A new approximate rate law for non-linear adsorption and diffusion in a spherical adsorbent particle is developed based on an equivalent him resistance model. The approximation provides a quantitatively correct description of the effect of the adsorption isotherm for parallel pore and solid diffusion as well as of the effect of a variable adsorbed-phase diffusivity. In general, uptake curves calculated with this new approximation compare favorably with the numerical solution of the adsorption-diffusion equation in spherical coordinates producing results of accuracy similar to that obtained when the LDF approximation is used for systems with a constant diffusivity.