Phase diagram, fractional distillation

J 12 Interpret a two-component phase diagram and discuss fractional distillation (Sections 8.18, 8.19, and 8.20). 

Although fractional crystallization has always been the most common method for the separation of diastereomers. When it can be used, binary-phase diagrams for the diastereomeric salts have been used to calculate the efficiency of optical resolution. However, its tediousness and the fact that it is limited to solids prompted a search for other methods. Fractional distillation has given only limited separation, but gas chromatography and preparative liquid chromatography have proved more useful and, in many cases, have supplanted fraetional crystallization, especially where the quantities to be resolved are small. 

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. 

The efficiency of the fractional distillation depends very much on the shape of the phase diagram. 

Liquid-vapor TX phase diagram for an ideal solution of A in B. An isopleth isshown. The line segment D E F- G H represents the path of sequential fractional distillation steps through two and a half stages (or two and a half "theoretical plates"). 

Liquid-vapor phase diagrams, and boiling-point diagrams in particular, are of importance in connection with distillation, which usually has as its object the partial or complete separation of a liquid solution into its components. Distillation consists basically of boiUng the solution and condensing the vapor into a separate receiver. A simple one-plate distillation of a binary system having no maximum or minimum in its boiling-point curve can be understood by reference to Fig. 3. Let the mole fraction of B in the initial solution be represented by... 

FIGURE 5.5-2 Ternary phase diagram for ethanol-benzene-water, showing distillation paths for the columns shown in Fig. 5.5-1. Composition in mole percent or mole fraction. (Based on Ref. 4.)... 

Since few liquid mixtures are ideal, vapor-liquid equilibrium calculations are somewhat more complicated than for the cases in the previous section, and the phase diagrams for nonideal systems can be more structured than Figs. 10.1-1 to 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 yt, the vapor-liquid equilibrium pressure in a fixed-temperature experiment will no longer be a linear function of mole fraction, so that no.nideal solutions exhibit deviations from Raoult s law. However, all the calculational methods discussed in the previous section for ideal mixtures, including distillation column design, can be used for nonideal mix-, tures, as long as the composition dependence of the activity coefficients is taken into account. 

Binary solutions that deviate significantly from ideal behavior (as exemplified in their temperature-composition phase diagrams) have important consequences for fractional distillation processes. Figure 9.16 shows two types of such phase diagrams for... 

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.

Phase diagram for a fractional distillation of an ideal two-component system. 

Figure 13.10 on the next page summarizes the general appearance of some relatively simple temperature-composition phase diagrams of binary systems. If the system does not form an azeotrope (zeotropic behavior), the equilibrated gas phase is richer in one component than the liquid phase at all liquid compositions, and the liquid mixture can be separated into its two components by fractional distillation. The gas in equilibrium with an azeotropic mixture, however, is not enriched in either component. Fractional distillation of a system with an azeotrope leads to separation into one pure component and the azeotropic mixture. 

Figure 13.11 Temperature-composition phase diagrams of binary systems with partially-miscible liquids exhibiting (a) the ability to be separated into pure components by fractional distillation, (b) a minimum-boiling azeotrope, and (c) boiling at a lower temperature than the boiling point of either pure component. Only the one-phase areas are labeled two-phase areas are hatched in the direction of the tie lines.

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 7.11 Fractional distillation can also be represented using temperature-composition phase diagrams. This diagram shows the same process as Figure 7.8. Can you explain the differences between the two representations of the same process ... 

Using a temperature-composition phase diagram like Figure 7.14, predict the general composition of the ultimate distillation product if a solution having a mole fraction of 0.9 is distilled. 

The goal Is to create a Txy phase diagram for mixtures of benzene and toluene, where T is the temperature, x is the mole fraction of benzene in the liquid, and y is the mole fraction of benzene In the vapor. A horizontal line drawn for a given T gives the compositions of liquid and vapor in equilibrium at that T. Such diagrams are very useful for distillation calculations... 

Figure 8.5 Vapor vs. liquid mole fractions (xy) phase diagram for methanol (a)-water (b) binary mixtures at a constant pressure of 1 atm. (a) xy diagram with 45° line indicated (b) stages in distillation at total reflux (c) stages in a five tray distillation column with operating lines shown. Stages in distillation are illustrated on the right of (b) and (c).

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