In this paper, computer simulation results of phase separation dynamics of ternary mixture (A, B, and C) coupled with an interfacial chemical reaction A + B=C in two-dimension are presented. The effect of reduction of interfacial free energy due to the presence of species C along the interface is taken into consideration in our study. In the case of fixed domain size, it is shown in simulations that for both reversible and irreversible reactions the generation of species C is not affected by the reaction rate constants, and it is a diffusion-controlled process. Also, the simulation reveals that for reversible chemical reaction in the case of fixed domain size, the equilibrium of concentrations is established. In the cases of coupling between domain growth and reversible reaction kinetics, it is shown in simulations that the domain growth eventually freezes regardless of the magnitude of the reaction rate constants. The higher the reaction rate constants are, the slower the evolution to reach the reach steady state is, the larger the steady state domain size is, and the smaller the average concentration of species C is.