Gibbs free energy, liquid mixture

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

Physical Equilibria and Solvent Selection. In nrder lor two separale liquid phases to exist in equilibrium, there must be a considerable degree of thermodynamically nonideal behavior. If the Gibbs free energy. G. nf a mixture of two solutions exceeds the energies of the initial solutions, mixing does not occur and the system remains in iwo phases. For the binary system containing only components A and B. the condition for the formation of two phases is... 

Partial Molar Properties, The properties of individual components in a mixture or solution play an important role in solution thermodynamics. These properties, which represent molar derivatives of such extensive quantities as Gibbs free energy and entropy, are called partial molar properties. For example, in a liquid mixture of ethanol and water, the partial molar volume of ethanol and the partial molar volume of water have values that are, in general, quite different from the volumes of pure ethanol and pure water at the same temperature and pressure (21). If the mixture is an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure material at the same temperature and pressure. 

FIGURE 3.15.3 Gibbs free energy curves for liquid and solid mixtures which result in a phase diagram with a maximum. 

An excellent discussion of the thermodynamics of LLE systems has been given by Sorensen and Arlt (1979,1980) and Sorensen et al. (1979). The following section is adapted from these references. Consider a binary liquid mixture of + n2 moles at fixed temperature and pressure. The necessary and sufficient condition for equilibrium is that the total Gibbs free energy of mixing, AG, for the mixture is a minimum with respect to all possible changes... 

We shall first illustrate, using Fig. 44, why a mixture will split into two or more liquid phases by examining the shape of the Gibbs free energy for a binary... 

Fig. 44. Gibbs free energy for binary mixture that breaks into two liquid phases at any composition between. V and. Vi.

At a fixed temperature and pressure, the stable state of a system has a minimum Gibbs free energy, indicated in Eq. (56), which is the basic equation of equilibrium. A liquid 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. 

To model a mixture that phase separates into two coexisting liquid phase, we need to add non-ideal terms (activity coefficients) to the ideal solution model. As an example of this, we examine the stability of the two-suffix Margules model, which has a molar Gibbs free energy of... 

Many mixtures of interest in the chemical indu.stry exhibit strong nonidealities that can not be described by the EOS with any form of the van der Waals mixing rules. Mixing rules that combine equations of state with liquid excess Gibbs free-energy (or, equivalently, activity coefficient) models are more suitable for the thermodynamic... 

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... 

For liquids it is convenient to chose a particular reference state, a standard state, that can be defined by the Gibbs free energy of 1 mole of pure s at the mixture temperature, T, and a specified pressure, say 1 bar. Hence, in this case is a function of temperature only, = /x°(T,p = Ibar, a —> 1). Alternatively, /i may be chosen as the chemical potential for pure species s at the system temperature and pressure in which = /x°(T,p). That is, numerous reference states are possible, which one to be chosen matters little provided that the model formulation is consistent. Henceforth, we are using the given standard state as defined above. 

When non-ideal liquid solutions are considered, we use excess thermodynamic functions, which are defined as the differences between the actual thermodynamic mixing parameters and the corresponding values for an ideal mixture. For constant temperature, pressure and molar fractions, excess Gibbs free energy is given as... 

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. 

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