Partial adsorption enthalpy and entropy

In the case of multi-components adsorption, the partial molar differential adsorption enthalpies and entropies of each component i present in the gas mixture cannot be directly measured by experiments. However, it is possible to estimate them by mean of the tangent method based on the well-known Gibbs-Duhem relation. 

Let us consider the adsorption of a binary gas mixture A+B and Z a function of state, which denotes either the enthalpy or the entropy. The differential molar coadsorption value ArZ is equal to  

The application of the Gibbs-Duhem relation 21 XidZ j = 0 leads to  

XAdArZ A + XBdArZ g = 0 The derivation of Eq. 7.96 with respect to xa gives  

the partial molar differential values and ArZ g can be graphically 

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