This paper develops a closed-form solution for the population-balance equations describing the dissolution of, polydisperse mixtures of spherical particles in the presence of external mass-transfer resistance. The general case, obtained by relaxing the assumption of an excess concentration of fluid reactants, is also considered. In mathematical terms, this leads to a nonlinear first-order functional equation that can be solved by making use of a warped-time transformation. The inclusion of the fragmentation dynamics of solid particles occurring during the chemical dissolution process is also briefly addressed.