Temperature-composition diagrams

Let us now take a phase of montmorillonite composition (fully expandable at low temperature) and subject it to an increase in temperature and 

ML = mixed layered mica-montmorillonite All = allevardite-like phase  

Mo = montmorillonites (in this case, beidellite) Kaol = kaolinite Py = pyrophyllite Mu = muscovite. 

The vapor that forms over a liquid as the pressure is reduced is richer in a particular component than the liquid. This fact is the basis of a method of separation isothermal distillation. The method is useful for those mixtures that would decompose if distilled by the ordinary method it is sufficiently inconvenient so that it is used only if other methods are not suitable. 

The system described above is an ideal solution. If the deviations from ideality are not very large, the figure will appear much the same except that the liquid composition curve is not a straight line. The interpretation is precisely the same as for the ideal solution. 

In the diagrams shown in Section 14.5, the temperature was constant. The equilibrium pressure of the system was then a function of either or y, according to Eqs. (14.9) or (14.12). In those equations, the values of pi and are functions of temperature. If, in Eqs. (14.9) and (14.12), we consider the total pressure p to be constant, then the equations are relations between the equilibrium temperature, the boiling point, and either x or y. The relations T = /(x ) and T = g(yi) are not such simple ones as between pressure and composition, but they may be determined theoretically through the Clapeyron equation or, ordinarily, experimentally through determination of the boiling points and vapor compositions corresponding to liquid mixtures of various compositions. 

The plot at constant pressure of boiling points versus compositions for the ideal solution corresponding to that in Fig. 14.3 is shown in Fig. 14.5. Neither the liquid nor the vapor curve is a straight line otherwise, the figure resembles Fig. 14.3. However, the lenticular liquid-vapor region is tilted down from left to right. This corresponds to the fact 

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Figure 3.8a shows the temperature-composition diagram for a minimum-boiling azeotrope that is sensitive to changes in pressure. This azeotrope can be separated using two columns operating at different pressures, as shown in Fig. 3.86. Feed with mole fraction of A Ufa)) of, say, 0.3 is fed to the high-pressure column. The bottom product from this high-pressure column is relatively pure B, whereas the overhead is an azeotrope with jcda = 0-8, jcdb = 0.2. This azeotrope is fed to the low-pressure column, which produces relatively pure A in the bottom and in the overhead an azeotrope with jcda = 0.6, jcdb = 0.4. This azeotrope is added to the feed of the high-pressure column.

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. 

Deviations from Raoult s law can make it impossible to separate liquids by distillation. The temperature-composition diagrams for mixtures of ethanol and benzene and of acetone and chloroform show why. A positive deviation from Raoult s law means that the attractive forces between solute and solvent are lower than those between the molecules of the pure components. As a result, the boiling point of the mixture is lower than that predicted by Raoult s law. For some pairs of components, the boiling point of the mixture is in fact lower than the boiling point of either constituent (Fig. 8.41). A mixture for which the lowest boiling temperature is below... 

FIGURE 8.41 The temperature composition diagram of a minimum-boiling azeotrope (such as ethanol and benzene). When this mixture is fractionally distilled, the (more volatile) azeotropic mixture is obtained as the initial distillate. 

Figure 2.6 A temperature-composition diagram showing the relationship of temperature and solvent miscibility for two partially miscible liquids...

The temperature-composition diagram can be used to calculate the composition of the two-phase system according to the amount of each solvent present. For example, at temperature T, the composition of the most abundant phase, which consists of liquid A saturated with liquid B, is represented by the point a and the composition of the minor phase, consisting of liquid B saturated with liquid A, is represented by point a. The horizontal line connecting these two points is known as a tie line as it links two phases that are in equilibrium with each other. From this line the relative amounts of the two phases at equilibrium can be calculated, using the lever rule, under the conditions described by the diagram. The lever rule gets its name from a similar rule that is used to relate two masses on a lever with their distances from a pivot, i.e. ... 

The temperature also affects the composition of the two phases at equilibrium, but the effect is not equivalent in all systems. In the example shown in Figure 2.6, raising the temperature increases the solubility of the two phases and this is what is usually observed. The diagram shows that by heating the system, more of A dissolves in B and vice versa. However, other solvent pairs become less miscible with raised temperature, for example, water and ethylamine. In the case of these liquid pairs, the temperature-composition diagram is essentially reversed, as shown in Figure 2.7. 

Figure 2.7 The temperature-composition diagram for a system with a lower critical temperature, such as water and ethylamine...

The composition of the vapour in equilibrium with a liquid of given composition is determined experimentally using an equilibrium still. The results are conveniently shown on a temperature-composition diagram as shown in Figure 11.3. In the normal case shown in Figure 11.3a, the curve ABC shows the composition of the liquid which boils at any... 

The pressure-temperature-composition diagram presented by Morey is shown in Fig. 8. The vapor pressure of pure water (on the P-T projection) terminates at the critical point (647 K, 220 bar). The continuous curve represents saturated solutions of NaCl in water, i.e., there is a three-phase equilibrium of gas-solution-solid NaCl. The gas-phase pressure maximizes over 400 bar at around 950 K. Olander and Liander s data for a 25 wt. % NaCl solution are shown, and T-X and P X projections given. At the pressure maximum, the solution phase contains almost 80% NaCl. 

Figure 1 shows the equilibrium data for the ethanol-water systems saturated with copper(II) chloride, strontium chloride, or nickel(II) chloride. Figure 2 shows the temperature-compositions diagrams corrected to 700 mmHg. 

Temperature-composition diagrams for mixtures of methane and ethane are given in Figure 2-24.3 Six saturation envelopes corresponding to six different pressures are shown. 

Fig. 2-24. isobaric temperature-composition diagrams of mixtures of methane and ethane. (Bloomer, et al., Institute of Gas Technology, Research Bulletin 22, 1953. Reproduced courtesy of Institute of Gas Technology, Chicago.)... 

Replot three isobars of the data given in Figure 2-37 as temperature against composition in weight percent. Use 300 psia, 600 psia, and 900 psia. This is called a temperature composition diagram. Label the bubble-point lines and dewpoint lines. 

If the temperature dependence of the free-energy curves is considered in addition to the (3 particle size, a temperature-composition diagram for the system can be plotted. This is illustrated in Fig. C.7, which shows clearly the way in which the solubility of component B in a increases with decreasing (3 particle size. 

FIGURE 4.3 Temperature-composition diagrams for methane and water. (Reproduced from Huo, Z Hester, K Miller, K.T., Sloan, E.D., AIChE /., 49, 1300 (2003). With permission from the American Institute of Chemical Engineers.)... 

Figure 10 shows the relationship between yx and xx for different values of an calculated from Eq. (8). When two components have close boiling points, by implication they have similar vapor pressures, so that an is close to unity. Separation of mixtures by distillation becomes more difficult as an approaches unity. Figure 11 indicates some of the x, y diagrams that can be obtained for distillation systems. Also shown are corresponding temperature-composition diagrams. The saturated vapor or dewpoint curve is determined by finding the temperature at which liquid starts to condense from a vapor mixture. Similarly, the saturated liquid or bubble-point curve corresponds to the temperature at which a liquid mixture starts to boil. For ideal mixtures, the dewpoint and bubble-point curves can be calculated as follows. From Eq. (3), at the dew point, since... 

In the study of miscibility of partially miscible liquid pairs, the external pressure is kept constant and, therefore, the vapour phase is ignored. The mutual solubilities are represented by means of temperature-composition diagram. 

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