Fractional distillation vapor-liquid composition diagrams

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. 

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]. 

Example 18.1. A mixture of 50 mole percent benzene and 50 mole percent toluene is subjected to flash distillation at a separator pressure of 1 atm. The vapor-liquid equilibrium curve and boiling-point diagram are shown in Figs. 18.2 and 18.3. Plot the following quantities, all as functions of f, the fractional vaporization (n) the temperature in the separator, b) the composition of the liquid leaving the separator, and (c) the composition of the vapor leaving the separator. 

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. 

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. 

Suppose you fractionated that liquid of composition A, collected a few drops of the condensed vapor at the top of the column, analyzed it by taking its refractive index, and found that this liquid had a composition corresponding to point J on our diagram. You would follow the same path as before (B-C-D, one distillation D-G-H, another distillation) and find that composition J falls a bit short of the full cycle for distillation 2. 

A PT diagram for the ethane/heptane system is shown in Fig. 12.6, and a yx diagram for several pressures for the same system appears in Fig. 12.7. According to convention, one plots as y and x the mole fractions of the more volatile species in the mixture. The maximum and minimum concentrations of the more volatile species obtainable by distillation at a given pressure are indicated by the points of intersection of the appropriate yx curve with the diagonal, for at these points the vapor and liquid have the same composition. They are in fact mixture critical points, unless y = x = 0 or y = x = 1. Point A in Fig. 12.7... 

You can calculate the number of theoretical plates in your column if you distill a two-component liquid mixture of known composition (isobutyl and isopropyl alcohol perhaps ) and collect a few drops of the liquid condensed from the vapor at the top of the column. You need to determine the composition of that condensed vapor usually from a calibration curve of known compositions versus their refractive indices [see Chapter 28, Re-fractometry ], and you must have the temperature-mole fraction diagram (Fig. 171). 

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.

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... 

---