The mathematical origins of the kinetic compensation effect: 1. the effect of random experimental errors

Abstract

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.

Compensation effect in isopropanol dehydration over heteropoly acid catalysts at a gas–solid interface

“…It has been demonstrated for a number of catalytic reactions that compensation is an automatic consequence of the use of apparent Arrhenius parameters, where activation energies are a function of surface coverage and reactant concentration [17]. Recent discussion of the enthalpy-entropy relation can be found in [19,20] and references cited therein.…”

The desorption of H2CO from interstellar grains analogues

“…It is however simpler, and as accurate, to model this desorption as a zeroth-order desorption, employing the Polanyi-Wigner equation with the parameters ν 0 = 10 28 mol cm −2 s −1 and E = 27.1 +/− 0.5 kJ/mol for the desorption from an ASW surface and with the parameters ν 0 = 10 28 mol cm −2 s −1 and E = 31.0 +/− 0.9 kJ/mol for a silicate surface. These parameters have been obtained by fixing the pre-exponential factor, ν 0 , as the physically relevant value of 10 15 mol cm −2 × 10 13 s −1 = 10 28 mol cm −2 s −1 , since the preexponential factor and the desorption energy are correlated due to either random experimental errors (Barrie 2012a) or systematic errors (Barrie 2012b). Since the physically relevant quantity is the desorption rate only, arbitrarily fixing the pre-exponential factor to a physical value allows comparison of the desorption of two different molecules, as well as offering a robust method to implement desorption in gas-grain chemistry codes, without attributing a pre-exponential factor for each molecule on different types of surfaces.…”

Kinetics of Carbon Dioxide with Amines. I. Stopped-Flow Studies in Aqueous Solutions. A Review

“…This indetermination can be a first explanation for the apparent compensation effect generally Response surface for average relative error below 1% for k 0 modelled with zwitterion mechanism for piperazine at 30°C (Rayer et al, 2011). Variation between 10 Barrie (2012). We determine for each molecule the confidence ellipse area in order to evaluate the impact of statistical compensation effect on our parameters.…”