The integrated rate equation for the main product [C] is , which is equivalent to . Concentration of B is related to that of C through The integrated equations were analytically obtained but during the process it was assumed that . Therefore, previous equation for [C] can only be used for low concentrations of [C] compared to [A]0 Stoichiometric reaction networks The most general description of a chemical reaction network considers a number of distinct chemical species reacting via reactions. The chemical equation of the -th reaction can then be written in the generic form which is often written in the equivalent form Here is the reaction index running from 1 to , denotes the -th chemical species, is the rate constant of the -th reaction and and are the stoichiometric coefficients of reactants and products, respectively. The rate of such a reaction can be inferred by the law of mass action which denotes the flux of molecules per unit time and unit volume. Here [\vec{X}]=([X1], [X2], \ldots ,[X_\mathit{N}]) is the vector of concentrations. This definition includes the elementary reactions: zero order reactions for which for all , first order reactions for which for a single , second order reactions for which for exactly two ; that is, a bimolecular reaction, or for a single ; that is, a dimerization reaction. Each of these is discussed in detail below. One can define the stoichiometric matrix denoting the net extent of molecules of in reaction . The reaction rate equations can then be written in the general form This is the product of the stoichiometric matrix and the vector of reaction rate functions. Particular simple solutions exist in equilibrium, , for systems composed of merely reversible reactions. In this case, the rate of the forward and backward reactions are equal, a principle called detailed balance. Detailed balance is a property of the stoichiometric matrix alone and does not depend on the particular form of the rate functions . All other cases where detailed balance is violated are commonly studied by flux balance analysis, which has been developed to understand metabolic pathways. General dynamics of unimolecular conversion For a general unimolecular reaction involving interconversion of different species, whose concentrations at time are denoted by through , an analytic form for the time-evolution of the species can be found. Let the rate constant of conversion from species to species be denoted as ,