Five types of BET isotherms

The generalized equation for these five types of isotherms is given by Equation 

For the first three types of isotherms g is assumed to be 2. This results in the following equation. If the adsorption takes place in a limited space, so that even at saturation pressure only a hmited number of layers can be adsorbed on the adsorbent, one obtains this expression. 

When n = 1, this results in Type I or the Langmuir isotherm as stated earlier. When n = 00 this results in Type II or rarely Type III isotherm given by the Equation 8.8 

Rearranging the above equation results in Equation 8.9 below. 

Types IV and V suggest that the complete or almost complete filling of the pores and capillaries of the adsorbent occurs at a pressure lower than the vapor pressure of the gas indeed, sometimes at a considerably lower pressure. This lowering of the vapor pressure indicates that as the pressure of the gas is increased some additional forces appear. There is additional heat of evaporation and the term g appears in the equation (Equation 8.6) which is a function of that additional heat. Therefore, for Type IV and V BET isotherms, the term g in Equation 8.6 is temperature dependent. The term decides the shape. When B2 1 one obtains Type IV isotherm and for B2 1 Type V isotherm. 

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