Diatomic molecules association-dissociation rates

If we move the chemisorbed molecule closer to the surface, it will feel a strong repulsion and the energy rises. However, if the molecule can respond by changing its electron structure in the interaction with the surface, it may dissociate into two chemisorbed atoms. Again the potential is much more complicated than drawn in Fig. 6.34, since it depends very much on the orientation of the molecule with respect to the atoms in the surface. For a diatomic molecule, we expect the molecule in the transition state for dissociation to bind parallel to the surface. The barriers between the physisorption, associative and dissociative chemisorption are activation barriers for the reaction from gas phase molecule to dissociated atoms and all subsequent reactions. It is important to be able to determine and predict the behavior of these barriers since they have a key impact on if and how and at what rate the reaction proceeds. 

Suppose now we are at equilibrium, when association and dissociation compensate each other. We may then apply the detailed balancing principle and say that the dissociation process must be a bimolecular reaction of the second order.4 From a knowledge of the equilibrium constant and of the experimental association rate, we may then infer the pseudoexperimental dissociation rate at equilibrium. It is rather fortunate that the association process does not require an activation energy, since in this case, its rate is the same out of equilibrium, where the experiments have been carried out, as it is at equilibrium, where the values are interesting. We then understand that the dissociation reactions of a diatomic molecule by a bimolecular process offer the two interesting possibilities ... 

A more complete mechanism can be formulated by considering the vibrational energy level ladder of a diatomic molecule as shown schematically in Fig. 6-7. The concentration of molecules in the ith state changes with time due to transitions within the energy level ladder and due to dissociation to atoms and association of atoms to form a molecule in the ith state. Thus the rate equation can be written as... 

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