Excess Gibbs free energy of mixing

By simple thermodynamic arguments Brown14 has shown that, consistent with the accuracy of this second-order approximation, one may obtain from the form of Eq. (87) the form of the excess Gibbs free energy of mixing (AG ), the enthalpy of mixing of a molten salt (AHm), and the deviation of the surface tension from linearity ... 

Interaction parameter does depend on T and P, and the excess Gibbs free energy of mixing is described as in the preceding model ... 

The excess Gibbs free energy of mixing is given by... 

If Aq = A = A2 = 0, the excess Gibbs free energy of mixing is zero throughout the compositional field and the mixture is idea/. 

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. 

According to the Hillert model (Hillert, 1980), the excess Gibbs free energy of mixing of a ternary mixture is given by... 

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... 

The first two terms describe mechanical mixing of endmembers A and B, the third is the ideal solution mixing term, and the last term is the regular solution contribution, in which solid solution composition. (If a> is not so independent, the solution is not regular). The term (oNJ n in Eq. (1.39) is also sometimes called the excess Gibbs free energy of mixing, or AG (excess). 

It has been found experimentally that for most mixtures the excess Gibbs free energy of mixing is not a symmetric function of mole fraction. In fact, the excess Gibbs free energy for many mixtures is closer to being a symmetric function of volume fraction than mole fraction. For generality we define a new composition variable Zi as follows ... 

Excess Gibbs free energy of mixing calculated with EOS approach =... 

The excess Gibbs free energy of mixing of the mixed polymer layer at the surface pressure jt can be obtained from... 

Figure 8.4. The excess Gibbs free energy of mixing as a function of the composition for a series of linear diblock copolymers of PEO and PMMA. After GabrieUi et al. (1982).

Uncertainties (T(x ) = 0.0002 c7(P)/103Pa = 0.04 Singh, P. P. Sharma, V. K. Thermodynamics of methylenebromide + aromatic hydrocarbon mixtures molar excess Gibbs free energy of mixing Fluid Phase Equilib. 1989,44,347-355... 

The reflection of inter-solvent attractions in reactivity trends in binary aqueous mixtures has been considered. In the particular case of dissociation of the [Fe(5-NOaphen)3] + cation, as indeed in Bu Cl solvolysis, there is a remarkably good correlation between AG" and G, the excess Gibbs free energy of mixing for the respective solvent mixtures, for the so-called typically aqueous mixtures. These are mixtures with positive G values, and IrA I > and include such commonly studied mixtures as aqueous methanol, ethanol, t-butyl alcohol, acetone, dioxan, and THF. A similar AG /G correlation has been reported for D substitution by cyanide at the [Fe(CN)5(3,5-Me2Py)] anion. ... 

Here, aG is the excess Gibbs free energy of mixing, and Xj is the molar fraction of component i. The spinodals in Fig. 1 indicate the boundary condition between the metastable and spinodal regions. They and the critical point are computed from the second and third derivatives ... 

Thermodynamic Parameters. In the previous Volume, the reflection of the excess Gibbs free energy of mixing for binary aqueous mixtures in reactivity trends for B. B. Hasinoff, Camd. J. Chem., 1977, 55, 3955. 

Ratzsch et al. [3] suggested the following model for the segment-molar excess Gibbs free energy of mixing (G ) in order to describe the deviation from the Flory-Huggins mixture ... 

The influence of the chemical composition in (5) can be derived using a simplified versicai of Barker s lattice theory [55], The most important consequence of (5) is the fact that the segment-molar excess Gibbs free energy of mixing and, hence, the activity coefficients depend only oti the average value (yw) of the distribution function, but not on the distribution function itself. In continuous thermod5mamics, the phase equilibrium conditions read ... 

REPRESENTATION OF THE EXCESS GIBBS FREE ENERGY OF MIXING... 

Sharma, B. R. Pundeer, G. S. Singh, P. P. Thermodynamics of weak interactions excess enflialpies and excess Gibbs free energies of mixing. Thermochim. Acta 1975, 11, 105-114. 

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