Derivation of adsorption isotherm from kinetics

An equation for adsorption isotherm can also be derived by equating the rates of adsorption and rate of desorption at equilibrium condition. From equations [3] and [4] at equilibrium, . For the simplest case of non dissociative adsorption where f( θ ) = (1- θ ) and . we obtain

 

Noting that E_d - E_a = - Δ H = heat of adsorption,

or

 

Or where

 

If heat of adsorption remains constant with coverage, b is a function only of temperature and

 

 

or -------------[6].

 

This equation [6] is the well known Langmuir isotherm.