Mixtures complete miscibility

To illustrate the criterion for parameter estimation, let 1, 2, and 3 represent the three components in a mixture. Components 1 and 2 are only partially miscible components 1 and 3, as well as components 2 and 3 are totally miscible. The two binary parameters for the 1-2 binary are determined from mutual-solubility data and remain fixed. Initial estimates of the four binary parameters for the two completely miscible binaries, 1-3 and 2-3, are determined from sets of binary vapor-liquid equilibrium (VLE) data. The final values of these parameters are then obtained by fitting both sets of binary vapor-liquid equilibrium data simultaneously with the limited ternary tie-line data. 

Some liquids are practically immiscible e.g., water and mercury), whilst others e.g., water and ethyl alcohol or acetone) mix with one another in all proportions. Many examples are known, however, in which the liquids are partially miscible with one another. If, for example, water be added to ether or if ether be added to water and the mixture shaken, solution will take place up to a certain point beyond this point further addition of water on the one hand, or of ether on the other, will result in the formation of two liquid layers, one consisting of a saturated solution of water in ether and the other a saturated solution of ether in water. Two such mutually saturated solutions in equilibrium at a particular temperature are called conjugate solutions. It must be mentioned that there is no essential theoretical difference between liquids of partial and complete miscibility for, as wdll be shown below, the one may pass into the other with change of experimental conditions, such as temperature and, less frequently, of pressure. 

System in which the solid phases consist of the pure components and the components are completely miscible in the liquid phase. We may now conveniently consider the general case of a system in which the two components A and B are completely miscible in the liquid state and the solid phases consist of the pure components. The equilibrium diagram is shown in Fig. 1,12, 1. Here the points A and B are the melting points of the pure components A and B respectively. If the freezing points of a series of liquid mixtures, varying in composition from pure A to pure B, are determined, the two curves represented by AC and BC will be obtained. The curve AC expresses the compositions of solutions which are in equilibrium, at different temperatures, with the solid component A, and, likewise, the curve BC denotes the compositions... 

The general case of two compounds forming a continuous series of solid solutions may now be considered. The components are completely miscible in the sohd state and also in the hquid state. Three different types of curves are known. The most important is that in which the freezing points (or melting points) of all mixtures lie between the freezing points (or melting points) of the pure components. The equilibrium diagram is shown in Fig. 7, 76, 1. The hquidus curve portrays the composition of the hquid phase in equihbrium with sohd, the composition of... 

If the substance is found to be far too soluble in one solvent and much too insoluble in another solvent to allow of satisfactory recrystallisation, mixed solvents or solvent pairs may frequently be used with excellent results. The two solvents must, of course, be completely miscible. Recrystallisation from mixed solvents is carried out near the boiling point of the solvent. The compound is dissolved in the solvent in which it is very soluble, and the hot solvent, in which the substance is only sparingly soluble, is added cautiously until a slight turbidity is produced. The turbidity is then just cleared by the addition of a small quantity of the first solvent and the mixture is allowed to cool to room temperature crystals will separate. Pairs of liquids which may be used include alcohol and water alcohol and benzene benzene and petroleum ether acetone and petroleum ether glacial acetic acid and water. 

Liquid crystals may be divided into two broad categories, thermotropic and lyotropic, according to the principal means of breaking down the complete order of the soHd state. Thermotropic Hquid crystals result from the melting of mesogenic soHds due to an increase in temperature. Both pure substances and mixtures form thermotropic Hquid crystals. In order for a mixture to be a thermotropic Hquid crystal, the different components must be completely miscible. Table 1 contains a few examples of the many Hquid crystal forming compounds (2). Much more is known about calamitic (rod-Hke) Hquid crystals then discotic (disk-like) Hquid crystals, since the latter were discovered only recendy. Therefore, most of this section deals exclusively with calamities, with brief coverage of discotics at the end. 

Physical properties of isopropyl alcohol are characteristic of polar compounds because of the presence of the polar hydroxyl, —OH, group. Isopropyl alcohol is completely miscible ia water and readily soluble ia a number of common organic solvents such as acids, esters, and ketones. It has solubiUty properties similar to those of ethyl alcohol (qv). There is a competition between these two products for many solvent appHcations. Isopropyl alcohol has a slight, pleasant odor resembling a mixture of ethyl alcohol and acetone, but unlike ethyl alcohol, isopropyl alcohol has a bitter, unpotable taste. 

Eor drown-out, look for MSA in which the component to be crystallised has low solubihty, while other components have high solubihty (MSA should be completely miscible with feed mixture). 

Carbon disulfide is completely miscible with many hydrocarbons, alcohols, and chlorinated hydrocarbons (9,13). Phosphoms (14) and sulfur are very soluble in carbon disulfide. Sulfur reaches a maximum solubiUty of 63% S at the 60°C atmospheric boiling point of the solution (15). SolubiUty data for carbon disulfide in Hquid sulfur at a CS2 partial pressure of 101 kPa (1 atm) and a phase diagram for the sulfur—carbon disulfide system have been published (16). Vapor—Hquid equiHbrium and freezing point data ate available for several binary mixtures containing carbon disulfide (9). 

