v₀ is volume of gas adsorbed per unit area of adsorbent surface and v_m is the volume of gas adsorbed when the entire adsorbent surface is covered with a complete unimoleculer layer.

For simplification it is assumed that the heat of adsorption of the 2^nd , 3^rd ………upto i^th layer are equal to each other and equal to heat of liquefaction of the adsorbate.

Or

and , g being an appropriate constant.

 

Now the s₁ ,s₂ ........................s_i can be expressed in term of s₀

              

Sum of the infinite geometric progression

Substituting ,

-----------------[2]

 

For adsorption on free surface, at saturation pressure of gas p₀, infinite no of layers can build up on the surface. Further to make at , x must be equal to unity in equation [2].