## Aqueousphase Reaction Rates

Rates of reaction of aqueous-phase species are generally expressed in terms of moles per liter (M) of solution per second. It is often useful to express aqueous-phase reaction rates on the basis of the gas-phase properties, especially when comparing gas-phase and aqueous-phase reaction rates. In this way both rates are expressed on the same basis.

To place our discussion on a concrete basis, let us say we have a reaction of S(IV) with a dissolved species A

the rate of which is given by

where Ra is in M s 1, the aqueous-phase concentrations [S(IV)] and [A(aq)] are in M, and the reaction constant k is in M"1 s1. The reaction rate can be expressed in moles of S02 per liter of air per second by multiplying Ra by the liquid water mixing ratio Wi = 10"6 L:

R'a = jkwL[A(aq)][S(IV)] = 10"6 JfcL[A(aq)][S(IV)] (mol(L of air)"1 s"1) (7.74)

The moles per liter of air can be then converted to equivalent S02 partial pressure for 1 atmosphere total pressure by applying the ideal-gas law to obtain

where L is in g m" ~3,R = 0.082 atmLK-1 mol-1, and T is in K. For example, an aqueous-phase reaction rate of 1 pM s_1 in a cloud with a liquid water content of 0.1 g m 3 at 288 K is equivalent to a gas-phase oxidation rate of 8.5 ppbh-1. A nomogram relating aqueous-phase reaction rates in pMs-1 to equivalent gas-phase reaction rates in ppbh"1 as a function of the cloud liquid water content L at 288 K is given in Figure 7.14.

"5

o o tu c10"2

 r ~t— t~ 11111-r- t i ri ni| i 1 1 ii i 111 1 1 1 1'' u r L=1.0 9 r = -^0.01 i t i i 1111 i i i i 11ill i 1 1 i 1 i 111

FIGURE 7.14 Nomogram relating aqueous reaction rates, in pMs~', to equivalent gas-phase reaction rates in ppb h 1, at T = 288 K, p -- 1 atm, and given liquid water content.

Reaction rates are sometimes also expressed as a fractional conversion rate in %h_1. The rate R" given above can be converted to a fractional conversion rate by dividing by the mixing ratio, i;sc,2, of S02 in ppb and multiplying by 100

where £S02 is in ppb. Let us assume that both S(IV) and A are in thermodynamic equilibrium with Henry's law constants Z/g(iv) ^a, respectively. Combining (7.73), (7.76), and (7.3), one obtains

Sa LRT

where k is in Ms-1, HA and H*SIWj are in M atm 1, cA is in ppb, L is in gm-3, R = 0.082 atm L K"1 mol and Tis in K. Note that the SOz oxidation rate given by (7.77) is independent of the S02 concentration and depends only on the mixing ratio of A, the cloud liquid water content, and the temperature. Equation (7.77) should be used only if A exists in both gas and aqueous phases and Henry's law equilibrium is satisfied by both S(IV) and A. If the two species do not satisfy Henry's law, (7.76) can still be used.

The characteristic time for S02 oxidation tso2 (s) can be calculated from (7.76) as tso2 =

Ra 103 Ra LRT

7.5 S(IV)-S(VI) TRANSFORMATION AND SULFUR CHEMISTRY

The aqueous-phase conversion of dissolved S02 to sulfate, also referred to as S(VI) since sulfur is in oxidation state 6, is considered the most important chemical transformation in cloudwater. As we have seen dissolution of S02 in water results in the formation of three chemical species: hydrated S02 (S02 • H20), the bisulfite ion (HSOJ), and the sulfite ion (SO2-). At the pH range of atmospheric interest (pH = 2-7) most of the S(IV) is in the form of HSOj, whereas at low pH (pH < 2), all of the S(IV) occurs as S02 • H20. At higher pH values (pH > 7), S02~ is the preferred S(IV) state (Figure 7.8). Since the individual dissociations are fast, occurring on timescales of milliseconds or less (see Chapter 12), during a reaction consuming one of the three species, S02 • H20, HS03, or SO2-, the corresponding aqueous-phase equilibria are reestablished instantaneously. As we saw earlier, the dissociation of dissolved S02 enhances its aqueous solubility so that the total amount of dissolved S(IV) always exceeds that predicted by Henry's law for S02 alone and is quite pH dependent.

Several pathways for S(IV) transformation to S(VI) have been identified involving reactions of S(IV) with 03, H202, 02 (catalyzed by Mn(II) and Fe(III)), OH, SOs, HS05, S04 , PAN, CH3OOH, CH3C(0)00H, H02, N03, N02, N(III), HCHO, and Cl2 (Pandis and Seinfeld 1989a). There is a large literature on the reaction kinetics of aqueous sulfur chemistry. We present here only a few of the most important rate expressions available.

7.5.1 Oxidation of S(IV) by Dissolved 03

Although ozone reacts very slowly with S02 in the gas phase, the aqueous-phase reaction

is rapid. This reaction has been studied by many investigators (Erickson et al. 1977; Larson et al. 1978; Penkett et al. 1979; Harisson et al. 1982; Maahs 1983; Martin 1984; Hoigne et al. 1985; Lagrange et al. 1994; Botha et al. 1994). A detailed evaluation of existing experimental kinetic and mechanistic data suggested the following expression for the rate of the reaction of S(IV) with dissolved ozone for a dilute solution (subscript 0) (Hoffmann and Calvert 1985):

R0 = _ÄXH = (fc0[SO2 ■ H20] + Id[HSO3 ] + £2[S02-]) (7.80)

with ko = 2.4 ± 1.1 x 104M-' s~\ki = 3.7 ±0.7 x 105M-' s"1 and, k2 = 1.5 ±0.6 x 109 M 1 s_1. The activation energies recommended by Hoffmann and Calvert (1985) are based on the work of Erickson et al. (1977) and are 46.0 kJ moT1 for k\ and 43.9 kJ mol 1 for k2.

The complex pH dependency of the effective rate constant of the S(IV)-03 reaction is shown in Figure 7.15. Over the pH range of 0 to 2 the slope is close to 0.5 (corresponding to an [H+]~°5 dependence), while over the pH range of 5 to 7 the slope of the plot is close to 1 (corresponding to an [H+]_1 dependence). In the transition regime between pH 2 and 4 the slope is 0.34. Some studies focusing on pH values lower than 4 have produced rate laws that yield erroneous rates when extrapolated to higher pH values.  