Site densities bimolecular surface reaction

The frequency factor of a catalytic reaction describes the maximum possible number of encounters between the two reactants on the surface under the given conditions (see Chapter 9). In bimolecular reactions this number depends on the density of sites on the surface, since sparse site densities make it unlikely that the two reactants will find themselves on adjacent sites that are close enough for reaction to take place. Thus we can expect that changes in site density can have a disproportionate effect on the rate of reaction via the frequency factor. Doubling site density in a reaction of the kind under discussion may increase the rate of reaction by more than the factor of 4 expected on the basis of site concentration alone, due to the effects of increased density on the entropy of activation and hence the frequency factor ofk/. 

In these expressions is the rate of adsorption of species j, which for A may be written as A + S AS, where A is the gas-phase molecule. S is an empty site on the surface, and AS is the adsorbed molecule. We can consider adsorption as a bimolecular chemical reaction that is proportional to the densities of the two reactants A and S to give... 

These requirements for reaction (adsorption) to occur look very similar to those we imposed on the bimolecular coUision number in order to derive the reaetive collision number, Z,(A, B), of equation (2-20). If we designate E as the activation energy required for chemisorption, as the eoneentration of sites available for chemisorption, the site density per unit area of surfaee, and f 6) some funetion of the fraction of surface covered by the adsorbate, 6p, the following analog to equation (2-20) may be written as... 

One can, assuming the mechanism is known, turn the equation around and then calculate the site density. We and others have done just that ( > ). Calculations have been made for both saturated and unsaturated surfaces, for both unimolecular and bimolecular reactions, for reactions in which the adsorbed molecule is immobile and also where it is mobile, and for reactions carried out at both low-conversion and high-conversion conditions. 

---