Model when reactant present in both liquid and vapor phases

4-3 MODEL WHEN REACTANT PRESENT IN BOTH LIQUID AND VAPOR PHASES 

The models described above assume that the reaction occurs only in the liquid phase. In some cases, such as isomerization of cyclopropane to propylene on a silica-alumina catalyst,43 reduction of crotonaldehyde over a palladium catalyst,45 and hydration of olefins to alcohols over tungsten oxide,58 the reactions could occur in the gas as well as in the liquid phases. 

If the concentrations of the stoichiometrically-limiting reactant in the two phases are in equilibrium and if the chemical potential is the driving force, then, from thermodynamics, it is clear that the reaction rate is unaffected by the nature of the phase with which the solid is in contact, provided that no mass- and heat-transfer gradients exist and no blockage of the catalyst sites by the impurities occurs. However, the competitive adsorption of impurities in the liquid, even if these are inert to reaction, can markedly affect catalytic behavior. 

Satterfield41 showed that, if the reactant is present in both phases under 

V is the volume of the reactor, Qc, and QL are the gas and liquid flow rates, B is the vapor-liquid equilibrium constant (B = y/x, where y and x are mole fractions in vapor and liquid phase, respectively), and SL and va are the molar volumes of the liquid and gas phases, respectively, at reactor conditions. Similarly, for the gas phase, the following relation41 can be derived  

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