Vapor temperature-composition phase

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 6.14 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).

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. ... 

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. 

For plots of X, and g , it is sometimes easier to use temperature-composition phase diagrams rather than pressure-composition phase diagrams. Figure 7.14 shows a positive deviation from Raoult s law. (Be sure to keep track of what the positive means that the vapor pressure is higher than expected from Raoult s law. With the temperature and pressure being inversely related, a positive deviation from Raoult s law leads to a lower temperature for the boiling point, which is what Figure 7.14 illustrates.)... 

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. 

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. 

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).

Assume that carbon tetrachloride and 1,1,1-trichloroethane form an ideal solution. Look up the normal boiling temperatures and the enthalpy changes of vaporization of the pure substances and plot a temperature-composition phase diagram for 1.000 atm. (Four points besides the end points should give an adequate plot.) Assume that the enthalpy changes of vaporization are tenqterature-independent. 

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.

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... 

High-temperature vaporization behaviors that yield high-temperature thermodynamic data such as activity and enthalpy are necessary for uses as nuclear reactor and fusion materials. High-temperature activity measurements make it possible to determine the Gibbs free energy of formation of compounds from the elements. Accurate high-temperature thermodynamic data serve to establish temperature-composition phase diagrams, i.e., limits for the formation of binary phases. 

The temperature and composition of each feed stream and the stream ratios are specified along with a common feed pressure (significant only for the vapor stream) and the flash pressure. For an isothermal flash the flash temperature is also specified. Resulting vapor and liquid compositions, phase ratios, vaporization equilibrium ratios, and, for an adiabatic flash, flash temperature are returned. 

As discussed in Sec. 4, the icomplex function of temperature, pressure, and equilibrium vapor- and hquid-phase compositions. However, for mixtures of compounds of similar molecular structure and size, the K value depends mainly on temperature and pressure. For example, several major graphical ilight-hydrocarbon systems. The easiest to use are the DePriester charts [Chem. Eng. Prog. Symp. Ser 7, 49, 1 (1953)], which cover 12 hydrocarbons (methane, ethylene, ethane, propylene, propane, isobutane, isobutylene, /i-butane, isopentane, /1-pentane, /i-hexane, and /i-heptane). These charts are a simplification of the Kellogg charts [Liquid-Vapor Equilibiia in Mixtures of Light Hydrocarbons, MWK Equilibnum Con.stants, Polyco Data, (1950)] and include additional experimental data. The Kellogg charts, and hence the DePriester charts, are based primarily on the Benedict-Webb-Rubin equation of state [Chem. Eng. Prog., 47,419 (1951) 47, 449 (1951)], which can represent both the liquid and the vapor phases and can predict K values quite accurately when the equation constants are available for the components in question. 

Fig. 1. The pressure-temperature-composition surfaces for the equilibrium between two pure solid phases, a liquid phase, and a vapor phase.

It is difficult to measure partial molar volumes, and, unfortunately, many experimental studies of high-pressure vapor-liquid equilibria report no volumetric data at all more often than not, experimental measurements are confined to total pressure, temperature, and phase compositions. Even in those cases where liquid densities are measured along the saturation curve, there is a fundamental difficulty in calculating partial molar volumes as indicated by... 

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