High-order approximations for unsteady-state diffusion, a linear adsorption and a first-order reaction in a slab, cylinder and sphere catalyst are developed. The approximations are based on a first-, a second-, a third- and a fifth-order approximation of the Laplace domain solutions of the exact model for the catalyst of three geometries. The coefficients in the approximations are functions of Thiele modulus of the respective geometry and easy to determine. The accuracy of the approximation is shown to increase markedly with the approximation order.