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.
T" exp(B/TI. 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.
With respect to the modified Arrhenius equation: k = A 1ntrod.uction Artides on. chemical kin.etics usu.ally present numerical values of rate coefficients (determined typically over a range of ternDerature) described by some form of Arrhenius-type equation. Unfortimately, in most cases, these important results are not accompanied by statistical analysis. The lack of common practice to publish uncertainty data resulted in the fact that in some cases the nature of the quoted error of parameters, if they are published a t all, is unknown (standard deviation, 2a, confidence interval, etc.). On the other hand, the proper utilization of published parameter values requires the knowledge of *To whom correspondence should be sent.