Adsorption thermodynamics molar volume

Figure 4,14. Diagram of the thermodynamic cycle used to explain retention in reversed-phase chromatography by solvophobic theory. Na = Avogadro number, AA = reduction of hydrophobic surface area due to the adsorption of the analyte onto the bonded ligand, y = surface tension, = energy correction parameter for the curvature of the cavity, V = molar volume, R = gas constant, T = temperature (K), Pq = atmospheric pressure, AGydw.s.i a complex function of the ionization potential and the Clausius-Moscotti functions of the solute and mobile phase. Subscripts i = ith component (solute or solvent), S = solute, L = bonded phase ligand, SL = solute-ligand complex, R = transfer of analyte from the mobile to the stationary phase (retention), CAV = cavity formation, VDW = van der Waals interactions, ES = electrostatic interactions.

It is seen in Eq. (29) that the DR equation requires two types of parameters (1) properties of the adsorbent-micropore volume Vo and characteristic energy Eq-, (2) properties of the adsorbate — saturation pressure Pg, affinity coefficient P, and liquid molar volume. Principally, the first group of parameters are temperature-independent and can be obtained from the adsorption of a reference adsorbate on the same adsorbent, while the second group of parameters are temperature-dependent but can be simply estimated from the thermodynamic properties of each species. Therefore, a limited set of data is required to describe binary adsorption over a wide range of pressure and temperature. Thus the advantages of using the DR equation deserve to be exploited. 

Let us consider the coadsorption of two components A and B in a closed system at constant temperature. As for the adsorption of a single component, we can define an equivalent thermodynamic system composed of a closed volume containing the gas mixture in contact with the sample (Fig. 7.17). The pressure of gas mixture is Po = Pao+Pbo in th initial condition and p= Pa+Pb at the equilibrium. The molar Gibbs energy of each component is Gmi-... 

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