Competitive and Multisite Langmuir Isotherms

When two or more adsorbates are present (A, B.) in contact with a solid, both will try to adsorb on the empty sites, whereas those occupied can hold either adsorbate. This is a situation of competitive adsorption, and the Langmuir isotherm 

Equations 4.48 through 4.51 are different forms of the Langmuir competitive adsorption isotherm it can easily be extended to more than two adsorbates. They have been written for gas phase, but equally they can apply to adsorption from solution, replacing the pressure by activity or (approximately) concentration of each solute. 

On the other hand, if the surface sites are not all equal, but of different kinds, which essentially means having substantially different adsorption energies, the Langmuir isotherm can be extended easily if all sites of either type are independent. Let the surface be composed of 2i sites of type 1 and Q2 sites of type 2, so that Qs = Qi + Q2 letfi = QJQs, the total amount adsorbed on the surface, because of the site independence, will be given by the following (Langmuir 1918 Adamson and Cast 1997 Hiemenz and Rajagopalan 1997)  

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