Assumptions     Final form of modified Langmuir adsorption isotherm

Derivation of isotherm

Equation 1

where S is the surface area,  is the absolute isotherm (expressed per unit of the surface area), b is the temperature dependent parameter,  a₁ is the intensive parameter connected with adsorption energy in the first layer: a₁ = a₀^.exp(-E_a/RT), and V_m is the monolayer capacity.

The polimolecular adsorption is given as

Equation 2

where  is the amount adsorbed in the j^th layer on the unit of the surface area of adsorbent.

For the following layers:
 
 

Equation 3

where  and  are the surface area accessible (surface coverage) for 2^nd and 3^rd layer, respectively.
The general expression is then

Equation 4

 

Equation 5

where b_j corresponds to the maximum amount adsorbed in the given layer on the absolute isotherm.

Assuming that b₁ = b₂ = ... = b_n = b and for i>1: a₂ = a₃ = ... = a_n = a_L

where a_L is the intensive parameter connected with the heat of  liquefaction ,

and taking into the account Equation 5 we obtain
 
 

Equation 6

where

is decreasing geometric series in which any term has a form:
 

Equation 7

After adding up the terms of this geometric series we obtain
 

Equation 8

Assumptions     Final form of modified Langmuir adsorption isotherm