The mutual and the self-diffusion coefficients of the acetone-cellulose acetate system are determined by using established gravimetric measurements of the acetone evaporation rate. The process is studied as a one-dimensional numerical experiment utilizing the Galerkin finite element method. The numerical technique provides simultaneous solution of the model equations and yields by comparison with gravimetric data the diffusion coefficients of acetone in cellulose acetate for a wide range of temperatures and compositions. The estimated diffusion coefficients based on free volume theory are in satisfactory agreement with the available experimental data. It-is believed that this method can be applied to other systems of interest.