Langmuir Isotherm and Reaction Kinetics

At a given temperature adsorption isotherms measure the number of adsorbed molecules as a function of pressure for the fluid that is in contact with the zeolite. The simplest form is the Langmuir isotherm which treats the zeolite as a collection of equivalent adsorption sites in the absence of adsorbate-adsorbate 

Here Ca is the number of adsorbed molecules A per unit volume, Q is the maximum loading of A, Ka is the adsorption equilibrium constant and Pa is the partial pressure of A. During adsorption there could be several energetically and topologically inequivalent adsorption sites and, in that case, total adsorption may simply become the sum of multiple Langmuir isotherms with contributions from different adsorption sites. The latter and several other isotherms that model 

The derivative of the equilibrium constant with respect to temperature at constant surface coverage is the isosteric heat of adsorption  

In the limit of low pressure the front end of the adsorption isotherm is approximated by the Henry regime which states that the number of adsorbed molecules per unit volume is proportional to the pressure and to the Henry coefficient, Kh.  

Based on Langmuir-Hinshelwood kinetics the rate expression for a first order reaction (A — R) that is surface reaction-controlled becomes equal to the following expression [2]  

---