  We present a fully discrete scheme for the numerical approximation of a
moving-boundary problem describing diffusants penetration into rubber. Our
scheme utilizes the Galerkin finite element method for the space discretization
combined with the backward Euler method for the time discretization. Besides
dealing with the existence and uniqueness of solution to the fully discrete
problem, we derive a \textit{a priori} error estimate for the mass
concentration of the diffusants, and respectively, for the position of the
moving boundary. Numerical illustrations verify the obtained theoretical order
of convergence in physical parameter regimes.
