On the errors of Arrhenius parameters and estimated rate constant values

A detailed statistical study is presented, based on simulated experimental data, on the estimation of activation parameters using the Arrhenius equation: k = A exp(B/T). The close correlation of the two parameters is shown, which requires the computation of the covariance matrix for the representation of uncertainties. This matrix facilitates the correct estimation of the confidence interval for interpolated (or extrapolated) values of rate coefficients. It is proposed that the full correlation matrix should be published in any article dealing with the determination of Arrhenius parameters. The importance of correct weighting is emphasized. Nonlinear fitting to the Arrhenius equation can be carried out without weighting only in case the (absolute) error of rate coefficient is independent of the temperature. Simulated experiments show that noncorrect weighting shifts the average values of fitted parameters and increases the variance of the parameters as well. With respect to the modified Arrhenius equation: k = A · Tⁿ exp(B/T), statistical analysis shows that the physically meaningful estimation of all three parameters is impossible. Nonlinear fitting of three parameters is suggested for interpolation (and extrapolation) of rate coefficients, whereas in case of activation parameter estimation, the fixing of “n” on the basis of theoretical considerations is advised followed by the estimation of the remaining two parameters.