In this paper, a classical film model is extended to account for unsteady-state multicomponent diffusion and reaction coupling. The governing matrix-form partial differential equation is complemented by the initial and boundary conditions formulated as general vector functions. An additional linearization of the reaction source term results in the formulation which allows an analytical handling of the problem. The latter is found to be successful even with the generally set initial and boundary conditions. The solution approach combines the superposition principle and the method of the separation of variables extended for the matrix operations. Thr: exact analytical matrix solution obtained is a generalization of many simpler problems and either can be employed by itself or provides suitable preset values for relevant numerical simulations of industrial-scale reactive separation operations.