and is also assumed to be in Henry's law equilibrium with the gas immediately adjacent to the interface. While Henry's law is commonly expressed as H = [X\/Px, with the Henry's law constant H in units of mol L 1 atm~', it can also be expressed in unitless form if the gas-phase concentration is expressed in units of mol L~' instead of in units of pressure. With this conversion (see Problem 5), the liquidphase concentration in the interface region, Nt = ^l.inierfacc Is related to the gas-phase concentration immediately adjacent to the interface, N, by N\ = NgHRT (where R is the gas constant). Substituting into Eq. (FFF), the rate of transfer of the gas is given by
plane under conditions where kt » f becomes independent of time and is given by
The normalized rate for reaction is then given by 4HRT
Normalizing the rate of gas-surface collisions using Eq. (PP), one obtains
Note that in this case, rsol decreases with increasing time of exposure of the liquid to the gas. This reflects reevaporation from the liquid becoming increasingly important as the concentration of the dissolved species increases.
If the liquid layer is very thin, as is the case for some particles in the atmosphere, the interface layer with thickness (D^t)^2 may comprise the entire particle, in which case the liquid is in Henry's law equilibrium with the gas, there is no net uptake, and Eq. (HHH) is not applicable. Similarly, at very long reaction times, i.e., as t —> oc, rsol —> 0. That is, at very long exposure times, there is no net uptake because the system has come to equilibrium and the rates of uptake and reevaporation are equal.
Reaction in the liquid phase (rrxn). Now consider the case where an irreversible, first-order reaction with rate constant k (s-1) takes place, in addition to diffusion and solubilization. Equation (CCC) becomes
(see Problem 6). This applies to irreversible reactions or to those where the solubility of the reaction product is very large.
Let us now return briefly to the question of the relationship between net reactive uptake coefficients measured in laboratory systems, where the liquid films are generally quite thick, and particles in the atmosphere, which can be quite small and hence effectively have thin liquid films. A measure of the distance from the interface in which the reaction occurs is the diffuso-reactive length, I, which is defined as
Associated with this is the diffuso-reactive parameter, q, where q = a q = a
and a is the particle radius. Using an approach similar to that discussed earlier, Hanson et al. (1994) showed that the effective reactive uptake coefficient for small drops, %, is related to that measured in thick laboratory films, ymeas, by
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