Microkinetics of Elementary Surface Processes

Let s assume we have determined a rate constant, k, for the desorption of species A from a surface. Recall that the rate constant is the rate for the desorption process, assuming that the adsorbate (A) is in the reactant (i.e., adsorbed) state. The rate at which desorption occurs from a given site on the surface is then proportional to the product of the rate constant and the probability that a given site is occupied. The probability that a site is occupied is equal to the fractional coverage of the adsorbate on the surface, 0. So we arrive at the expression 

When adsorption and desorption are equilibrated, the rates for adsorption and desorption are equal in magnitude  

We can think of the Equation (5.4) as expressing the adsorption rate as the product of 2 terms (i) the rate constant at a flux of A toward the surface corresponding to standard pressure (1 bar), p, which describes the flux variation due to variations in the pressure relative to the standard pressure, and (ii) the coverage of free sites, 6 which is the probability that the site we are trying to adsorb in is a free site. Since this point of view makes sense even when the system is not in equilibrium, we shall assume Equation (5.4) holds for nonequilibrium situations. 

The expression (5.5), which states that the equilibrium constant for an elementary reaction (here adsorption/desorption) is equal to the forward divided by the backward rate constant, is actually very general. We observe that 

The rate expressions for surface processes thus take the same form as well-known expressions for chemical reactions in gas phase or in solution. Whereas the activities of gas- or liquid-phase reactants are expressed as pressures or concentrations, the activities of surface reactants are expressed in terms of the fractional coverages of adsorbates and of free sites. For surface processes, we can define reaction fractions by taking the product of the activities of the left-hand side of a reaction equation and dividing it by the right-hand side. For example, with the adsorption-desorption reaction given by 

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