Thermodynamics of Adsorption Phenomenological Perspective

To see how the equation of state of two-dimensional matter and the adsorption isotherm are related, we return to the Gibbs equation (Equation (7.46))  

Since we are concerned here with adsorption from the gas phase, the chemical potential may be related to the pressure of the gas by 

In the present context it is convenient to use Equation (7.43) to eliminate T2 from Equation (3) and express the surface excess as the number of moles adsorbed per unit area  

Next we substitute the product of sample weight times specific area for A in this equation to obtain 

For a given adsorbent and an isothermal experiment, T and Asp are constants. The ratio n/w is the equilibrium amount adsorbed that will be a function of p. Therefore Equation (5) may be integrated as follows  

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