Derivation of the Langmuir Isotherm by Other Approaches

The Langmuir isotherm can also be derived by other methods including statistical mechanics, thermodynamics, and chemical reaction equilibrium. The last approach is especially straightforward and useful, and it is developed as follows. For nondissociative chemisorption, the adsorption step is represented as a reaction, i.e., for an adsorbing gas-phase molecule. A, which adsorbs on a site,  

In similar fashion, the dissociative adsorption of a diatomic gaseous molecule A2 is written  

A site balance again gives equation 5.30 (or 5.31) and substitution into equation 5.35 leaves 

Taking the square root of both sides of the equation and rearranging gives  

The K s in these Langmuir isotherms represent adsorption equilibrium constants, thus they can be represented in the following ways  

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