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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 one of the mathematical, rather than physicochemical, explanations for the compensation effect and for the isokinetic relationship. It is demonstrated, both theoretically and by numerical simulations, that random errors in kinetic data generate an apparent compensation effect (sometimes termed the statistical compensation effect) when the true Arrhenius parameters are constant. Expressions for the gradient of data points on a plot of ln A against E are derived when experimental kinetic data are analysed by linear regression, by non-linear regression and by weighted linear regression. It is shown that the most appropriate analysis technique depends critically on the error structure of the kinetic data. Whenever data points on a plot of ln A against E are in a straight line with a gradient close to 1/RT, then confidence ellipses should be calculated for each data point to investigate whether the apparent compensation effect arises from random errors in the kinetic measurements or has some other origin.

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.

The fundamental interactions of dimethyl methylphosphonate (DMMP) and dimethyl chlorophosphate (DMCP) on amorphous silica nanoparticles have been investigated with transmission infrared spectroscopy and temperature-programmed desorption (TPD). DMMP and DMCP both adsorb molecularly to silica through the formation of hydrogen bonds between isolated silanols and the phosphoryl oxygen of the adsorbate. The magnitude of the shift of the ν(OH) mode upon simulant adsorption is correlated to the adsorption strength. The activation energies for desorption for a single DMMP or DMCP molecule from amorphous silica varied with coverage. In the limit of zero coverage, after the effects of defects were excluded, the activation energies were 54.5 ± 0.3 and 48.4 ± 1.0 kJ/mol for DMMP and DMCP, respectively.

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