Classical Methods:

(b) BET equation

BET (after Brunauer, Emmett and Teller) equation is used to give specific surface area from the adsorption data. The BET equation is used to give the volume of gas needed to form a monolayer on the surface of the sample. The actual surface area can be calculated from a knowledge of the size and the number of the adsorbed gas molecules. Nitrogen is used most often to measure BET surface, but if the surface area is very low, argon or krypton may be used as both give a more sensitive measurement, because of their lower saturation vapor pressures at liquid nitrogen temperature.

Where, V = volume of gas adsorbed at pressure p; V^_m = amount of gas corresponding to one monolayer;
z = p/p*, ratio of pressure of gas and pressure at saturation; c = a constant.

A plot of vs z gives slope and intercept at , and cV^_mono could be determined. The results can be combined to give c and V^_mono.

When the coefficient c is large, the isotherm takes the simpler form as follows.

This is applicable to unreactive gases on polar surfaces, for their c is 10². Higher value of c will mean mainly monolayer formation. The value of V_^mono, the volume of gas required to form monolayer, is of considerable interest because it helps in the calculation of surface area of a porous solid. The surface area occupied by a single molecule of adsorbate on the surface can be calculated from the density of the liquefied adsorbate. For example, the area occupied by a nitrogen molecule at -195^o C estimated to be 16.2x10^-20 m² assuming molecules to be spherical and close packed in the liquid. Thus, from the value of V_^mono obtained from the BET theory, surface area of the adsorbent could be determined.