The interpretation of apparent activation energies derived by the least-squares treatment of kinetic data

Abstract

The majority of reported values of activation energy and pre-exponential factor have been obtained by fitting experimental results to the logarithmic form of the Arrhenius equation, In k = In A — E a a RT where E a and A are the apparent activation energy and pre-exponential factor and both are, to a first approximation, considered to be independent of temperature. The statistical technique of line-fitting by least-squares is frequently used to obtain E a and In A. Theoretical treatments of rate constant give equations in which the activation energy and pre-exponential factor may vary with temperature so that the graph of In k vs. 1 T is actually a curve and not a straight line. The apparent and theoretical activation energies will, therefore, differ. In this paper the differences between E a derived by the least-squares method and the theoretical activation energy have been calculated for a wide range of experimental conditions and for two types of theoretical equation. In addition, conditions for detection of curvature in the graph of In k vs l T have been determined. Because in practice the curvature is slight and not usually detected, the most interesting conclusion drawn from these calculations is that differences between apparent and theoretical values as great as 5 kcal/mole can exist while the experimental results still appear to fit the Arrhenius equation. Further, if apparent activation energies from two different reactions are compared, as a rough approximation, only differences greater than 3–4 kcal/mole are likely to be significant.