We analyze the long time behavior of an initial value problem that models a chemical reaction-diffusion process A + B → C. The problem has previously been studied by Gálfi and Rácz, who predicted the critical indices associated with the reaction by using a scaling ansatz motivated by numerical simulations. In this paper we point out some difficulties which appear in problems of this type due to the non-uniform convergence of the solution towards the scaling limit, and solve them by giving an explicit description of the corrections scaling that have to be concluded to prove bounds on the solution that are uniform in space and time. This allows us to relate rigorously the critical exponents as computed from the scaling ansatz to the exponents of the reaction.