A procedure based on combining the method of characteristics with a Galerkin finite element method is analyzed for approximating reactive transport in groundwater. In particular, we consider equations modeling contaminant transport with nonlinear, non-equilibrium adsorption reactions. This phenomena gives rise to non-Lipschitz but monotone nonlinearities which complicate the analysis. A physical and mathematical description of the problem under consideration is given, then the numerical method is described and a priori error estimates are derived.