A variety of settings involve reaction/diffusion systems in a thin film, e.g., in the `film' surrounding an individual bubble in a bubble reactor. With suitable scaling, most reactions are negligible but it remains necessary to consider some few fast rections. We consider a model problem involving one reaction [A+C-->*] fast enough to be retained coupled with another, much faster, reaction [A+B-->C] --- asymptotically, `infinitely fast' in comparison. The talk discusses some properties of the system as providing a free boundary problem in the limit, with particular attention to the system in steady state.