Binary excess Gibbs free energy

Figure 3.9D shows the form of the curve of the excess Gibbs free energy of mixing obtained with Van Laar parameters variable with T. the mixture is subregular— i.e., asymmetric over the binary compositional field. 

The Kohler model is a general model based on linear combination of the binary interactions among the components in a mixture, calculated as if they were present in binary combination (relative proportions) and then normalized to the actual molar concentrations in the multicomponent system. The generalized expression for the excess Gibbs free energy is... 

A more recent model (Ghiorso, 1984) is based on the binary interaction parameters of Thompson and Hovis (1979) for the NaAlSi30g-KAlSi30g join and on the experimental results of Newton et al. (1980), coupled with the A1 avoidance principle of Kerrick and Darken (1975) extended to the ternary field. Ghiorso (1984) expressed the excess Gibbs free energy of mixing in the form... 

Calculation of the excess Gibbs free energy of mixing (third term on right side of eq. 6.78) involves only binary interactions. Although there is no multiple interaction model that can be reduced to the simple summation of binary interactions used here (cf Acree, 1984 see also section 3.10), this choice is more than adequate for the state of the art, which does not allow precise location of the miscibility gap in the chemical space of interest. 

Once the standard state potentials at the P and T of interest have been calculated (ix° = Gf for a pure single-component phase), the ideal and excess Gibbs free energy of mixing terms are easily obtained on the basis of the molar fractions of the various melt components and the binary interaction parameters listed in table 6.15 (cf eq. 6.78). 

As a demonstration of quantitative LLE calculations, we now consider in more detail some of the binary mixtures that we have discussed qualitatively in section 6.3. In Fig. 6.13 we see the excess Gibbs free energy of mixing Gex, the heat of mixing Hex, and the excess entropy of mixing Sex for mixtures of acetone and... 

Determine the heat and work needed to reversibly and isothermally separate an equimolar binary mixture into its pure species if the excess Gibbs free energy for the mixture is... 

Figure 11. Excess Gibbs free energy of binary Na(NOs)s-HNOS-H20 electrolyte mixture as a function of the fraction of Nd(NOs)s in mixture...

Gaw, W. J. Swinton, F. L. Thermodynamic properties of binary systems containing hexafluorobenzene. Part 4. Excess Gibbs free energies of fhe three systems hexafluorobenzene -I- benzene, fouene, and /)-xylene. Trans. Faraday Soc. 1968, 64, 2023-2034. 

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. ... 

Wilson presented the following expressions for the molar excess Gibbs free energy of a binary solution ... 

In the Non-Random-Two-Liquid (NRTL) model of Renon and Prausnitz (1968), the molar excess Gibbs free energy for a binary mixture is given as... 

The correlation of data for the methane and pentane binary system is shown in Figure 4.2.1. In this case the van Laar excess Gibbs free-energy model has been used in the HVO model the two model parameters were fitted to VLE data on the 277 K isotherm, and the vapor-liquid equilibria at higher temperatures were predicted with the same temperature-independent parameters. The results are very good in this case and similar to those obtained with the IPVDW and 2PVDW models. 

Figure 5.1.5. Excess Gibbs free-energy predictions for the acetone and water binary system at 298 K. The circles are calculated from experimental data (see text), the solid line with crosses reflects the UNIFAC predictions, and the smooth solid line denotes the results of the WS model. The large, medium, and short dashed lines are from the HVOS, HVO, and MHVl models, respectively the dotted line is from the MHVl model and the dot-dash line represents the results of the LCVM model.

Figure 6.2.1. Excess Gibbs free energy and excess enthalpy of the acetone and water binary mixture at 293 K. The excess Gibbs free energy was calculated from VLE data as described in Section 5.1, The excess enthalpy data are as reported in the DECHEMA Chemistry Data Series Heat of Mixing Collection, Christiansen et al. 19S4, Vol, l,Pt. lb, pp. 148-9.

Let s consider some experimental data, as those presented in the Table 6.3 for the binary methyl-ethyl-ketone (1) / toluene (2) at 50°C (Smith and Van Ness, 1987). Activity coefficients may be computed with (6.38), then Iny, and Iny, and finally excess Gibbs free energy by the relation (6.42). Figure 6.4 presents the plot. A quasi-parabolic shape is obtained with maximum deviation of 0.0T5RT at Xj 0.5. ... 

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 ... 

It was found that when the cosolvent power of the binary mixture increases, the complexing capacity decreases. These results were explained by taking into account the excess Gibbs free energy, G , and the order of the liquid. 

Birdi, G. S. Vij, J. N. Mahl, B. S. Thermodynamics of binary mixtures excess Gibbs free energies of 1,2-dibromoethane... 

Nagata, L Ohta, T. Uchiyama, Y. Excess Gibbs free energies for binary systems isopropanol with benzene, cyclohexane, methylcyclohexane J. Chem. Eng. Data 1973,18, 54-59... 

Kolasinska, G. Goral, M. Giza, J. Vapour-liquid equilibria and excess Gibbs free energy in binary systems of acetone with aliphatic and aromatic hydrocarbons at 313.15 KZ Phys. Chem. (Leipzig) 1982,265, 151-160... 

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