Bounds for the first-order approximation of the Langmuir-Hinshelwood kinetics under internal diffusion limitations

In heterogeneous catalysis, the Langmuir-Hinshelwood reaction kinetics is sometimes approximated by first-order kinetics at low reactant concentration. This approximation may be valid for a description of the intrinsic reaction rate. However, the situation is more complex if the rate of a heterogeneous catalytic process faces intraparticle diffusion limitations. The ad hoc utilization of the approximation leads to either considerable underestimation or overestimation of the effectiveness factor. Under internal diffusion limitations, the first-order approximation only holds for a limited range of the reactant concentration, and the condition of low reactant concentration is not necessarily fulfilled. The range of the reactant concentration for which the approximation holds may depend on, inter alia, the equilibrium constant of the reactant adsorption step. The experimental proof is demonstrated using the analysis of the effectiveness factors based on the first-order and Langmuir-Hinshelwood reaction kinetics for heterogeneously catalyzed reactions of various alcohol dehydration.