This paper addresses the overall behavior of a reaction mixture in which many irreversible bimolecular reactions occur in catalyst particles of three different shapes (slab, long cylinder, and sphere). Specifically, we develop a priori upper and lower bounds on the effectiveness factor for the mixture as a whole. These bounds provide information on the asymptotic behavior of the mixture under severe diffusion limitation. Improved bounds are obtained by reducing the problem to that of finding the effectiveness factor for a single second-order reaction. The bounds are used to estimate the mixture’s effectiveness factor-based on information about the average and the spread of the Thiele moduli.