Surface-Catalyzed Bimolecular Gas Phase Reaction

Question:

Consider a surface-catalyzed bimolecular gas phase reaction,
2CO(g) + O2(g) → 2CO2(g)
The Langmuir-Hinshelwood mechanism for this reaction is as follows:
CO(g) → CO(ads)
O2 (g) → 2O (ads)
CO(ads) + O(ads) → CO2(g)
The overall rate law for this mechanism is r = kθCO θO2. The binding affinities for the molecules of CO and O2  are K(CO) and K(O2 ), respectively.
a) Calculate θO2.
b) Calculate θCO .
c) Calculate the rate of the reaction. What is the rate of reaction at very large [CO]?
d) The Eley-Rideal mechanism of this reaction differs from the Langmui- Hinshelwood mechanism in the last step, CO(g) + O(ads) → CO2(g). The overall rate law for this mechanism is r = k[CO]θO2 . Calculate this rate explicitly. What is the rate of reaction at very large [O2] for both mechanisms?

Solution:
a and b)
Adsorption of CO and O2 on surface sites, S, can be written as,

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