Residual Gibbs free energy

The UNIQUAC method of Abrams and Prausnitz divides the excess Gibbs free energy into two parts, the combinatorial part and a part describing the inter-molecular forces. The sizes and shapes of the molecule determine the combinatorial part and are thus dependent on the compositions and require only pure component data. As the residual part depends on the intermolecular forces, two adjustable binary parameters are used to better describe the intermolecular forces. The UNIQUAC equations are about as simple for multicomponent solutions as for binary solutions. Parameters for the UNIQUAC equations can be found by Gmehling, Onken, and Arlt. ... 

Step 13. Calculate the molar heat capacity at constant pressure (Cp) and use it to estimate the increase of the enthalpy (H), entropy (S) and Gibbs free energy (G) relative to their residual values at absolute zero temperature. Polystyrene has Tg=382K (Step 10), and... 

At this point we may introduce an important class of thermodynamic functions called residual or departure functions. In this case, the residual Gibbs free energy may be defined as ... 

In UNIQUAC the excess Gibbs free energy is computed from two contributions. The first called combinatorial part represents the influence of the structural parametejs, as size (parameter r) and shape (area parameter q). The second called the residual part account for the energy of interactions between segments. In the case of a binary mixture the expression for the excess Gibbs free energy is ... 

The starting point of phase equilibrium is eq. 7.4. which establishes the equality of the molar Gibbs energy of the phases that are present. In this Section we will obtain alternative forms of that equation that are suitable for calculations. First, we express the Gibbs free energy in terms of its residual... 

This equation can be written for the liquid and for the vapor. The ideal-gas term is the same in both phases because it depends only on temperature and pressure, which are the same in both phases. We conclude then that the residual Gibbs free energies of the two phases are also equal ... 

To obtain the chemical potential of component in a real mixture, we write the Gibbs free energy in terms of the residual Gibbs energy ... 

The name of this model is an acronym of universal quasichemical, the name of the theory used to drive it. Like the Flory-Huggins model, UNIQUAC separates nonideal contributions to the excess Gibbs free energy into a combinatorial and a residual term ... 

To reach this conclusion we write G = G + Gk Since both phases are the same pressure and temperature, the term G is common in both phases. Then, the phase with the lower fugacity coefficient has the lower residual Gibbs free energy and also the lower molar Gibbs free energy. 

Figure 5.10. An embodiment of the comprehensive hydrophobic effect in terms of a plot of the temperature for the onset of phase separation for hydrophobic association, Tb, versus AGha. the Gibbs free energy of hydrophobic association for the amino acid residues, calculated by means of Equation (5.10b) using the heats of the phase (inverse temperature) transition (AH,). Values were taken from Table 5.3. Tb and T, were determined from the onset of the phase separation as defined in Figure 5.1C,B, respectively. The estimates of AGha utilized the AH, data listed in Table 5.1 for fx = 0.2 but extrapolated to fx = 1, and the Gly (G) residue was taken as the...

Table 5.3. Hydrophobicity Scale in terms of AGha, the change in Gibbs free energy for hydrophobic association, for amino acid residue (X) of chemically synthesized poly[fv(GVGVP), fx(GXGVP)], 40m ml, mw = 100 kDa in 0.15 N NaCl, 0.01 M phosphate, using the net heat of the inverse temperature transition, AGha = [AH,(GGGVP) - AH.(GXGVP)] for the fx = 0.2 data extrapolated to f = 1.

Figure 8.15. By the use of white for charged residues and gray to black for increasingly hydrophobic residues, it becomes apparent by inspection of the involved surface areas, without calculation of the Gibbs free energy for hydrophobic association, AGha, that the Q site is much more hydrophobic than the cytochrome Ci site. The hydrophobicity of the globular component of the RIP that associates with either the Qo site or the cytochrome Ci site is even more apparent. The very dark tip, shown in end view and in side view in Figures 8.16A,B, respectively, makes clear that the interaction of the FeS center with the Qo site would clearly be dominated by hydrophobic association.

Hie hydrophobicity scale in Table 5.3 lists the contribution of each amino add residue to the Gibbs free energy of hydrophobic association, AGha- Table 5.3 also provides the information required to calculate numbers for the relative hydrophobidties of the faces of the y-rotor. The resulting numbers are tabulated and summed in Table 8.2, where the LAGHA(P-empty face) = -20 kcal/mole. This is indeed a very hydrophobic value. 

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