Abstract: For the one-dimensional catalyst pellets, the perturbation method can be employed to get asymptotic solutions of isothermal heterogeneous diffusion-reaction equations with arbitrary kinetics when Thiele moduli are small or large. From the asymptotic solutions, a new analytical expression of effectiveness factor valid throughout the whole range of Thiele modulus is obtained. Compared with the exact analytical solutions of first order irreversible reaction, the approximate solutions are satisfactory in a larger scope.