In this paper, a general unsteady-state model of particle dissolution is applied to a case of ore leaching in a batch process. The model equations are solved numerically with an implicit finite-difference method which is second-order approximate in space and time. It is shown how a non-constant concentration of liquid leachants outside the pore may highly condition the yield of the global process. The results are discussed and compared with experimental data concerning a dissolution process of manganese dioxide dispersed in a porous matrix.