Mass transfer in a gas mixture with chemical precipitation of the components on the wall and a high speed of bulk reactions is investigated. The analysis is based on the method of splicing asymptotic expansions. The solution in a chemical-nature nonequilibrium boundary layer and the diffusion flows of the components towards the wall are expressed in terms of an equilibrium-core solution extrapolated to this wall. The core solution is found by using an ingenious computational approach based on the concept of equilibrium reaction rates which are not explicit functions of the reagent concentrations, but determined implicitly by the equilibrium conditions. The procedure proposed is tested for a simple model problem admitting an analytical solution in the core and a direct numerical solution all over the calculation region. Good agreement of the results is demonstrated for both the core solution and the wall-directed diffusion flows.