It is possible that oxygen and other gases dissociate when adsorbed on a solid surface, and in catalysis it is important to know whether such a dissociation occurs. If oxygen did not dissociate, that is, the adsorption process was

the amount of oxygen adsorbed would be given by 

where a_H2 is the activity of molecular oxygen in the gas phase. However, if oxygen dissociates, the following two-step process occurs at the surface

Using the notation that K₂ is the activity-based equilibrium constant for the dissociation reaction, develop expressions for the amount of molecular oxygen adsorbed as a function of the equilibrium constants and the oxygen partial pressure for the two cases, adsorption without dissociation and adsorption with dissociation. How would you discern which process was occurring if you only had experimental data on the total oxygen adsorption as a function of its partial pressure?  

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