K k iOi

with kg = 1000 M_1 s 1 (Martin and Hill 1987b). It is still not clear which rate law is appropriate for use in atmospheric calculations, although Martin and Hill (1987b) suggested the provisional use of the first-order, low S(IV) rate.

Iron/Manganese Synergism When both Fe3+ and Mn2+ are present in atmospheric droplets, the overall rate of the S(IV) reaction is enhanced over the sum of the two individual rates. Martin (1984) reported that the rates measured were 3 to 10 times higher than expected from the sum of the independent rates. Martin and Good (1991) obtained at pH 3.0 and for [S(IV)] < 10 pM the following rate law:

_®X11 = 750[Mn(II)][S(IV)] + 2600[Fe(III)][S(IV)] + 1.0 x 1010[Mn(II)][Fe(III)][S(IV)]

and a similar expression for pH 5.0 in agreement with the work of lbusuki and Takeuchi (1987).

7.5.6 Comparison of Aqueous-Phase S(IV) Oxidation Paths

We will now compare the different routes for S02 oxidation in aqueous solution as a function of pH and temperature. In doing so, we will set the pH at a given value and calculate the instantaneous rate of S(IV) oxidation at that pH. The rate expressions used and the parameters in the rate expressions are given in Table 7.6. Figure 7.19 shows the

TABLE 7.6 Rate Expressions for Sulfate Formation in Aqueous Solution Used in Computing Figure 7.19

Oxidant Rate Expression, — i/[S(IV)]/<ii Reference

Oj (Ms°2 ■ H20] + kx [HSO^] + jfc2[S0^-])[03(aq)] Hoffmann and Calvert (1985)

ko = 2.4 x 104M-' s-1 kx = 3.7 x 105 s_I k2 = 1.5 x 109M-' s"1

H202 fc,[H+][HS03][H202(aq)]/(l + A"[H+]) Hoffmann and Calvert (1985)

Fe(III) k5 [Fe(III)] [SO^f Hoffmann and Calvert (1985)

k5 = 1.2 x 106 NT1 s"1 for pH <5 Mn(II) /fc6[Mn(II)][S(IV)] Martin and Hill (1987b)

kb = 1000 M"1 s"1 (for low S(IV)) N02 jt7[N02(aq)][S(IV)] Lee and Schwartz (1983)

"This is an alternative reaction rate expression for the low-pH region. Compare with (7.92) and (7.95).

FIGURE 7.19 Comparison of aqueous-phase oxidation paths. The rate of conversion of S(IV) to S(VI) as a function of pH. Conditions assumed are [S02(g)] = 5 ppb; [N02(g)] = 1 ppb; [H202(g)] = 1 ppb; [03(g)] = 50 ppb; [Fe(III)] = 0.3 pM; [Mn(II)] = 0.03 pM.

FIGURE 7.19 Comparison of aqueous-phase oxidation paths. The rate of conversion of S(IV) to S(VI) as a function of pH. Conditions assumed are [S02(g)] = 5 ppb; [N02(g)] = 1 ppb; [H202(g)] = 1 ppb; [03(g)] = 50 ppb; [Fe(III)] = 0.3 pM; [Mn(II)] = 0.03 pM.

oxidation rates in pM h 1 for the different paths at 298 K for the conditions

[S02(g)] = 5 ppb [H202(g)] = 1 ppb [N02(g)] = 1 ppb [03(g)] = 50 ppb

We see that under these conditions oxidation by dissolved H202 is the predominant pathway for sulfate formation at pH values less than roughly 4-5. At pH > 5 oxidation by 03 starts dominating and at pH 6 it is 10 times faster than that by H202. Also, oxidation of S(IV) by 02 catalyzed by Fe and Mn may be important at high pH, but uncertainties in the rate expressions at high pH preclude a definite conclusion. Oxidation of S(IV) by N02 is unimportant at all pH for the concentration levels above.

The oxidation rate of S(IV) by OH cannot be calculated using the simple approach outlined above. Since the overall rate depends on the propagation and termination rates of the radical chain, it depends, in addition to the S(IV) and OH concentrations, on those of H02, HCOOH, HCHO, and so on, and its determination requires a dynamic chemical model.

The inhibition of most oxidation mechanisms at low pH results mainly from the lower overall solubility of S02 with increasing acidity. H202 is the only identified oxidant for which the rate is virtually independent of pH.

The effect of temperature on oxidation rates is a result of two competing factors. First, at lower temperatures, higher concentrations of gases are dissolved in equilibrium (see Figure 7.7 for S02), which lead to higher reaction rates. On the other hand, rate constants in the rate expressions generally decrease as temperature decreases. The two effects therefore act in opposite directions. Except for Fe- and Mn-catalyzed oxidation, the increased solubility effect dominates and the rate increases with decreasing temperature. In the transition-metal-catalyzed reaction, the consequence of the large activation energy is that as temperature decreases the overall rate of sulfate formation for a given S02 concentration decreases.

As we have noted, it is often useful to express aqueous-phase oxidation rates in terms of a fractional rate of conversion of S02. Assuming cloud conditions with 1 g m-3 of liquid water content, we find that the rate of oxidation by H202 can exceed 500% h~' (Figure 7.16).

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