Derivation of Composite Isotherm

Kipling has derived a composite isotherm equation that has been used widely. According to this derivation, when mass m of a solid adsorbent is brought into contact with n moles of the solution, there is a decrease in the mole fraction of the solution. Let this decrease in the mole fraction of the solution with respect to component 1 as a result of adsorption be Ax. Let x and x be the initial and final mole fractions of the solution with respect to component 1. Then 

Let us further suppose that this change is concentration Ax, and it is brought about by the transfer of moles of component 1 and of component 2 to the 

The composite isotherm is sometimes expressed in terms of (x - Xj) when xj is the mole fraction of component 1 in the adsorbed phase. This relationship can be written as 

This isotherm equation can be derived from Equation 3.17 as follows  

Sometimes it is convenient to express the results in terms of weights and weight fractions instead of moles and mole fractions. In that case, Equation 3.17 can be expressed as 

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