Pressure on the Excess Free Energy

Comparison between case (i), (a) and case (ii) shows that the sign of 

Inversions of the sign of the excess functions with p are especially interesting. The comparison with experiment data will be studied in Ch. XI. 

These results illustrate once more the complicated and interesting relations between excess functions and intermolecular forces. 

Influence of pressure on the excess free energy in the case (/ = 0) 0 

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Influence of Pressure on the Excess Free Energy 177. 7. Conclusions 179. 

The second equation in their mixing rule is based on the observation that the excess Helmholtz tree-energy of mixing calculated from a cubic EOS is much less sensitive to pressure than the Gibbs free-energy, as can be seen in Figure 4.3.1. Consequently, to an excellent approximation ... 

For calculations of the dependence of the excess free energy on h+, according to Equation 2.34, a disjoining pressure isotherm should be selected. It is selected for the calculation as follows (Figure 2.9) ... 

The equation also applies to the adsorption of a gas on a solid. At low gas pressures, p. the equilibrium pressure of the gas can be substituted for a, the activity of the solute. The amount of gas adsorbed v/V is equivalent to the surface excess T, where v is equal to the volume of gas adsorbed per gram of solid and V is the molar volume of the gas. The total free energy change at constant pressure is E[Pg.1582]

The attractive forces between molecules in the bulk liquid are uniform in all directions (zero net force). However, the molecules at the liquid surface cannot form uniform interaction because the molecules on the gas side are widely spaced and the molecular interactions are mainly between surface molecules and the subsurface liquid molecules (non-zero net force). As a result, the molecules at the liquid surface have greater free potential energies than the molecules in the bulk liquid. This excess free energy per unit area that exists in the surface molecules is defined as surface tension (y). Surface tension is a thermodynamic property and can be measured under constant temperature and pressure and its value represents... 

The origin of the excess stress on liquid/vapor interfaces follows from the tendency of the liquid surface to contract. As a molecule inside a mass of liquid is under the effect of the forces of the surrounding molecules, while a molecule on the surface is only partly surrounded by other molecules, some work is necessary to bring molecules from the inside to the surface. This indicates that the force must be applied along the surface in order to increase the area of the surface. This force on the surface appears as excess stress (a difference between normal and transverse components of pressure tensor in the region of the interface) and defines the surface tension of the liquid. Excess stress a, for liquid/vapor interfaces, is always a positive quantity and is equal to the interfacial free energy. 

Because the WS mixing rule uses VLE information only at low pressure, it can also be used to make predictions at high pressure based on low-pressure prediction techniques such as UNIFAC and other group contribution methods (Orbey, Sandler, and Wong 1993). This completely predictive method using the WS and other excess free-energy-based EOS models is discussed in Chapter 5. 

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