A mathematical model, based on the dusty-gas model extended with surface diffusion, is presented that describes mass transport owing to molecular diffusion and viscous flow, as well as an instantaneous reversible reaction inside a membrane reactor. The reactants are fed to opposite sides of the membrane, considering masstransfer resistances in the gas phase outside the membrane. The Claus reaction is chosen as a model reaction to study this membrane reactor. The model is used to validate a previously presented simplified model. The simplified model predicts correct molar fluxes when it is very dilute and can therefore be considered a pseudo-binary system. Occurrence of a maximum or a minimum in the pressure profile inside the membrane, in the absence of an overall pressure difference over the membrane, depends not only on the stoichiometry of the reaction but on mobilities of the different species. The Claus reaction is used to verify experimentally the transport model for a nonpermselective membrane reactor with a mean pore diameter of 350 nm. At 493 K and 542 K, molar fluxes experimentally determined are 10 to 20% lower than those predicted by the transport model. Conversions measured at pressures of 220 kPa and 500 kPa demonstrate that surface diffusion occurs as a transport mechanism despite the large pore diameter of the membrane. In the presence of a pressure difference over the membrane, there is a reasonable agreement between experimentally determined molar fluxes and those calculated by the transport model.