To compare the rates of various aqueous-phase chemical reactions we have been calculating instantaneous rates of conversion as a function of solution pH. In the atmosphere a droplet is formed, usually by nucleation around a particle, and is subsequently exposed to an environment containing reactive gases. Gases then dissolve in the droplet, establishing an initial pH and composition. Aqueous-phase reactions ensue and the pH and composition of the droplet start changing accordingly. In this section we calculate that time evolution. We neglect any changes in droplet size that might result; for dilute solutions such as those considered here, this is a good assumption. We focus on sulfur chemistry because of its atmospheric importance.

In our calculations up to this point we have simply assumed values for the gas-phase partial pressures. When the process occurs over time, one must consider also what is occurring in the gas phase. Two assumptions can be made concerning the gas phase:

1. Open System. Gas-phase partial pressures are maintained at constant values, presumably by continous infusion of new air. This is a convenient assumption for order of magnitude calculations, but it is often not realistic. Up to now we have implicitly treated the cloud environment as an open system. Note that mass balances (e.g., for sulfur) are not satisfied in such a system, because there is continuous addition of material.

2. Closed System. Gas-phase partial pressures decrease with time as material is depleted from the gas phase. One needs to describe mathematically both the gas-and aqueous-phase concentrations of the species in this case. Calculations are more involved, but the resulting scenarios are more representative of actual atmospheric behavior. The masses of the various elements (sulfur, nitrogen, etc.) are conserved in a closed system.

The basic assumption in the closed system is that the total quantity of each species is fixed. Consider, as an example, the cloud formation (liquid water mixing ratio wl) in an air parcel that has initially a H202 partial pressure p^2q2 and assume that no reactions take place. If we treat the system as open, then at equilibrium the aqueous-phase concentration of H202 will be given by

Note that for an open system, the aqueous phase concentration of H202 is independent of the cloud liquid water content.

For a closed system, the total concentration of H202 per liter (physical volume) of air, [H202]total, will be equal to the initial amount of H202 or

After the cloud is formed, this total H202 is distributed between gas and aqueous phases and satisfies the mass balance

where pn2o2 is the vapor pressure of H202 after the dissolution of H202 in cloudwater. If, in addition, Henry's law is assumed to hold, then

[H202(aq)]closed = HH2o2pu2o2 (7.106)

Combining the last three equations,

The aqueous-phase concentration of H202, assuming a closed system, decreases as the cloud liquid water content increases, reflecting the increase in the amount of liquid water content available to accommodate H202. Figure 7.20 shows [H202(aq)] as a function of the liquid water content L = 10~6 wi, for initial H202 mixing ratios of 0.5, 1, and 2 ppb. For soluble species, such as H202, the open and closed system assumptions lead to significantly different concentration estimates, with the open system resulting in the higher concentration.

cr o

FIGURE 7.20 Aqueous-phase H202 as a function of liquid water content for 0.5, 1, and 2 ppb H202, Dashed lines correspond to an open system and solid lines to a closed one.

The fraction of the total quantity of H2O2 that resides in the liquid phase is given by (7,9) and is shown in Figure 7.12. A species like H202 with a large Henry's law coefficient (1 x ]05Matm [) will have a significant fraction of the fixed total quantity in the aqueous phase. As wi increases, more liquid is available to accommodate the gas and the aqueous fraction increases, while its aqueous-phase concentration, as we saw above, decreases.

For species with low solubility, such as ozone, 1 + Hw^RT ~ 1, and the two approaches result in essentially identical concentration estimates (recall that wi < 10-6 for most atmospheric clouds).

Aqueous-Phase Concentration of Nitrate inside a Cloud (Closed System) A cloud with liquid water content w/, forms in an air parcel with HN03 partial pressure equal to p°w0j. Assuming that the air parcel behaves as a closed system, calculate the aqueous-phase concentration of [N<X], Using the ideal-gas law, we obtain

The available HN03 will be distributed between gas and aqueous phases

where Henry's law gives

[HN03(aq)] = J?hno3Phno3 {7.110) and dissociation equilibrium is

" [HNO3(aq)j (7-1U) Solving these equations simultaneously yields

1 +wLHm0;iKJ

The last equation can be simplified by using our insights from Section 7.3.5, that is: wlH^q^RT s> 1 for typical clouds and that //hno3 ^ whno, Kn\/[h+]. Using these two simplifications, we find that [N03 ] =p"INOi/(wL/fr)}. This is the expected result for a highly water soluble strong electrolyte. All the nitric acid will be dissolved in the cloud water and alt of it will be present in its dissociated form,

7.6.2 Calculation of Concentration Changes in a Droplet with Aqueous-Phase Reactions

Let us consider a droplet that at / = 0 is immersed in air containing S02, NH3, H2G2, 03, and HNO3. Equilibrium is immediately established between the gas and aqueous phases. As the aqueous-phase oxidation of S(IV) to S(VI) proceeds, the concentrations of all the ions adjust so as to satisfy electro neutrality at all times

[H+] + [NH+] = [OH"] 4- [HSO3] +2[SOj~] + 2[S02"] + [HSO4] + [NO3

where the weak dissociation of H202 has been neglected. The concentrations of each ion except sulfate and bisulfate can be expressed in terms of [H '] using the equilibrium constant expressions:

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