A new perturbation solution for the oxidation of silicon that properly accounts for diffusion of molecular oxygen and reaction kinetics at the silicon-silicon dioxide interface is presented. The perturbation treatment is based on the assumption of a dilute solution of O-2 in SiO2 phase. We show that the solution obtained by Deal and Grove [J. Appl. Phys. 36. 3770 (1965)] is the zeroth perturbation solution and formally prove that it is a quasi-steady-state solution. in the limiting case of instantaneous reaction, the perturbation solution is shown to be equivalent to the result obtained by Peng, Wang, and Slattery [J. Vac. Sci. Technol B 14, 3316 (1996)]. The proposed perturbation scheme is developed here for first-order reaction kinetics, but can easily be extended to other rate expressions. The higher order corrections offered to Deal and Grove model predictions might provide a needed method for assessing the error incurred when these predictions are used to estimate oxide film thickness in practical situations.