A linearization scheme is presented that enables near-exact solution of the nonlinear ordinary differential equations associated with Film Theory-based modeling of absorption with multiple reversible chemical reactions. The technique, a variant of singular perturbation methods, is applied here to the analysis of absorption of carbon dioxide in aqueous monoethanolamine and stripping of CO2 from the same solutions. Enhancement factors by which reactions multiply mass transfer rates are in excellent agreement with values obtained via numerical methods. Unlike previously published approximate techniques, the computationally efficient method outlined here is applicable whether the reversible reactions are fast or slow, and whether the solvent is lean or loaded.