The BET constant and site occupancy

Equation (4.44) is used to calculate the fraction of surface unoccupied when W =W, that is, when just a sufficient number of molecules have been adsorbed to give monolayer coverage. LowelP has derived an equation that can be used to calculate the fraction of surface covered by adsorbed molecules of one or more layers in depth. Lowell s equation is 

Equations (4.44) and (4.45) should not be taken to mean that the adsorbate is necessarily arranged in neat stacks of various heights but rather as an indication of the fraction of surface covered with the equivalent of i molecules regardless of their specific arrangement, lateral mobility, and equilibrium with the vapor phase. 

Of further interest is the fact that when the BET equation (4.38) is solved for the relative pressure corresponding to monomolecular coverage, W = iV ), one obtains 

The subscript m above refers to monolayer coverage. Equating (4.46) and (4.44) produces the interesting fact that 

That is, the numerical value of the relative pressure required to make W equal to is also the fraction of surface unoccupied by adsorbate. 

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