Temperature-composition phase diagrams liquid-vapor

In systems that exhibit ideal liquid-phase behavior, the activity coefficients, Yi, are equal to unity and Eq. (13-124) simplifies to Raoult s law. For nonideal hquid-phase behavior, a system is said to show negative deviations from Raoult s law if Y < 1, and conversely, positive deviations from Raoult s law if Y > 1- In sufficiently nonide systems, the deviations may be so large the temperature-composition phase diagrams exhibit extrema, as own in each of the three parts of Fig. 13-57. At such maxima or minima, the equihbrium vapor and liqmd compositions are identical. Thus,... 

Another common way of representing a binary liquid-vapor equilibrium is through a temperature-composition phase diagram, in which the pressure is held fixed and phase coexistence is examined as a function of temperature and composition. Figure 9.13 shows the temperature-composition phase diagram for the benzene-toluene system at a pressure of 1 atm. In Figure 9.13, the lower curve (the boiling-point curve)... 

Figure 9.13 Temperature-composition phase diagram for the liquid-vapor equihbrium in benzene-toluene mixtures at 1 atm. The boihng points of toluene and benzene are 110.6°C and 80.1°C, respectively.

Toluene and benzene form liquid mixtures that are practically ideal and closely obey Raoult s law for partial pressure. For the binary system of these components, we can use the vapor pressures of the pure liquids to generate the liquidus and vaporus curves of the pressure-composition and temperature-composition phase diagram. The results are shown... 

Fractional distillation can also be illustrated using temperature-composition phase diagrams. A solution of initial composition vaporizes into a vapor having a different composition. If this vapor is cooled, it condenses into a liquid having the same composition. This new liquid can establish an equilibrium with another vapor having a more enriched composition, which condenses, and so on. Figure 7.11 illustrates the stepwise process. Three theoretical plates are shown explicitly. 

FIGURE 7.14 Temperature-composition phase diagram for a nonideal solution showing a positive deviation from Raoult s law. Notice the appearance of a point at which liquid and vapor have the same composition. 

Figure 6.3 The Liquid-Vapor Temperature-Composition Phase Diagram of Benzene andToiuene at 1.000 atm. Drawn from data of M. A. Rosanoff, C. W. Bacon, and F. W. Schulze, J. Am. Chem. Soc., 36, 1993 (1914).

Figure 6.6 The Solid-Liquid Temperature-Composition Phase Diagram of Silicon and Germanium. Since both the solid and liquid phases are nearly ideal solutions, this diagram resembles the liquid-vapor phase diagram of an ideal liquid solution. From C. D. Thurmond, J. Phys. Chem., 57, 827 (1953).

Figure 6.11 shows a pressure-composition liquid-vapor phase diagram of ethanol and diethyl ether for a fixed temperature of 20 C. Compare Figure 6.11 with Figure 6.2, which represents the nearly ideal mixmre of benzene and toluene. Figure 6.12 shows the temperature-composition phase diagram of the same mixture for a fixed pressure of 1.84 atm. Compare this figure with Figure 6.3. This system exhibits positive deviation from Raoult s law. The vapor pressure is larger than it would be if the solution were ideal, and the solution boils at a lower temperature than if it were an ideal solution.

Figure 6.12 Temperature-Composition Phase Diagram for Diethyl Ether-Ethanol at 1.84 atm. The lower curve represents the temperature as a function of mole fraction in the liquid, and the upper curve represents the temperature as a function of mole fraction in the vapor. Drawn from data in J. Timmermans, Physicochemical Constants of Binary Systems, Vol. 2, Interscience Publishers, New York, 1959, p. 401.

Figure 6.14 Liquid-Vapor Temperature-Composition Phase Diagram of Acetone and Chloroform.

Figure 6.16 Liquid-Vapor Temperature-Composition Phase Diagram of Furfurai and Water at 1.000 atm. After G. H. Mains, Chem. Met. Eng., 26, 779 (1922).

If the positive deviation from ideality is even greater than that of Figure 6.15, the two-phase region can extend to the liquid-vapor region and produce a phase diagram like that of Figure 6.16, which shows the temperature-composition phase diagram of furfural and water at a constant pressure of 1.000 atm. The horizontal tie line at... 

Sketch the solid-liquid and liquid-vapor temperature-composition phase diagram of titanium and uranium. The two substances form a nearly ideal liquid solution with a uranium boiling temperature of 1133°C and a titanium boiling temperature of 1660°C. The melting temperature of uranium is 770°C, and that of titanium is 882°C. There is a compound, TiUa, which melts at 890°C. The eutectic between the compound and uranium is at uranium mole fraction 0.95 and 720°C, and the eutectic between titanium and the compound is at uranium mole fraction 0.28 and 655°C. Label each area with the number of independent intensive variables. ... 

The derivation of this formula is assigned in Problem 6.1. Figure 6.2 shows the liquid-vapor pressure-composition phase diagram of benzene and toluene at a constant temperature of 80°C. The lower curve represents the total pressure as a function of the mole fraction of benzene in the vapor phase at equilibrium with the liquid phase. The area below this curve represents possible equilibrium intensive states of the system when it is a one-phase vapor. The upper curve (a line segment) represents Eq. (6.1-24), giving the total pressure as a function of the benzene mole fraction in the liquid. The area above this line represents possible equilibrium states of the system when it is a one-phase liquid. 

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. 

GIBBS-KONOVALOV THEOREMS. Consider a binary system containing two phases (e.g.. liquid and vapor). Both components can pass from one phase lo another. The Gibbs Konovalov theorems refer to the properties of the phase diagrams of such systems (see also Azeotropic System). The lirst theorem is At constant pressure, the temperature of coexistence passes through tin extreme value (maximum, minimum or inflexion with a horizontal value), if the comfutsirlon of the two phases is the same. Conversely, al a point at winch the temperature passes through an extreme value, the phases have the same composition. The second theorem is similar. It refers lo the coexistence pressure at constant temperature. 

Fractional distillation can be represented on a liquid/vapor phase diagram by plotting temperature versus composition, as shown in Figure 11.18. The lower region of the diagram represents the liquid phase, and the upper region represents the vapor phase. Between the two is a thin equilibrium region where liquid and vapor coexist. 

FIGURE 11.18 A phase diagram of temperature versus composition (mole fraction) for a mixture of benzene and toluene. Liquid composition is given by the lower curve, and vapor composition is given by the top curve. The thin region between curves represents an equilibrium between phases. Liquid and vapor compositions at a given temperature are connected by a horizontal tie line, as explained in the text. 

Fig. 4.7 shows a temperature versus composition diagram for an ethanol-water mixture. It is slightly idealized to make a pedagogical point. If one starts with initial composition Q in the liquid (point A in Fig. 4.7), the vapor mixture will have the composition B. If this vapor is condensed, the liquid mixture will have composition C2 at point C the vapor phase will have the composition C3 at point D. Further cycles will achieve ever smaller increases in ethanol liquid content until the azeotrope (constant-boiling) composition is reached at 95.6 mass% and 78.2°C... 

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