We obtain a general formula for reactant conversion in diffusion-reaction TAP systems over single nonporous catalyst particles as a product of two terms: alpha = P-H x H. The first term, P-H. is a purely geometric factor dependent only on the shape of the reactor and the shape and position of the catalyst particle, interpreted as the probability that an individual molecule of reactant will hit the catalyst before leaving the reactor. The second term, H = k tau(H)/(1 + k tau(H)), is a geometrical/chemical term involving the kinetic constant k and a transport characteristic (residence time in the catalyst zone, tau(H)). Both P-H and tau(H) can be effectively calculated for any given reactor-particle configuration. Our formula greatly extends the validity of a formula given in Shekhtman et al. [1999. Thin-zone TAP-reactor-theory and application. Chem. Eng. Sci. 54, 4371-4378] for thin-zone TAP-systems. It is derived by a probabilistic analysis of the residence time of individual molecular trajectories in chemically active regions. Our results are based on the theory previously developed in our paper [Feres, R., Yablonsky, G.S., Mueller, A., Baernstein, A., Zheng. X., Gleaves, J., 2009. Probabilistic analysis of transport-reaction processes over catalytic particles: theory and experimental testing. Chem. Eng. Sci. 64, 568-581]. (C) 2009 Elsevier Ltd. All rights reserved.