It is generally recognized that the optimal distribution of catalyst activity in a spherical catalyst is a Dirac δ-function.However,catalyst with other alternative distribution may accomplish the same reaction task without necessarily concentrating the catalyst activity in an inside thin layer.Moreover,the alternative with activity on catalyst surface may offer higher reaction rate and better utilization of reaction heat (higher exergy output).Simple cases of first-order exothermal reactions,in particular when the catalyst is limited by the maximum working temperature,are presented to demonstrate the above advantages and to show the importance of studying the optimal activity distribution with the consideration on exergy maximization and entropy production minimization.