Calculation of Aqueous-Phase Reaction Rates

The discussion above indicates that appreciable mass transport limitation is absent under most atmospheric conditions of interest, although instances of substantial limitations under certain conditions of pH, temperature, and reagent concentrations exist. In the latter cases we would like to estimate the aqueous-phase reaction rate taking into account reductions in these rates due to the mass transport limitations. The graphical method presented in the previous sections is a useful method to estimate if there are mass transport limitations present. Our goal in this section is to derive appropriate mathematical expressions to quantify these rates. 

No Mass Transport Limitations In this case there are no appreciable concentration gradients outside or inside the droplet, or across the interface. As a result, Henry s law is applicable and for the first-order reaction 

Aqueous-Phase Mass Transport Limitation The concentration of a species A, specifically, C(r, t), undergoing aqueous-phase diffusion and irreversible reaction inside a cloud droplet, is governed by 

Because of the linearity of the system (first-order reaction), the average reaction rate over the drop (R), will be proportional to the average concentration of A, namely, (C) 

FIGURE 12.12 Steady-state radial concentration profiles of concentration of reactant species C(r) relative to the concentration at the surface of the drop Cs for a drop radius Rp as a function of the dimensionless parameter q (Schwartz and Freiberg 1981). 

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