Optimal designs for the Arrhenius equation

The influence of temperature on the rate of kinetic processes is usually interpreted in terms of what is known as Arrhenius equation k(T)=Ae−B/T. Such a relation represents the temperature dependence of the rates of chemical reactions, conductivity coefficients and viscosity or diffusion phenomena. ters A and B are taken as constants, independent from temperature, and their measurements have a great importance for the correct modelization of the above mentioned phenomena. However, their measurements frequently meet experimental and numerical difficulties. er to improve the accuracy of the inferences on the parameters, optimal designs have been discussed. In this work, a D-optimal design has been calculated based on the Equivalence Theorem and c-optimal designs have been found to estimate a linear combination of the parameters using Elfvingʹs Method. Compound designs have also been calculated to deliver greater efficiency for the estimation of a particular parameter. ional designs have been compared to the optimal designs discussed and, as a result, a valuable tool has been provided for researchers to choose the most appropriate design comparing each one to the optima and calculating its efficiency. procedures have been applied to parameter measurements made in atmospheric chemistry, used primarily to model stratospheric and upper tropospheric processes. In these phenomena, special experimental difficulties are present, increasing the uncertainty factor of the parameters, making crucial the election of an adequate design.