where Hs is the Henry's law solubility coefficient of the gas. (In practical units, ps in bar and [S(aq)J in mol/L, i.e., M, Hs has units M/bar.) Abundance of a gas-phase species is expressed in terms of the molar mixing ratio in air x, which is applicable equivalently to substances in gas, aerosol, or solution phases (Schwartz and Warneck, 1995). Characterization of the Henry's law solubility is the first step to understanding the uptake and reaction of a gas in cloudwater. Henry's law solubility coefficients of many gases of atmospheric importance are given in Figure 1.
The ratio of the amount of material in solution to gas phase (distribution ratio), under assumption of Henry's law equilibrium, is given by
moles in aqueous phase moles in gas phase
If this is written as <Daq/g = H/Hy2 where H\/2 = 10"2 LRgT, then for any specified value of L, the value of Henry's law solubility coefficient for which the gas is equally distributed between the gas phase and cloudwater is given by Hiß-Consider a cloud of rather high liquid volume fraction L = 10 6 (i.e., ~1 g/m~3 liquid water content); the corresponding value of Hl/2 is ~4 x 104 M/bar; //, /2 would be correspondingly higher for lower values of L. Comparison with the values of Henry's law solubility coefficients given in Figure 1 shows that virtually all such coefficients are orders of magnitude less than this value, supporting the assertion that reaction of the dissolved gas is required for substantial uptake into cloudwater.
In the case of gases that undergo rapid reversible reaction with water, for example, hydration or acid dissociation, it is necessary to consider the overall solubility equilibrium, not just the Henry's law equilibrium. Consider the solubility equilibrium for the dissolution of an acidic gas, for example, formic acid, HCOOH. The overall equilibrium for this dissolution may be thought to consist of the following steps:
HCOOH(g) = HCOOH(aq) HCOOH(aq) = H+(aq) + COOH"(aq)
where Ka is the acid dissociation constant of aqueous formic acid. Depending on the situation, it may be more useful to deal with the overall solubility or with the individual equilibria.
The total concentration of the dissolved gas can be written (here staying with the example of formic acid) as
It is often a good assumption that the cloudwater is well buffered against change in acid concentration [H+] resulting from the incremental uptake of gases present at low partial pressures characteristic of the ambient atmosphere. Under this assumption, [H+] is a constant and hence the aqueous concentration is linear in gas-phase partial pressure with an effective Henry's law solubility coefficient defined as:
so that one obtains a Henry's law-like expression for the overall solubility,
In the case of S02 there are two acid dissociation equilibria. The effective Henry's law solubility coefficient for S(IV) (the Roman numeral IV denotes the oxidation state) is where Ka] and Kal denote the first and second dissociation constants, respectively.
Values of effective Henry's law solubility coefficients are shown in Figure 1 as a function of solution pH for the range of pH values typical of cloudwater. The effective solubility coefficient can greatly exceed the Henry's law coefficient for physical dissolution, especially for strong acids, such as nitric acid, and also for ammonia, which is highly soluble in the form of ammonium ion NH4+. These effective Henry's law solubility coefficients can also substantially exceed Hl/2, indicating that at equilibrium, such highly soluble gases as HN03 are essentially entirely taken up by cloudwater.
Because the chemical kinetics of acid dissociation reactions are generally quite rapid, the uptake of acidic gases such as HN03 is itself quite rapid, under control of mass transport processes rather than chemical kinetics. The mass transport processes governing this uptake are essentially identical to those governing the transfer of water vapor itself to and from cloud droplets, and the solubility of a gas such as HN03 is such that the uptake of soluble gases occurs on the time scale of cloud droplet activation and growth, that is taking place on a time scale of a few seconds to
[Formic acid] = [HCOOH] + [COOH~] = //HcooH*HCooH/>a»m ( 1
atm a few tens of seconds. This can result in such soluble gases being preferentially concentrated in the initially formed drops rather than being distributed uniformly throughout the cloud droplet spectrum (Wurzler et al., 1995); this can influence subsequent uptake and reaction of less soluble gases such as S02. A gas such as HN03 that dissolves in a growing cloud droplet contributes soluble material to the droplet, thereby adding to the Raoult effect of the solute already serving as the cloud condensation nucleus and increasing its cloud nucleating potential. This can have a further influence on cloud droplet composition and can also lead to situations of free cloud droplet growth at relative humidity slightly below 100% (Kulmala et al., 1997).
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