The mathematical origins of the kinetic compensation effect: 2. The effect of systematic errors

The kinetic compensation effect states that there is a linear relationship between Arrhenius parameters ln A and E for a family of related processes. It is a widely observed phenomenon in many areas of science, notably heterogeneous catalysis. This paper explores mathematical, rather than physicochemical, explanations for the compensation effect in certain situations. Three different topics are covered theoretically and illustrated by examples. Firstly, the effect of systematic errors in experimental kinetic data is explored, and it is shown that these create apparent compensation effects. Secondly, analysis of kinetic data when the Arrhenius parameters depend on another parameter is examined. In the case of temperature programmed desorption (TPD) experiments when the activation energy depends on surface coverage, it is shown that a common analysis method induces a systematic error, causing an apparent compensation effect. Thirdly, the effect of analysing the temperature dependence of an overall rate of reaction, rather than a rate constant, is investigated. It is shown that this can create an apparent compensation effect, but only under some conditions. This result is illustrated by a case study for a unimolecular reaction on a catalyst surface. Overall, the work highlights the fact that, whenever a kinetic compensation effect is observed experimentally, the possibility of it having a mathematical origin should be carefully considered before any physicochemical conclusions are drawn.