A new approach to the mathematical modelling of mass transfer processes based on the advanced unified least squares method is presented. Contrary to the classical approach, all experimental results are proposed to be included into a mathematical model to enable direct and objective model verification. Special attention is paid to the mass transfer processes during autocatalytic reactions and as an example a numerical mathematical mass transfer model of the autocatalytic dissolution of metallic copper in oxygen-containing ammonia solutions using the rotating disc technique has been worked out.