Mixing excess free energy, binary

Consideration of the thermodynamics of nonideal mixing provides a way to determine the appropriate form for the activity coefficients and establish a relationship between the measured enthalpies of mixing and the regular solution approximation. For example, the excess free energy of mixing for a binary mixture can be written as... 

The regular solution approximation is introduced by assuming definition) that the excess entropy of mixing is zero. This requires that the excess free energy equal the excess enthalpy of mixing. For binary mixtures the excess enthalpy of mixing is ordinarily represented by a function of the form... 

We have deduced a set of equations with such properties based on empirical modifications of the quasi-chemical theory. (7 8) For binary systems the excess free energy of mixing is given by the expression... 

Figure 4.2.2. VLB correlation (dashed lines) of the carbon dioxide and propane binary system at 277, 310, and 344 K with the Huron-Vidal original (HVO) mixing rule with the van Laar excess free-energy model and the PRSV equation of state. The van Laar model parameters used are = A 2/A2 = 1.1816/1.6901. Solid hnes represent the 1PVDW model correlations presented earlier in Figure 3.4.2. (Points are experimental data from the DECHEMA Chemi.stry Data Series, Gmehling and Onken 1977, Vol. 6, p. 589 data files for this system on the accompanying disk are C02C3277.DAT, CO2C3310.DAT and C02C3344.DAT.)...

Figure 4.2.4. VLE correlation of the acetone and water binary system at 523 K with the Huron-Vidal original (HVO) mixing rule combined with the van Laar excess free-energy model and the PRSV equation of state. The dashed lines represent results calculated with van Laar model parameters = A12/A21 =...

A desirable characteristic of an excess free-energy-based mixing rule is that it goes smoothly to the conventional van der Waals one-fluid mixing rule for some values of its parameters. This is useful because in multicomponent mixtures only some of the binary pairs may form highly nonideal mixtures requiring mixing rules such as... 

This equation introduces the binary interaction parameter in a manner similar to that of eqn. (3.3.6) of the van der Waais one-lluid mixing rule. Next, the following modified form of the NRTL equation was used for the excess free-energy term ... 

Figure 4.3.4. VLE correlation (solid lines) of the 2-propanol and water binary system at 353 K with the Wong-Sandler (WS) mixing rule combined with the NRTL excess free-energy model and the PRSV equation of state. The dashed lines are calculated with a = 0.2529, ri2/T2i =0,1562/2,7548, and with the Wong-Sandler mixing rule parameter k 2 = 0.2529 obtained by fitting the experimental data. The solid lines represents results calculated with a =0.2893 and T 2/t2i =0.1509/1.8051 obtained from the DECHEMA Chemistry Series at 303 K (Gmehling and Onken 1977, Vol.l, Pt. 1, p.

With this command, all three parameters in the WS mixing mle, the two excess free-energy model parameters, and the binary interaction pai ametcv, kjj, are optimized.)... 

D.6. Program WSUNF Binary VLE Predictions Using the Wong-Sandler Mixing Rule Combined with the UNIFAC Excess Free-Energy Model... 

HVUNF BINARY VLE CALCULATIONS WITH HUROM-VXDAL TYPE MIXING RULES AND THE UNIFAC EXCESS FREE ENERGY MODEL... 

The data of excess free energy of mixing and activity coefficient of components of liquid alloys are very useful for the process design in pyrometallurgy. Table 7.3 lists some data of excess free energies (at 50/50 composition) and atomic parameters of 33 binary liquid alloys [72]. The correlation between these data is investigated by SVM. 

A third expression for the excess free energy of mixing in a ternary solution may be obtained by summing terms, without compositional weighing factors, that represent "subregular mixing in the constituent binary systems (e.g. equation (18). Thus,... 

Molar excess free energy of mixing The molar excess free energy of mixing for binary solutions is... 

Once it has been established that the components of a binary monolayer are to some degree miscible, the energetics of their interaction may be calculated directly from the 11/A isotherms of the mixture and its individual components. As proposed by Goodrich (1957), this technique employs the differences in the work of compression of the binary film and the work required to compress each of the films of the pure components to the same surface pressure. The result is the total free energy of mixing as expressed by the sum of the excess and ideal free energies of mixing in (14), where Nt... 

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. 

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... 

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