Applicability of Smoluchowski-type kinetics to Eley-Rideal reactions between gaseous and adsorbed reactants in porous solids

An analysis is carried out considering the applicability of Smoluchowski-type kinetics to gas-phase target-annihilation (Eley-Rideal) reactions in porous solids. Previous reports have argued that, within the Knudsen regime, the reaction rate should be governed by Knudsen's diffusion which, coupled to Smoluchowski's expression, leads to a linear dependence of the rate constant on the pore diameter. We show that, for any feasible target-annihilation reaction in a porous material, concentration gradients associated with Smoluchowski-type kinetics cannot be generated. Consequently, the reaction rate is not controlled by Knudsen's diffusion. Thus, such reaction rates should simply depend on the reactant's pressure but not on pore diameter.