Apparent activation energies on catalysts with heterogeneous surfaces: I. General derivation

Abstract

Many catalysts are likely to have surfaces which are energetically heterogeneous. The overall rate of reactions on such surfaces will, therefore, be the sum of rates of concurrent reactions each proceeding with different activation energies. Apparent activation energies are, however, commonly derived by treating the overall rate as if it were governed by a single activation energy. The majority of reported values of activation energy have been obtained by fitting experimental results to the logarithmic form of the Arrhenius equation and measuring the slope. The method of linefitting used is often the statistical technique of least-squares or some visual equivalent. In this paper, equations are derived which relate the apparent activation energy derived by the least-squares technique to any postulated type of heterogeneity and the experimental error in the rate determination. In this derivation the dependence upon temperature and surface concentration of the activation enthalpy and entropy is included in the calculations. The graph of log (rate constant) vs. 1 T for catalysts with heterogeneous surfaces may not be linear. The degree of curvature introduced by any postulated heterogeneity has been calculated and may be compared with experimental error in order to decide whether it would be detectable.