Based on Site Number Variation

Equation (1) may be derived by assuming that the number of sites available for adsorption decreases exponentially with the number on which adsorption has already taken place, i.e., with extent of adsorption q Thus 

Equation (8) describes by a second-order process, the rate of removal or destruction of bare sites as a function of the number present on the surface, i.e., the normal concept that the total number of free-plus-covered sites on the surface is constant during the adsorption processs is abandoned. In order to obtain the Elovich expression, a simultaneous first-order creation of sites by the act of adsorption must be also assumed. 

Since the act of adsorption eliminates more sites than by actual occupancy, bare sites are in short supply and the rate of adsorption is therefore governed by the availability of sites. As an example of a specific model to conform with these requirements, we cite that proposed by Cimino et al. 76) for the adsorption of hydrogen on ZnO. They argue that, since both Zn + and 0 ions have closed electron shells, no orbitals are available to form a surface bond for chemisorption. However, free electrons may be thermally excited from the valence band (or 

Combination of these equations [cf. Eq. (8)] then leads to Eq. (6), and, hence, to the Elovich equation (1). 

Similar models had been proposed previously by Taylor and Thon 13, 77, 78) following Volkenshtein s theory of activated excitation of surface sites by the act of adsorption e.g., the consequences of a spontaneous unimolecular decay and a bimolecular destruction of exited sites were deduced, and a possible alternative interpretation of interaction between sites in the course of adsorption was also indicated. 

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