Single-step methods for calculating activation parameters from raw kinetic data

A general procedure is described for calculating activation parameters from raw kinetic data in one step. The method is applicable to any kinetic order of reaction, and to kinetic experiments carried out either at constant temperature (the conventional method) or under conditions where the temperature varies during the course of each kinetic run. The principle of the new method is to substitute the Arrhenius dependence of the rate constant into the integrated form of a kinetic rate equation. This gives an expression for the concentration of a reactant as a function of time, temperature, initial concentration, activation energy, and pre-exponential factor. Using experimental values of the time, temperature, and initial substrate concentration, the amounts of reactant left unreacted under different conditions may be fitted iteratively to obtain the best values of the activation parameters. These agree closely with those calculated by traditional methods, but the new method has the advantage that the calculated uncertainties in the activation parameters reflect directly the scatter in the experimental observables.