In this work, we present the solution of the equations that govern the reactant transport in a well mixed system that contains particles where diffusion and first-order reaction occur. The transport equations are coupled by an interfacial boundary condition that includes mass transfer resistance. The statement of the problem allows arbitrary time depending feed functions. The evaluation of the solution obtained by the Laplace method requires the solution of an eigenvalue problem. We discuss the evaluation of the solution, and typical results for three different feed functions: step, pulse and oscillatory functions are presented. The resulting equations are able to show the effect of internal and external mass transfer limitations on the particle and fluid concentrations and on kinetic experimental results.