Binary liquid mixture phase diagrams

Example 1.15 Binary liquid mixture phase diagrams Prepare phase diagrams for acetone(l)-water(2) mixture using Raoult s law  

From this equation, we estimate the liquid composition x, 

Example 1.16 Estimation of fugacity coefficients from virial equation Derive a relation to estimate the fugacity coefficients by the virial equation 

the exponential term is the Poynting correction factor, which may be negligible at low to moderate pressures. Disregarding the Poynting factor, Eq. (1.218) becomes 

For moderate pressures, the virial equation allows for the estimation of the fugacity coefficient  

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Example 1.24 Binary liquid mixture phase diagrams... 

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. 

Fig. 2 Top solubilization of [Cu(bipy)Cl2] by a TSIL and the temperature dependent phase separation. Bottom liquid-liquid equilibrium phase diagram of the binary mixture TSIL-water. Figure adapted from [64]. Image Copyright American Chemical Society (2006). For color image see online version...

Figure 1. Liquid-vapor phase diagram for pure liquid (1, 2) and binary mixture (3, 4) the lines of attainable superheat (1, 3), binodals Ts(p c = const) (2, 4) and liquid-gas critical curve (5). Symbols CP indicate the critical point, "w — the way of superheating ofpure liquid.

Figure 9.29 One of the many isomorphisms that exist between vapor-liquid and liquid-solid phase diagrams for binary mixtures. (1(0) An isobaric Txy diagram with a minimum boiling-point azeotrope and a miscibility gap above an LLE situation (right) an isobaric Txx diagram with a minimum melting-point solutrope and a miscibility gap above an SSE situation.

The plots of the total vapor pressure as functions of the mole fraction of A in both the liquid and vapor phases are shown in Figure 9.12(a) and (b), respectively. The combined plot shown in Eigure 9.12(c) is a liquid-vapor phase diagram for an ideal binary solution at a fixed temperature T—often called a pressure-composition diagram. At any pressure and composition above the upper curve (the liquid line) the mixtnre is a liquid. Below the lower curve (the vapor line), the mixture is entirely vapor. The region between the two curves is a region of phase coexistence, that is, both liquid and vapor phases are present in the system. 

Figure 9.16 Different types of liquid-vapor phase diagrams for a binary liquid mixture of component A and B as functions of the mole fraction of the component with the higher boiling temperature, (a) The phase diagram for a system with a low-boiling azeotrope (minimum boiling point) and (b) the phase diagram for a system with a high-boiling azeotrope (maximum boiling point). The arrows show how the paths for various distillation processes depend upon the position of the initial composition relative to the azeotrope.

Figure 13.5 on page 431 shows a phase diagram for a typical binary liquid mixture that spontaneously separates into two phases when the temperature is lowered. The thermodynamic conditions for phase separation of this kind were discussed in Sec. 11.1.6. The phase separation is usually the result of positive deviarions from Raoult s law. Typically, when phase separation occurs, one of the substances is polar and the other nonpolar. 

Figure 13.1 on the next page is a temperature-eomposition phase diagram at a fixed pressure. The eomposition variable zb is the mole fraction of component B in the system as a whole. The phases shown are a binary liquid mixture of A and B, pure solid A, and pure solid B. 

The most successful form of the theory is briefly outlined in the Theory Section. In the Section on Results the theory is used to classify mixture phase diagrams in terms of the intermolecular forces involved, and also to predict vapor-liquid equilibria for several binary and ternary mixtures. 

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

Figure 7.2 A three-dimensional phase diagram for a Type I binary mixture (here, CO2 and methanol). The shaded volume is the two-phase liquid-vapor region. This is shown ti uncated at 25 °C for illustration purposes. The volume surrounding the two-phase region is the continuum of fluid behavior.

The liquid line and vapor line together constitute a binary (vapor + liquid) phase diagram, in which the equilibrium (vapor) pressure is expressed as a function of mole fraction at constant temperature. At pressures less than the vapor (lower) curve, the mixture is all vapor. Two degrees of freedom are present in that region so that p and y2 can be varied independently. At pressures above the liquid (upper) curve, the mixture is all liquid. Again, two degrees of freedom are present so that p and. v can be varied independently/... 

When two metals A and B are melted together and the liquid mixture is then slowly cooled, different equilibrium phases appear as a function of composition and temperature. These equilibrium phases are summarized in a condensed phase diagram. The solid region of a binary phase diagram usually contains one or more intermediate phases, in addition to terminal solid solutions. In solid solutions, the solute atoms may occupy random substitution positions in the host lattice, preserving the crystal structure of the host. Interstitial soHd solutions also exist wherein the significantly smaller atoms occupy interstitial sites... 

OC10H21)], in which rearrangement does not occur. All the mixtures studied display liquid crystal behavior with improved properties with respect to the pure components. A representative binary phase diagram and their corresponding DSCtraces are presented in Figures 8.24 and 8.25 respectively, and reveal the eutectic nature ofthese systems. 

A melt is a liquid or a liquid mixture at a temperature near its freezing point and melt crystallisation is the process of separating the components of a liquid mixture by cooling until crystallised solid is deposited from the liquid phase. Where the crystallisation process is used to separate, or partially separate, the components, the composition of the crystallised solid will differ from that of the liquid mixture from which it is deposited. The ease or difficulty of separating one component from a multi-component mixture by crystallisation may be represented by a phase diagram as shown in Figures 15.4 and 15.5, both of which depict binary systems — the former depicts a eutectic, and the latter a continuous series of solid solutions. These two systems behave quite differently on freezing since a eutectic system can deposit a pure component, whereas a solid solution can only deposit a mixture of components. 

Phase diagrams are often constructed to provide a visual picture of the existence and extent of the presence of solid and liquid phases in binary, ternary and other mixtures of substances. Phase diagrams are normally two-component (binary) representations but multicomponent phase diagrams can also be constructed. Interactions between active substances and excipients can often be evaluated using phase diagrams. 

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