  We show that solutions of the chemical reaction-diffusion system associated
to $A+B\rightleftharpoons C$ in one spatial dimension can be approximated in
$L^2$ on any finite time interval by solutions of a space discretized ODE
system which models the corresponding chemical reaction system replicated in
the discretization subdomains where the concentrations are assumed spatially
constant. Same-species reactions through the virtual boundaries of adjacent
subdomains lead to diffusion in the vanishing limit. We show convergence of our
numerical scheme by way of a consistency estimate, with features generalizable
to reaction networks other than the one considered here, and to multiple space
dimensions. In particular, the connection with the class of complex-balanced
systems is briefly discussed here, and will be considered in future work.
