In this study, three approximations for unsteady-state diffusion, a linear adsorption, and a first-order reaction in a catalyst particle are presented. The time-domain approximations are based on a first-, a second-, and a third-order approximation of the Laplace-domain solution of the exact partial differential equation for the catalyst. All the coefficients in the approximate equations are obtained as explicit functions of the Thiele modulus and easy to evaluate. In reactor modeling with the approximations, it is observed that the ratio of the space time in the reactor and the diffusion time in the catalyst is also an important parameter affecting the accuracy of the resulting model. A longer space time or shorter diffusion time improves the prediction of the approximate reactor model so that even the first-order approximation is found to be sufficiently accurate when the ratio is over 0.9. (C) 2009 American Institute of Chemical Engineers.