Mass-transport limitation to the rate of reaction of gases in liquid droplets: Application to oxidation of SO 2 in aqueous solutions

Abstract

Aqueous-phase oxidation of SO 2 occurs via a sequence of steps consisting of gas-phase diffusion, mass transfer at the gas-water interface, hydrolysis and ionization of the dissolved sulfur-IV, aqueous-phase diffusion, and oxidation reaction. Expressions are given for the characteristic times of these several processes for reaction in aqueous droplets. Readily applicable criteria are developed in terms of these characteristic times to delimit the conditions, in the laboratory or in the ambient atmosphere, under which the rate of reaction in an aqueous droplet is equal to the intrinsic oxidation rate or is restricted by the finite rates of the several other processes. Under most conditions of concern in the ambient atmosphere, or in laboratory simulation of these conditions, the characteristic times of hydrolysis and ionization are sufficiently short compared to that of aqueous-phase reaction that the several dissolved sulfur-IV species may be considered to be a single pool of equilibrated reactant species. Similarly, the S(IV) solubility equilibria at the gas-water interface may also be considered to be achieved on a time scale that is short compared to that of aqueousphase reaction, except perhaps at high pH (pH > 7) where the characteristic time of this process becomes long (~ 10 sec at 25°C) because of the high solubility of S(IV). A more detailed treatment of the problem of simultaneous diffusion and reaction establishes the domain of applicability of the steady-state assumption for reaction in aqueous droplets. Within the steady state approximation, we examine the magnitude of limitation to the overall rate of reaction resulting from the finite rate of mass transport in the gas and aqueous phases and from the finite rate of achieving the solubility equilibrium at the interface. Expressions are presented that permit this treatment to be readily applied to laboratory kinetic data. The foregoing treatment also permits examination of the conditions under which limitation to the overall rate of reaction is controlled by one or another of the above mechanisms. For gas- and aqueous-phase mass transport by molecular diffusion it is found (again for 25°C) that gas-phase mass transport is more controlling than aqueous-phase mass transport for pH > 3.3, and that the onset of departure from the solubility equilibrium at the phase interface is more controlling than gas-phase diffusion only for very small droplets (radius < 0.16 μm). For SO 2 oxidation by atmospheric O 2, aqueous-phase diffusion of O 2 is more controlling than gas-phase diffusion of SO 2 only for quite high SO 2 partial pressure ( p SO 2 > 10ppm).