On the basis of the software package "MathCad", by solving the Stefan-Maxwell diffusion equations, the evolution of the features of mass transfer in a three-component gas mixture, depending on pressure changes, has been numerically studied. In this analysis, the mixing process is studied in a vertical cylindrical channel of a finite size and at the isothermal conditions. The governing equations are solved at the boundary conditions assuming the absence of matter transfer through the walls of diffusion channel. Through the Rayleigh partial numbers, the influence of the pressure change on the behaviour of diffusion and convective flows is examined. The numerical results reveal that an increase in the pressure leads to a change of modes in ternary gas mixture. The present results are in good agreement with the existing experimental data.