In recent years, there has been increasing interest in porous catalysts which contain nonuniform activity. For example, Kasaoka and Sakata ( 1968), Villadsen ( 1976), Corbett and Luss (1974), Shadman-Yazdi and Petersen (1972), and Becker and Wei (1977u, b) have recently developed theoretical models to describe the performance of catalysts with nonuniform activity. Some catalysts contain nonuniform activity as a result of preparation methods employed, while others develop this feature because of poisoning. The deliberate inclusion of nonuniform activity in porous catalysts provides a means of tailoring a catalyst to a specific process to improve activity or selectivity, or to reduce the rate of poisoning.This note develops the theoretical basis for an experimental study of the effect of catalyst activity distribution on selectivity. The reaction examined is the deuterium exchange with neopentane on supported platinum, It is a series reaction with many steps and resembles industrially important reactions such as the isomerization of certain olefins (see Haag and Pines, 1960) and the hydrogenolysis of polynuclear aromatics (see Sullivan et al., 1964;Germain, 1969). It was used as a test reaction in previous experimental studies of laboratory flow reactors (Zahner, 1970) and diffusion effects in porous catalysts (Dwyer et al., 1968;Ernst and Wei, 1975) because of several desirable features: negligible heat of reaction, single step surface exchange mechanism, and first order in neopentane ,
THEORYIn a mass spectrometer, neopentane undergoes fragmentation such that the major peak corresponds to a t-butyl fragment, and the parent neopentane peak is negligible. Kemball (1954) has provided a means of following the course of the deuterium-neopentane exchange reaction via the deuterium exchanged t-butyl fragments. Thus, there are nine deuterated products that must be monitored during the course of the reaction.For brevity, the model will be developed for the singlestep exchange of methane: The model can be readily extended to the reaction of neopentane. The following assumptions will be made: a large excess of Dz is used so that q is approximately equal to 1, and all reverse reactions are insignificant; the reaction occurs within a spherical catalyst particle containing the activity distributionwhere k, is the catalytic activity at the particle surface