The application of polynomial expressions to determine the initial concentrations and rate constants of chemical reactions

Abstract

The rates of chemical reactions are frequently followed by measuring the change of a physical property, such as pressure changes in a gaseous reaction, with time. In many cases a value of the physical property at zero time is necessary to calculate the rate constant. Often it is not practical to measure this quantity directly. Several methods are available to evaluate the rate constant and initial conditions for firstorder reactions from experimental data. The methods of Guggenheim,l H a r t l e ~ , ~ and Swinbourne3 depend on a reaction obeying the first-order rate law for a considerable part of the reaction. Swinbourne4 also described a method for determining the initial and final pressures and the rate constant of a gas reaction of order n. Roseveare5 has described a method which can be applied to a second-order reaction of a single reactant or equal concentrations of two reactants. All of these methods require orthogonal data. These methods are not satisfactory when the reaction is complicated by the decon~position of product as a consecutive reaction, or where a product inhibits or accelerates the rate of reaction. For such cases it is necessary to determine the initial physical property and rate constant from data over the early part of the reaction. In gaseous elimination reactions, such as the pyrolyses of alliyl halides and the hydrogen halide-catalysed pyrolyses of alcohols, the reaction can be represented by a stoicheiometric equation of the type