, respectively. These rather low concentrations result in relatively low S(IV) oxidation rates on the order of 1 pMh-1 (for a S02 mixing ratio of 1 ppb), or equivalently in rates of less than 1% S02 h 1 for a typical cloud liquid water content of 0.2 gm"3 (Figure 7.18). As a result these reactions are of minor importance for S(IV) oxidation under typical atmospheric conditions and represent only small sinks for the gasphase methyl hydroperoxide (0.2% CH3OOHh ') and peroxyacetic acid (0.7% CH3C(0)00H h~1) (Pandis and Seinfeld 1989a).

7.5.4 Uncatalyzed Oxidation of S(IV) by 02

The importance of the reaction of S(IV) with dissolved oxygen in the absence of any metal catalysts (iron, manganese) has been a controversial issue. Solutions of sodium sulfite in the laboratory oxidize slowly in the presence of oxygen (Fuller and Crist 1941; Martin 1984). However, observations of Tsunogai (1971) and Huss et al. (1978) showed that the rate of the uncatalyzed reaction is negligible. The observed rates can be explained by the existence of very small amounts of catalyst such as iron (concentrations lower than 0.01 pM) that are extremely difficult to exclude. It is interesting to note that for real cloud droplets there will always be traces of catalyst present (Table 7.5), so the rate of an "uncatalyzed" reaction is irrelevant (Martin 1984).

TABLE 7.5 Manganese and Iron Concentrations in Aqueous Particles and Drops

Medium

Manganese (uM)

Iron (liM)

Aerosol (haze)

0.1-100

100-1000

Clouds

0.01-10

0.1-100

Rain

0.01-1

0.01-10

Fog

0.1-10

1-100

I rieviuus rage

7.5.5 Oxidation of S(IV) by 02 Catalyzed by Iron and Manganese

Iron Catalysis S(IV) oxidation by 02 is known to be catalyzed by Fe(III) and Mn(II):

This reaction has been the subject of considerable interest (Hoffmann and Boyce 1983; Hoffmann and Jacob 1984; Martin 1984; Hoffmann and Calvert 1985; Clarke and Radojevic 1987), but significantly different measured reaction rates, rate laws, and pH dependences have been reported (Hoffmann and Jacob 1984). Martin and Hill (1987a,b) showed that this reaction is inhibited by increasing ionic strength, the sulfate ion, and various organics and is even self-inhibited. They explained most of the literature discrepancies by differences in these factors in various laboratory studies.

In the presence of oxygen, iron in the ferric state, Fe(III), catalyzes the oxidation of S(IV) in aqueous solutions. Iron in cloudwater exists both in the Fe(II) and Fe(III) states and there are a series of oxidation-reduction reactions cycling iron between these two forms (Stumm and Morgan 1996). Fe(II) appears not to directly catalyze the reaction and is first oxidized to Fe(III) before S(IV) oxidation can begin (Huss et al. 1982a,b). The equilibria involving Fe(III) in aqueous solution are

FeOH2+ + H20 ^ Fe(OH)2 + H+ Fe(OH)2 + H20 ^ Fe(OH)3(s) + H+

with Fe3+, FeOH2+ Fe(OH),+ , and Fe2(OH)2+ soluble and Fe(OH)3 insoluble. The concentration of Fe3+ can be calculated from the equilibrium with solid Fe(OH)3 (Stumm and Morgan 1996)

For pH values from 0 to 3.6 the iron-catalyzed S(IV) oxidation rate is first order in iron, is first order in S(IV), and is inversely proportional to [H+] (Martin and Hill 1987a):

This reaction is inhibited by ionic strength and sulfate. Accounting for these effects the reaction rate constant is given by

where [S(VI)] is in M. A rate constant k-, 9, =6 s 1 was recommended by Martin and Hill (1987a). Sulfite appears to be almost equally inhibiting as sulfate. This does not pose a problem for regular atmospheric conditions ([S(IV)] <0.001 M), but the preceding rate expressions should not be applied to laboratory studies where the S(IV) concentrations exceed 0.001 M. This reaction, according to the rate expressions presented above is very slow under typical atmospheric conditions in this pH regime (0-3.6).

The rate expression for the same reaction changes completely above pH 3.6. This suggests that the mechanism of the reaction differs in the two pH regimes and is probably a free radical chain at high pH and a nonradical mechanism at low pH (Martin et al. 1991). The low solubility of Fe(III) above pH 3.6 poses special experimental problems. At high pH the reaction rate depends on the actual amount of iron dissolved in solution, rather than on the total amount of iron present in the droplet. In this range the reaction is second-order in dissolved iron (zero-order above the solution iron saturation point) and first order in S(IV). The reaction is still not very well understood and Martin et al. (1991) proposed the following phenomenological expressions (in Ms-1)

for the following conditions:

[S(IV)] ~ lOpM, [Fe(III)] > 0.1 pM, I < 0.01 M, [S(VI)] < lOOpM, and T = 298K.

Note that iron does not appear in the pH 5 to 7 rates because it is assumed that a trace of iron will be present under normal atmospheric conditions. This reaction is important in this high pH regime (Pandis and Seinfeld 1989b; Pandis et al. 1992).

Martin et al. (1991) also found that noncomplexing organic molecules (e.g., acetate, trichloroacetate, ethyl alcohol, isopropyl alcohol, formate, allyl alcohol) are highly inhibiting at pH values of 5 and above and are not inhibiting at pH values of 3 and below. They calculated that for remote clouds formate would be the main inhibiting organic, but by less than 10%. On the contrary, near urban areas formate could reduce the rate of the catalyzed oxidation by a factor of 10-20 in the high-pH regime.

Manganese Catalysis The manganese-catalyzed S(IV) oxidation rate was initially thought to be inversely proportional to the [H+] concentration. Martin and Hill (1987b) suggested that ionic strength, not hydrogen ion, accounts for the pH dependence of the rate. The manganese-catalyzed reaction obeys zero-order kinetics in S(IV) in the concentration regime above 100 pM S(IV),

with ¿fcj$ = 680 M_I s"1 (Martin and Hill 1987b). For S(IV) concentrations below 1 |iM the reaction is first order in S(IV)

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