Correlations in Kinetics

The lower limit refers to the most active sites and the upper limit refers to the least active sites. Integration of this expression gives  

Because E2 Ei and the term (1/b — 1/RT) was found experimentally to be negative, the first term in the brackets in equation 8.4, i.e., the upper limit, can be ignored and it simplifies to  

Consequently, this model of a nonuniform surface not only showed that the most active sites dominate the observed kinetics, but it also provided an explanation for the compensation effect that was periodically observed between the preexponential factor and the activation energy in a given reaction. 

There are several relationships in homogeneous kinetics that are very useful, not only in these systems, but also in heterogeneous catalytic reactions [2,3]. These include the Polanyi relation [4,5], which states that for a family of exothermic elementary reactions, the steps are correlated by the expression 

The next is the Bronsted relation, which was originally observed in acid-catalyzed organic reactions in the liquid phase [6], but which also exists for base-catalyzed reactions [7]. It provides a relationship between the rate constant for an acid-catalyzed reaction, kA, and the ionic strength of the acid as represented by its dissociation constant, Ka  

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