A mathematical method is a powerful tool for the study of chemical reactions. This model is based on reaction-diffusion equations that contain a non-linear term analogous to the enzymatic kinetics of response of Michaelis-Menten and the hill binding. In this paper, an approximate analytical solution of the non-linear differential equations that describe the concentrations in mass-action kinetics has been derived for all values of parameter using the new homotopy perturbation method. These results are compared with the numerical result, and satisfactory agreement is noted.