Vapor/liquid composition diagrams solutions

A vapor-liquid composition-phase diagram like the one in Figure 15.4 can be used to explain the operation of a fractionating column with an ideal solution of two liquids, A and B. An ideal solution is one in which the two liquids are chemically similar, miscible (mutually soluble) in all proportions, and do not interact. Ideal solutions obey Raoult s Law. Raoult s Law is explained in detail in Section 15.3. 

Solution To determine the location of the azeotrope for a specified pressure, the liquid composition has to be varied and a bubble-point calculation performed at each liquid composition until a composition is identified, whereby X = y,-. Alternatively, the vapor composition could be varied and a dew-point calculation performed at each vapor composition. Either way, this requires iteration. Figure 4.5 shows the x—y diagram for the 2-propanol-water system. This was obtained by carrying out a bubble-point calculation at different values of the liquid composition. The point where the x—y plot crosses the diagonal line gives the azeotropic composition. A more direct search for the azeotropic composition can be carried out for such a binary system in a spreadsheet by varying T and x simultaneously and by solving the objective function (see Section 3.9) ... 

Given in the literature are vapor pressure data for acetaldehyde and its aqueous solutions (1—3) vapor—liquid equilibria data for acetaldehyde—ethylene oxide [75-21-8] (1), acetaldehyde—methanol [67-56-1] (4), sulfur dioxide [7446-09-5]— acetaldehyde—water (5), acetaldehyde—water—methanol (6) the azeotropes of acetaldehyde—butane [106-97-8] and acetaldehyde—ethyl ether (7) solubility data for acetaldehyde—water—methane [74-82-8] (8), acetaldehyde—methane (9) densities and refractive indexes of acetaldehyde for temperatures 0—20°C (2) compressibility and viscosity at high pressure (10) thermodynamic data (11—13) pressure—enthalpy diagram for acetaldehyde (14) specific gravities of acetaldehyde—paraldehyde and acetaldehyde—acetaldol mixtures at 20/20°C vs composition (7) boiling point vs composition of acetaldehyde—water at 101.3 kPa (1 atm) and integral heat of solution of acetaldehyde in water at 11°C (7). 

The mutual solubility of ozone and oxygen at —183° and —195.5° C. has been determined by measuring the magnetic susceptibility and vapor pressure (4) of solutions, and a critical solution temperature of —180° C is indicated. The vapor pressure-composition data, combined with vapor pressure data for liquid ozone (1), were used to interpret the phase diagram of the system ( ). Measurements of the density and viscosity of solutions and the surface tension of liquid ozone are reported. 

Ethanol, with a boiling point of 78.3°C, has a vapor pressure of 760 mmHg at this temperature and consequently forms a higher mole fraction in the vapor space above a heated ethanol/water mixture than it does in the liquid phase. Condensation of the alcohol-enriched vapor mixture obtained in this way produces a solution of ethanol in water again, but now enriched in the concentration of ethanol. In a laboratory batch distillation the process described above may be carried out very easily, but this only achieves a limited (by the liquid-vapor composition diagram) improvement in concentration of ethanol obtained with each repetition of the distillation (Eig. 16.5a). Also, as the distillation proceeds, the concentration of alcohol in the distilling vessel becomes depleted. Consequently there is also a gradual depletion in the alcohol concentration obtained in the vapor, and the condensate from this. Despite these problems, many small distilleries still use batch distillation to raise the alcohol concentrations to the requirement of their product [44]. 

Figure 14-12 A boiling point diagram for a solution of two volatile liquids, A and B. The lower curve represents the boihng point of a liquid mixture with the indicated composition. The upper curve represents the composition of the vapor in equilibrium with the boiling liquid mixmre at the indicated temperature. Pure liquid A boUs at a lower temperamre than pure hquid B hence, A is the more volatile liquid in this illustration. Suppose we begin with an ideal equimolar mixmre = Xg = 0.5) of liquids A and B. The point P represents the temperature at which this solution boils, Tj. The vapor that is present at this equilibrium is indicated by point Q (X = 0.8). Condensation of that vapor at temperature Ti gives a liquid of the same composition (point E). At this point we have described one step of simple distillation. The boiling liquid at point if is in equilibrium with the vapor of composition indicated by point S (X > 0.95), and so on.

Few liquid mixtures are ideal, so vapor-liquid equilibrium calculations can be more complicated than is the case for the hexane-triethylamine system, and the system phase diagrams can be more structured than Fig. 10.1-6. These complications arise from the (nonlinear) composition dependence of the species activity coefficients. For example, as a result of the composition dependence of y, the equilibrium pressure in a fixed-temperature experiment will no longer be a linear function of mole fraction. Thus nonideal solutions exhibit deviations from Raoult s law. We will discuss this in detail in the following sections of this chapter. However, first, to illustrate the concepts and some of the types of calculations that arise in vapor-liquid equilibrium in the simplest way, we will assume ideal vapor and liquid solutions (Raoult s law) here, and then in Sec. 10.2 consider the calculations for the more difficult case of nonideal solutions.. ... 

Enthalpy-concentration data. An enthalpy-concentration diagram for a binary vapor-liquid mixture of A and B takes into account latent heats, heats of solution or mixing, and sensible heats of the components of the mixture. The following data are needed to construct such a diagram at a constant pressure (1) heat capacity of the liquid as a function of temperature, composition, and pressure (2) heat of solution as a function of temperature and composition (3) latent heats of vaporization as a function of composition and pressure or temperature and (4) boiling point as a function of pressure, composition, and temperature. 

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 9.12 Vapor-liquid phase equilibrium in a benzene-toluene solution as a function of pressure at 23°C. (a) The total vapor pressure as a function of the mole fraction of benzene in the liquid, (b) The total vapor pressure as a function of the mole fraction of benzene in the vapor, (c) The pressure-composition phase diagram constructed by combining plots (a) and (b). The line/-g is the tie line corresponding to the system at point c.

For a liquid mixture, the composition of the vapor in equilibrium with the heated solution is different from the composition of the solution itself. This is shown in Figure 14.3, which is a phase diagram of the typical vapor-liquid relationship for a two-component system (A + B). 

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 this equation, a and b are constants characteristic of the system. The modified mole fraction is the one defined by Lu (34) from the compositions on a salt-free basis and from the vapor pressure of the pure components and of the salt plus pure liquid solutions. Figures 5 and 6 show the values of X i and X+i corresponding, respectively, to ethanol and water for each of the three systems. For nickel(II) chloride and strontium chloride, the experimental data follow a straight line, while for copper(II) chloride the data form three straight lines, as was expected (24) from the maximum and minimum in the temperature diagram. 

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