Graph theoretical exploration for the solutions of the kinetics rate equations of nonchain complex reaction networks

Nonchain complex reactions involving active center, intermediate(s), by‐products, and the final product(s) are explored with the use of graph theory for solving their rate equations. Three such reaction schemes in a varying number of intermediates are solved for the concentrations of the species involved at any instant of time ( t ). Time derivatives of these solutions result in the reaction rates of the species concerned. The time functions of rates and concentrations for three successive reaction schemes are then used to generalize the respective solutions for reaction scheme having n intermediates. The rate equations are approximated in three different time regions and are found that: (i) at time t  = 0, the rate of reaction of each of the intermediate(s), by‐products, and final product is zero; (ii) at t  < < <  τ (average life‐time of the active center and intermediate(s)), the reaction rate of an m th intermediate, an m th by‐product, or the final product bears proportionality relationship with t m ; and (iii) at t  > > >  τ , the reaction rate of each of the intermediates is zero whereas that for each by‐product or final product is constant and is expressed from an initial rate multiplied by the product of the probabilities of reaction of the intermediate(s) concerned.