Binary solutions, nonideal

Cruz, Jose-Luis and H. Renon, "A New Thermodynamic Representation of Binary Electrolyte Solutions Nonideality in the Whole Range of Concentrations," AIChE J., 1978, 24, 817. 

Let us now briefly describe some broader phenomenological aspects of the P-x diagrams for binary solutions, ranging from the ideal solution limit to extreme nonideal deviations of either positive or negative sign. 

A very important feature of nonideal solutions is their departure from Raoult s Law in later sections we shall repeatedly examine and make use of the information provided here. Positive and negative departures from Raoult s Law for a binary solution are schematically illustrated in Fig. 3.3.1. Attention is directed to the following facts (a) If one component exhibits a positive (negative) departure from Raoult s Law, the other must do likewise a proof for this statement is to be furnished in Exercise 3.3.2. (b) As the mole fraction xt of component i (i - 1,2) approaches unity (i.e., as the solution becomes very dilute by virtue of a large excess of component i as solvent), the partial pressure Pi of... 

Mixtures of nonpolar solvents are normally characterized by the term solubility parameter (5). The difference in solubility parameters of mixture components provides a measure of solution nonideality.Mixtures of aliphatic hydrocarbons are nearly ideal, whereas mixtures of aliphatic hydrocarbon with aromatics show appreciable nonideality. Sometimes, it is difficult to predict the behavior of highly nonideal mixtures. Thermodynamic properties of binary and multicomponent mixtures have been dealt with extensively in the literature. " ... 

In the remainder of this section we examine several EOS-G models using three prototype binary mixtures that form sti ongly nonideal solutions. For comparison, we also include the predictions of the UNIFAC model used directly in the y-(p method wherever applicable. The systems considered are the methanol and benzene (Butcher and Medani 1968), the acetone and water (Gmehling and Onken 1977), and the 2-propanol and water (Barr-David and Dodge 1959) binary mixtures. Note that there are many systems with small to moderate solution nonideality for which all or most of the methods mentioned above work reasonably well. We are not concerned with such systems here because the method selection would not be a problem in such cases. Rather we consider only those systems that are more nonideal and for which the differences between the models discussed here are clearly evident. 

Polar molecules interact more strongly at large distances than do nonpolar molecules, and generally form nonideal solutions. One model for solution nonidealities in a binary mixture consisting of a nonpolar species, which we denote by A, and a polar substance, designated by the symbol B, is based on the supposition that the polar substance partially dimerizes,... 

A number of attempts have been made to use the simple solution model to represent the solution nonidealities in binary (23,29-32) and ternary (23,33-41) III—V systems. In the simple solution model, the integral Gibbs excess energy is given in terms of an interaction energy a)( T) by the equation... 

Usually, but not always, yT is the extreme (maximum or minimum) value assumed by 7/ for a component in a binary mixture. Hence, the 7,° are often used as measures of the magnitudes of nonidealities of binary liquid mixtures. Another measure is provided by gF or g /RT for the equimolar mixture for many binary solutions, this is near to the maximum (or minimum) value. For liquid solutions exhibiting positive deviations from ideal-solution behavior (activity coefficients greater than unity), a yl" of about 5 or an equimolar tFfRTof about 0.5 is considered large. ... 

The gas-phase mixture is considered an ideal gas, and in this case Dalton s law states that concentrations are equal to partial pressures divided by the overall pressure p (N m" ). According to HEA, these partial pressures are equal to the saturation pressures of the liquid aerosols. The appropriate description of such saturation pressures depends on the circumstances (see Table 18.2). A hydrocarbon gas does not readily dissolve in water, and therefore two sets of immiscible aerosols will exist in independent equilibrium with the gas phase. Raoult s law describes equilibrium over dilute mixtures, whereas equilibrium over nonideal binary solution requires contaminant-specific empirical models. An example of the latter is Wheatley s model, which states that ... 

Cruz JL, Renon H (1978) A new thermodynamic representation of binary electrolyte solutions nonideality in the whole range of concentrations. AIChE J 24 817-830... 

We briefly review here thermodynamics of a nonideal binary solution. The osmotic pressure Ft is the extra pressure needed to equilibrate the solution with the pure solvent at pressure p across a semipermeable membrane that passes solvent only. The equilibration is attained when the chemical potential of t e pure solvent becomes equal to the chemical potential of the solvent molecule in solute volume fraction at temperature T ... 

It is worthwhile to consider these equations for the following cases (a) a pure phase, (b) an ideal binary solution, and (c) a nonideal binary solution. 

It should be clear from the examples cited, and from the inapplicability of Eq. (1-32) to nonideal binary solutions, that the partial molal volume should not be interpreted as the molar volume. The.se are two different kinds of quantities and should not be confused with each other. Their numerical values happen to be equal only for a pure phase, or for an ideal solution. In hydrodynamic applications, as we shall see, the partial molal volume (or, as more commonly used, th( partial. specific volume) appears correctly in the Sv( dberg e< Uatioiis for sedimentation velocity and sedimentation eciuilibrium [e.g., lOq. (1-12)]. However, any attempt to identify... 

Physical Equilibria and Solvent Selection. In order for two separate Hquid phases to exist in equiHbrium, there must be a considerable degree of thermodynamically nonideal behavior. If the Gibbs free energy, G, of a mixture of two solutions exceeds the energies of the initial solutions, mixing does not occur and the system remains in two phases. Eor the binary system containing only components A and B, the condition (22) for the formation of two phases is... 

Density and Specific Gravity For binary or pseudobinary mixtures of hquids or gases or a solution of a solid or gas in a solvent, the density is a funcrion of the composition at a given temperature and pressure. Specific gravity is the ratio of the density of a noncompress-ible substance to the density of water at the same physical conditions. For nonideal solutions, empirical calibration will give the relationship between density and composition. Several types of measuring devices are described below. 

This approach to solution chemistry was largely developed by Hildebrand in his regular solution theory. A regular solution is one whose entropy of mixing is ideal and whose enthalpy of mixing is nonideal. Consider a binary solvent of components 1 and 2. Let i and 2 be numbers of moles of 1 and 2, 4>, and 4>2 their volume fractions in the mixture, and Vi, V2 their molar volumes. This treatment follows Shinoda. ... 

Let us now focus attention on the common case where all three binaries exhibit positive deviations from Raoult s law, i.e., afj- > 0 for all ij pairs. If Tc for the 1-3 binary is far below room temperature, then that binary is only moderately nonideal and a13 is small. We must now choose a gas which forms a highly nonideal solution with one of the liquid components (say, component 3) while it forms with the other component (component 1) a solution which is only modestly nonideal. In that event,... 

The extension of the simple ideal binary system considered in the preceding section to a nonideal multicomponent column is not diflicult. The only changes that have to be made to the basic structure of the solution algorithm arc ... 

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 case of binary solid-liquid equilibrium permits one to focus on liquid-phase nonidealities because the activity coefficient of solid component ij, Yjj, equals unity. Aselage et al. (148) investigated the liquid-solution behavior in the well-characterized Ga-Sb and In-Sb systems. The availability of a thermodynamically consistent data base (measurements of liquidus, component activity, and enthalpy of mixing) provided the opportunity to examine a variety of solution models. Little difference was found among seven models in their ability to fit the combined data base, although asymmetric models are expected to perform better in some systems. 

An amine oxide surfactant solution can be modeled as a binary mixture of cationic and nonionic surfactants, the composition of which is varied by adjusting the pH. The cationic and nonionic moieties form thermodynamically nonideal mixed micelles, and a model has been developed which quantitatively describes the variation of monomer and micelle compositions and concentrations with pH and... 

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