Gibbs free energy of the binary

Vittal Prasad, T. E. Kumar, A. Naresh, S. Prasad, D. H. L. Excess Gibbs free energies of the binary mixtures of acetonitrile with butanols at 94.83 kPa. J. Chem. Thermodyn. 2007, 39, 202-205. 

For analytical comprehension of the kinetics of spinodal decomposition processes, we must be able to evaluate the Gibbs free energy of a binary mixture of nonuniform composition. According to Cahn and Hilliard (1958), this energy can be expressed by the linear approximation... 

Effect of the eluent composition could be discussed on the basis of equation (2-55). In the simple case of binary eluent (organic/water mixture), we can consider in the first approximation that Gibbs free energy of the eluent interaction with the packing material surface is a linear function of the eluent composition... 

Gaw, W. J. Swinfon, F. L. Thermodynamic properties of binary systems containing hexafluorobenzene. Part 3. Excess Gibbs free energy of the system hexafluorobenzene + cyclohexane. Trans. Faraday Soc. 1968, 64, 637-647. 

Figure 2-1 shows the Gibbs free energy profile of a binary system, where G on the y-axis represents the Gibbs free energy of the system and X on the x-axis represents the mole fraction of the desired compound. Specifically, the first component in this system can be the desired compound, and the second component can simply be the solvent. Both temperature and pressure are maintained constant in this case. 

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

Illustrative Problem. The intensive Gibbs free energy of a binary mixture gmixture is expressed as a function of temperature, pressure, and mole fraction yi in equation (29-133) ... 

Multiphase phenomenon is more frequently encountered in multicomponent mixtures, such as reaction mixtures. From a thermodynamic perspective, multiphase phenomena exist because multiple phases reduce the Gibbs free energy of the system. More components mean more ways and phases in which to partition this energy. Due to the Gibbs phase rule, a third component extends multiphase equilibrium as seen in binary mixtures, such as LLV and SLV equihbrium, from a lirte to a region of pressure and concentration at a given temperature. 

The equilibrium state of a system at constant temperature and pressure is characterized by a minimum in the Gibbs free energy of the system. For a multicomponent, multiphase system, the minimum free energy corresponds to uniformity of the chemical potential (gi) of each component throughout the system. For a binary system, the molar free energy (G) and chemical potentials are related by Equation (2.1),... 

The theoretical analysis of the thermodynamics of supercooled silicon, presented by Aptekar [14] treats the liquid as a pseudo-binary regular solution of two components, along lines explored in related contexts by Rappaport [41], Ponya-tovsky and coworkers [15,42], The two components are characterized by different local bonding environments (covalent or metallic). Correspondingly, the Gibbs free energy of the liquid is written as... 

Phase relationships in equilibrium are determined by the free enthalpy (Gibbs free energy) of the system. The thermodynamic bdiaviour of polymer solutions can be very well described with the free enthalpy of mixing function derived, independently, by Florv (6,7) and Huggins (8—10) on the basis of the lattice theory of the liquid state. For the simplest case conceivable — a solution of a polydisperse polymer in a single solvent quasi-binary system) — we have... 

Figure 12.3 The Gibbs free energy of a binary liquid mixture for various values of (Eq. 12.10.2).

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. 

So far, we have seen several ways of calculating the Gibbs free energy of a two-component mixture. To extend calculations to ternary and higher-order mixtures, we use empirical combinatory extensions of the binary properties. We summarize here only some of the most popular approaches. An extended comparative appraisal of the properties of ternary and higher-order mixtures can be found in Barron (1976), Grover (1977), Hillert (1980), Bertrand et al. (1983), Acree (1984), and Fei et al. (1986). 

Figure 5.11 Gibbs free energy of mixing in binary join Mg2Si04-Ca2Si04 dXT = 600 °C and P = bar, calculated with a static interionic potential approach. Reprinted from G. Ottonello, Geochimica et Cosmochimica Acta, 3119-3135, copyright 1987, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.

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