Optimum reference temperature for reparameterization of the Arrhenius equation. Part 1: Problems involving one kinetic constant

The Arrhenius equation is one of the most well-known equations in the chemical field and is widely used to describe the temperature dependence of kinetic constants. This equation contains two parameters, the frequency factor and the activation energy, which are usually estimated from experimental data. However, the correlation between the two parameter estimates is usually very high and in many cases is practically equal to one. This makes the precise identification of the parameter values very difficult. The high parameter correlation can be diminished through reparameterization of the Arrhenius equation and definition of a reference temperature. For problems involving a single kinetic constant, it is shown here both analytically and through numerical examples that the proper definition of the reference temperature allows for estimation of the parameters of the Arrhenius equation without correlation and with minimum relative error, leading to improvement of the parameter estimation procedure.