Gibbs free energy of a mixture

Recalling the general formulation of the Gibbs free energy of a mixture ... 

In many situations, we need to predict the properties of a mixture, given that we already know the properties of the pure species. To do this requires a model that can describe how various components mix. In mathematical terms, this means that we need to relate the Gibbs free energy of a mixture to the Gibbs free energy of the various pure components. One of the simplest models that achieves this is the ideal solution model. In this lecture, we present the ideal solution model. Then we apply this model to describe vapor-liquid equilibria, and as a result, derive Raoult s law. 

Thus, the minimum rate of work equals the change in Gibbs free energy between the feed(s) and products. The Gibbs free energy of a mixture is the mole fraction summation of the partial molal free energies of the components. 

Liu, A. Beck, T. L., Determination of excess Gibbs free energy of quantum mixtures by MC path integral simulations, Mol. Phys. 1995, 86, 225-233... 

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). 

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... 

At Ty, the Gibbs free energy of phase a (i.e., melt) at all compositions is lower than that of mechanical mixture y + y" phase a is then stable over the whole compositional range. At T2, the chemical potential of component 1 in a is identical to the chemical potential of the same component in y . Moreover, the equahty condition is reached at the standard state condition of the pure component T2 is thus the temperature of incipient crystallization of y. At T, the Gibbs free energy of a intersects mechanical mixture y + y" on the component 1-rich side of the diagram and touches it at the condition of pure component 2. Applying the prin-... 

The calculation of the Gibbs free energy of a gaseous mixture can be performed, starting from the chemical potentials of the various pure gaseous components at the P and T of interest, assuming that the mixture is ideal ... 

Equation 9.20 gives the pressure dependence of the Gibbs free energy of a pure substance. More generally, for a mixture one should consider the chemical potential /r, which is defined as the partial molar free energy of species k ... 

McDonald and Floudas (1994) and Michelsen (1994) also present methods to find the phase conditions for a given mixture. Both methods discover the number of phases and the compositions of these phases. McDonald and Floudas globally minimize the Gibbs free energy of the mixture using a computer pack-... 

For mixtures, the relationship between the Gibbs free energy of a reaction and the composition of the system is obtained by substituting the expression for the chemical potential in terms of the activity of a species /... 

J. H. Vera, S. G. Sayegh, and G. A. Ratcliff. 1977. A quasi lattice-local composition model for the excess Gibbs free energy of liquid mixtures. Fluid Phase Equilib. 1 113. 

This calculation precludes development of the Einstein diffusion equation for forced diffusion in the presence of a gravitational field. The coefficient of (ge — gA) in equation (25-77) for the diffusional mass flux of species A can be evaluated via thermodynamics. The extensive Gibbs free energy of a one-phase binary mixture with 3 degrees of freedom requires four independent variables for complete description of this thermodynamic state function. Hence, ( (T, p, N/, Nb) is postulated where Ni represents the mole numbers of species i, and the total differential of is... 

The extensive Gibbs free energy of a one-phase mixture of N components with - -1 degrees of freedom requires N + 2 independent variables for complete description of this thermodynamic state function. Hence,... 

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) ... 

Matteoli, E. Lepori, L. Isothermal Uquid-vapor equilibria of mixtures containing organic compounds. 2. Excess Gibbs free energies of a hydrocarbon or tetrachloromethane + a cyclic ketone at 298.15 K /. Chctti. Eng. Data 1988,33 247-250... 

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