Vapor-liquid composition curves benzene-toluene

Fig. 1-16. Vapor-liquid composition curve lor benzene-toluene mixtures.

When an ideal solution of two liquids, such as benzene (bp 80°C) and toluene (bp 110°C), is distilled by simple distillation, the first vapor produced will be enriched in the lower-boiling component (benzene). However, when that initial vapor is condensed and analyzed, the distillate will not be pure benzene. The boiling-point difference of benzene and toluene (30°C) is too small to achieve a complete separation by simple distillation. Following the principles outlined in Technique 14, Section 14.2, and using the vapor-liquid composition curve given in Figure 15.1, you can see what would happen if you started with an equimolar mixture of benzene and toluene. 

The vapor-liquid composition curve for mixtures of benzene and toluene. 

Let us again consider the vapor-liquid equilibrium curve for benzene and toluene (Fig. 1-25). If one started with a mixture of 20 mole per cent benzene and 80 mole per cent toluene, the vapor in equilibrium with this mixture (upper curve) would have about 40 mole per cent benzene. This percentage corresponds to the composition of... 

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. 

This linear relationship between the total pressure, P, and the mole fraction, x, of the most volatile species is a characteristic of Raoult s law, as shown in Figure 7.18a for the benzene-toluene mixture at 90°C. Note that the bubble-point curve (P-x) is linear between the vapor pressures of the pure species (at x, = 0, 1), and the dew-point curve (P-yJ lies below it. When the (x, yi) points are graphed at different pressures, the familiar vapor-liquid equilibrium curve is obtained, as shown in Figure 7.18b. Using McCabe-Thiele analysis, it is shown readily that for any feed composition, there are no limitations to the values of the mole fractions of the distillate and bottoms products from a distillation tower. 

Thus, by knowing aAB from vapor-liquid equilibrium and by specifying xA, A can be calculated. Figure 4.3a also shows a typical vapor-liquid equilibrium pair, where the mole fraction of benzene in the liquid phase is 0.4 and that in the vapor phase is 0.62. A diagonal line across the x-y diagram represents equal vapor and liquid compositions. The phase equilibrium behavior shows a curve above the diagonal line. This indicates that benzene has a higher concentration in the vapor phase than toluene, that is,... 

To understand how the diagram works, let s imagine starting with the 50 50 benzene/toluene mixture and heating it to its boiling point (92.2°C on the diagram). The lower curve represents the liquid composition (50 50), but the upper curve represents the vapor composition (approximately 71 29 at 92.2°C). The two points are connected by a short horizontal line called a tie line to indicate that the... 

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. 

Assuming the relative volatility of a benzene-toluene mixture is 2.90, the vapor-liquid equilibrium compositions can be calculated as shown in Table 5.1. The resultant curve is plotted in Fig. 5.1a. 

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 4.1.1(c) illustrates the equilihrium vapor and liquid compositions for the henzene-toluene system at a constant total pressure of 1 atmosphere. The vapor phase is enriched in the lighter component, benzene, at all compositions, except in the case of pure benzene and pure toluene. If such vapor-phctse enrichment of benzene did not occur, the straight reference line (xi = Xk) would have represented the VLB. The actual curved equilibrium line relating X to xu may be obtained in the following manner. Consider first Raoult s law expressions for i = 1 and i = 2 ... 

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 8.37 A temperature-composition diagram for benzene and toluene. The lower, blue curve shows the boiling point of the mixture as a function of composition. The upper, orange curve shows the composition of the vapor in equilibrium with the liquid at each boiling point. Thus, point B shows the vapor composition for a mixture that boils at point A. 

The normal boiling point of a binary liquid mixture is the temperature at which the total vapor pressure is equal to 1 atm. If we were to heat a sample of pure benzene at a constant pressure of 1 atm, it would boil at 80.1°C. Similarly, pure toluene boils at 110.6°C. Because, at a given temperature, the vapor pressure of a mixture of benzene and toluene is intermediate between that of toluene and benzene, the boiling point of the mixture will be intermediate between that of the two pure liquids. In Fig. 8.37, which is called a temperature-composition diagram, the lower curve shows how the normal boiling point of the mixture varies with the composition. 

Curve ABC in each figure represents the states of saturated-liquid mixtures it is called the bubble-point curve because it is the locus of bubble points in the temperature-composition diagram. Curve ADC represents the states of saturated vapor it is called the dewpoint curve because it is the locus of the dew points. The bubble- and dew-point curves converge at the two ends, which represent the saturation points of the two pure components. Thus in Fig. 3.6, point A corresponds to the boiling point of toluene at 133.3 kPa, and point C corresponds to the boiling point of benzene. Similarly, in Fig. 3.7, point A corresponds to the vapor pressure of toluene at 100°C, and point C corresponds to the vapor pressure of benzene. 

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... 

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