Since Ag is a function of pressure, it follows that, under certain conditions, a change in pressure may produce immiscibility in a completely miscible system, or, conversely, such a change may produce complete miscibility in a partially immiscible system. The effect of pressure on miscibility in binary liquid mixtures is closely connected with the volume change on mixing, as indicated by the exact relation... 

In the previous sections, we indicated how, under certain conditions, pressure may be used to induce immiscibility in liquid and gaseous binary mixtures which at normal pressures are completely miscible. We now want to consider how the introduction of a third component can bring about immiscibility in a binary liquid that is completely miscible in the absence of the third component. Specifically, we are concerned with the case where the added component is a gas in this case, elevated pressures are required in order to dissolve an appreciable amount of the added component in the binary liquid solvent. For the situation to be discussed, it should be clear that phase instability is not a consequence of the effect of pressure on the chemical potentials, as was the case in the previous sections, but results instead from the presence of an additional component which affects the chemical potentials of the components to be separated. High pressure enters into our discussion only indirectly, because we want to use a highly volatile substance for the additional component. 

We consider a binary liquid mixture of components 1 and 3 to be consistent with our previous notation, we reserve the subscript 2 for the gaseous component. Components 1 and 3 are completely miscible at room temperature the (upper) critical solution temperature Tc is far below room temperature, as indicated by the lower curve in Fig. 27. Suppose now that we dissolve a small amount of component 2 in the binary mixture what happens to the critical solution temperature This question was considered by Prigogine (P14), who assumed that for any binary pair which can be formed from the three components 1, 2 and 3, the excess Gibbs energy (symmetric convention) is given by... 

Liquid-Fluid Equilibria Nearly all binary liquid-fluid phase diagrams can be conveniently placed in one of six classes (Prausnitz, Licntenthaler, and de Azevedo, Molecular Thermodynamics of Fluid Phase Blquilibria, 3d ed., Prentice-Hall, Upper Saddle River, N.J., 1998). Two-phase regions are represented by an area and three-phase regions by a line. In class I, the two components are completely miscible, and a single critical mixture curve connects their criticsu points. Other classes may include intersections between three phase lines and critical curves. For a ternary wstem, the slopes of the tie lines (distribution coefficients) and the size of the two-phase region can vary significantly with pressure as well as temperature due to the compressibility of the solvent. 

The chemical potential jU, of the components of an ideal mixture of liquids (the components of an ideal mixture of liquids obey the Raoult law over the whole range of mole fractions and are completely miscible) is... 

Alloys are classified broadly in two categories, single-phase alloys and multiple-phase alloys. A phase is characterized by having a homogeneous composition on a macroscopic scale, a uniform structure, and a distinct interface with any other phase present. The coexistence of ice, liquid water, and water vapor meets the criteria of composition and structure, but distinct boundaries exist between the states, so there are three phases present. When liquid metals are combined, there is usually some limit to the solubility of one metal in another. An exception to this is the liquid mixture of copper and nickel, which forms a solution of any composition between pure copper and pure nickel. The molten metals are completely miscible. When the mixture is cooled, a solid results that has a random distribution of both types of atoms in an fee structure. This single solid phase thus constitutes a solid solution of the two metals, so it meets the criteria for a single-phase alloy. 

A rams, D. S., and J. M. Prausnitz, "Statistical Thermodynamics of Liquid Mixtures A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems," AIChE J., 1975, 21, 116. 

A phase is defined as a state of matter that is uniform throughout in terms of its chemical composition and physical state in other words, a phase may be considered a pure substance or a mixture of pure substances wherein intensive properties do not vary with position. Accordingly, a gaseous mixture is a single phase, and a mixture of completely miscible liquids yields a single hquid phase in contrast, a mixture of several solids remains as a system with multiple solid phases. A phase rule therefore states that, if a limited number of macroscopic properties is known, it is possible to predict additional properties. 

Figure 7,1 Relationships between chemical potential and composition in binary phases with different miscibility behavior a = complete miscibility ]8 = partial miscibility y = lack of miscibility or mechanical mixture. ...

Figure 7.2 G-X and T-X plots for a binary system with a molten phase with complete miscibility of components at all T conditions and a solid phase in which components are totally immiscible at all proportions (mechanical mixture, 7 = 7 + V )-...

Figure 7.3 depicts phase stability relations in the pseudobinary system CaMgSi206-CaAl2Si208 (diopside-anorthite). The original study of Bowen (1915) described crystallization behavior identical to the previously discussed case a mechanical mixture (Di-An) in equilibrium with a completely miscible melt. A later investigation (Osborn, 1942) showed that the system is not strictly binary... 

Figure 7.4 Gibbs free energy curves and phase stability relations for two binary mixtures with complete miscibility of components (types I, II, and III of Roozeboom, 1899).

There are two possible geometrical configurations between a mixture with a saddle-shaped Gibbs free energy curve (indicative of unmixing) and a phase with a concave curve, indicating complete miscibility of components (figure 7.7). 

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