Adsorption Equilibrium on Uniform Ideal Surfaces-Langmuir Isotherms

With this introduction, the derivation of an adsorption isotherm, which represents an equilibrium adsorption process, can be conducted [5]. The Langmuir isotherm is obtained based on the assumptions associated with an ideal uniform surface on which all sites are identical [5], i.e., 

Localized adsorption occurs only on vacant sites, 

Only one adsorbed species can exist per site, that is, saturation coverage is achieved at one monolayer, and 

The heat of adsorption is constant and independent of coverage, which assumes that no interaction occurs between adsorbed species. 

At equilibrium, the rates of adsorption and desorption must be equal and, with the above assumptions, equations 5.6 and 5.8 can be used as written. Setting these two equations equal to each other and rearranging gives  

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