Significance It is shown, based on pulse-response experiments, that under special conditions the activity profile of a prepared catalytic system depends only on the total amount of admitted substance. This property, previously found computationally, is here established mathematically for porous and nonporous catalysts in different pulse reactors. This result can be used as a theoretical guidance for the design of systems or materials with an optimal activity profile, in particular a catalyst bed or a catalyst particle. Consequently, it can be used for understanding and developing the different diffusion-reaction processes, e.g., wet impregnation, deactivation of active materials, and so forth. (c) 2014 American Institute of Chemical Engineers AIChE J, 61: 31-34, 2015