To treat a realistic chemical system, such as a liquid phase dehydrogenation reaction, a chemical scheme, which describes the chemical kinetics in terms of the small number of reaction progress variables is needed. Based onthe matrix algebra, we analyse the key components, elements and reactions in the mechanism, C-matrix. Reduction techniques exploit the time-scale separation into fast and slow modes by computing the dimension reduced model via the elimination of fast mode subjecting them to the slow one. The two-step reversible reaction mechanism is considered for model reduction and to simplify the complexity of reaction mechanisms. They give a meaningful picture, but for maximum clarity, the phase flow of the solution trajectories near the equilibrium point is exploited. The Lyapunov function is applied for the stability analysis. To describe the physical behaviour of the reaction mechanism, graphical results are measured while refinement of the initial approximation is tabulated at the end.