Graphical rules of steady-state reaction systems

Abstract

Four rules to deal with first-order or pseudo-first-order steady-state reaction systems are presented.By means of Rule 1, we can immediately write down the apparent rate constants of consecutive reaction systems. This rule is actually the same as the "Rule of Thumb" proposed by Gilbert, but here its mathematical proof is given.Rule 2 and Rule 3 may serve to derive the apparent rate constants of various complex reaction systems. In comparison with the general algebraic methods, these two rules can simplify laborious calculations that would otherwise be tedious and liable to errors.Rule 4 presents a new schematic method to calculate the concentrations of the reactants. The new method, in simplifying the calculation of complex problems, is extraordinarily efficacious in comparison with the existing schematic methods. For complex mechanisms which are too complicated to be treated with the general manual calculation method, the practical calculations show that we can easily write down the desired results by means of Rule 4.In addition, Rules 2, 3, and 4 include corresponding check formulae, by use of which we can avoid missing subgraphs to be counted. Their advantages will be manifested particularly in dealing with complex mechanisms.The mathematical proofs of these rules are given in the Appendices.