How is Langmuir adsorption isotherm different from Freundlich's?

I see no difference between the two. Both say that the degree of adsorption reaches a limiting value at high pressures and at very low pressures degree of adsorption is directly proportional to the pressure.


Where does the difference lie?




There is a fundamental difference between both models.


*Langmuir*'s model was a theoretical construct, while the *Freundlich* isotherm is empirical.


In the *Langmuir* model, it is assumed that at maximum coverage, there is only a **monomolecular** layer on the surface. This means that there is **no stacking** of adsorbed molecules. The *Freundlich* isotherm does not have this restriction.


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Freundlich gives you the amount absorbed per unit mass of absorbate, and has this absorbtion fraction be the nth root of the pressure, with n being a material-specific constnat. Langmiur gives the surface coverage, so it only allows the surface of a material to be used for sorption. Also, the functional relationship is not a root, but an inverse of the pressure multiplied by the pressure. 


Qualitatively, in the limits, both seem similar, but they differ in their details and will give different answers. 


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The difference is that cation exchange reactions involving clay minerals are analogous to the Langmuir isotherm because the concentration of cations adsorbed can never be greater than the cation exchange capacity of the solid.


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