An analytical solution for a constant molar flow semi-batch adsorber loaded with inert core adsorbents is obtained for the linear isotherm coupled with intraparticle diffusion and external film diffusion. The solution obtained in this study consists of two parts. One is the asymptote, to which the bulk concentration approaches as time is sufficiently large. The other is the relaxation term, which dictates how the mass in the bulk phase flows into the adsorbent within the adsorption vessel. For a given value of the inert core radius, the slope of the asymptote is a function of the equilibrium parameter only and the intercept is a function of the kinetic parameter as well as the equilibrium parameter. The intercept of the asymptote consists of two parts. One is the contribution due to the external film resistance; the other is the contribution due to the intraparticle diffusion resistance. Hence, we can obtain the information of the equilibrium constant, the film mass transfer coefficient, and the effective diffusivity from the asymptote of the solution presented in this study.