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xE , Mol fraction of ether in liquid * * In the two-phase region mol fraction values are based on total of both phases. Fig. 4-10. Estimation of vapor-liquid equilibria for system ethyl ether-water at 60°C.

for the water, but the assumptions are probably not so good as those made for the water phase because of the high solubility of water in ether. With these assumptions, the pressure-composition diagram can be completed.

At 60°C. the vapor pressures of ether and water are 1,730 and 149.4 mm. Hg, respectively. Thus for mol fractions of ether of 0.9 or less, the partial pressure of water by Raoult's law is pw = 149.4#tf, and the partial pressure of ether is Pe = HExE. For mol fractions of ether of 93.3 or greater, pE = l,730xE, and pw = Hwxw, where He and Hw are the Henry's law constants for ether in water and water in ether, respectively. The partial pressures of a component must be the same in both liquid phases in the two-liquid-phase region and the above equations can be equated.

For water,

For ether,

It is interesting to note that ether at a mol fraction of 0.009 in water exerts a partial pressure equal to 93.3 per cent of that of pure ether. Thus its volatility, p/x, is extremely high.

The results of such calculations are shown in Figs. 4-9 and 4-10. The latter figure is an expansion of the left-hand side of Fig. 4-9. Raoult's law for ether is shown as a straight line from the vapor pressure of ether at the right-hand side of the diagram to zero at the left-hand side. On the basis of the above assumptions, this line is used only for values xB from 0.933 to 1.0. From xB = 0.009 to 0.933 the partial pressure of ether is constant, and from xE = 0,009 the partial pressure drops on a straight line to 0 at xE = 0. A similar construction is used for water. The sum of the two partial-pressure curves is the total pressure. This is also shown.

If these data are replotted as mol fraction of ether in the vapor vs. mol fraction of ether in the liquid, assuming that the vapors obey the perfect-gas law, one obtains the results given in Fig. 4-11. The value of the mol fraction of ether in the vapor increases very rapidly with the mol fraction in the liquid and becomes constant at 0.915 in the two-phase-liquid region. The vapor-liquid curve crosses the 45° line at a composition of 0.915 mol per cent ether. The mixture of this composition is a pseudo-azeotrope. For mol fractions of ether greater than

0.915, water is more volatile than ether in spite of the fact that the vapor pressure of ether is over eleven times that of water. If a liquid corresponding to a composition in the ether phase region were distilled at 60°C., water would tend to pass off in the vapor leaving ether in the still. Thus, ether could be dried by fractionally distilling water overhead.

This simplified analysis is probably of sufficient accuracy for most distillation calculations, but it is not suitable for cases of partially

Water phase Two phases

' Equilibrium i curve

"0 001 092 094 096 098 1.0 x- Mol fraction ether in liquid

* In the two-phase region mol fraction values are based on total of both phases.

Fig. 4-11. Estimated vapor-liquid equilibria for ethyl ether-water at 60°C.

miscible liquids in which the mutual solubility is much greater. The experimental data on such systems indicate that the partial pressure vs. mol fraction curves pass from the one-phase region to the two-phase region in a smooth type of curve; ¿.e., the corner at the end of the horizontal line rounds into the Henry law region. The construction used for Fig. 4-9 indicated a sharp corner. This rounding effect tends to make the Henry law constant larger. If one component obeys Raoult's law, the Duhem equation indicates that the other component must obey Henry's law, which in the special case may also be Raoult's law. It follows that, in the region where the curvature occurs and Henry's law does not apply, the other components cannot agree with Raoult's law.

These effects are more clearly illustrated by mixtures in which the immiscibility is limited to a narrow region. In such cases the straight-line construction applied in Fig. 4-9 is entirely unsatisfactory. The data of Sims (Ref. 3) for the system phenol-water for the constant-temperature conditions of 43.4°C. are presented in Fig. 4-12. In this

* In the two-phase region mol fraction values are based on total of both phases.

* In the two-phase region mol fraction values are based on total of both phases.

nire of the pure component at 43.4°C. is plotted vs. the mol fraction n the liquid. This method of plotting is applied since the vapor pressures of water and phenol are so greatly different that it is difficult .o represent both of them on the same graph.

The limit of solubility of water in phenol corresponds to a mol frac-ion of water of 0.74, while the solubility of phenol in water is 0.0225 nol fraction phenol. For mol fractions of water between 0.74 and ).9775, the components exist as two liquid layers. Throughout this 4ange in which two liquid phases are present and where the composi-;ions of these phases are therefore constant, the partial pressures renain constant and are represented by the horizontal line EF and CD. The 45° lines corresponding to Raoult's law are drawn for both com-)onents. The data for the water phase cover such a short region that deviations from Raoult's law for the water component are not obvious. In the phenol phase a moderate deviation from Raoult's law is apparent. It will be noted in the figure that the curves tend to approach the immiscible region with rounded corners instead of with sharp angles.

The two points of importance regarding the diagram are (1) constancy of partial pressure so long as two liquid phases are present and (2) the character and extent of the deviation from Raoult's law. The diagram shows that the partial pressure in phenol, when dissolved in water is abnormally high; i.e., it is much greater than is called for by Raoult's law, the line ab. Limited miscibility of two liquids implies that the molecules of one find it difficult to force their way into the other. Thus, it requires a relatively high pressure for phenol to force a small amount of itself into water. This is equivalent to saying that, when phenol has been dissolved in water, the volatility of phenol is abnormally high. The less the mutual solubility, the more abnormal the partial pressure; hence the greater the volatility of the dissolved component. The practical results of these relationships are shown in the following example.

Despite the fact that phenol boils almost 80° higher than water, in certain regions, i.e., low concentrations of phenol, the volatility of phenol is greater than that of water; i.e., the vapor given off by such a solution is richer in phenol than the solution itself. If a solution in this low concentration region is distilled, the water is discharged from the bottom of the column essentially free of phenol, which is found in the distillate.

These data for phenol and water are replotted in Fig. 4-13 as the vapor-liquid equilibrium, i.e., the mol fraction of the phenol in the vapor as a function of the mol fraction of phenol in the liquid. The data curve is labeled "experimental." These data indicate that this system forms a minimum boiling azeotrope at a concentration of about 0.0073 mol fraction phenol. At concentrations lower than this, phenol is more volatile than water. At all concentrations greater than this, water is more volatile than phenol. This y,x curve indicates the constancy of vapor composition in the two-phase region. The procedure involving the use of Raoult's and Henry's laws employed for the ethyl ether-water system is probably not suitable for the phenol-water system because of the high mutual solubilities. However, such calculations were made for illustrative purposes and the results are shown on Figs. 4-13 and 4-14. The latter figure gives the relative volatilities corresponding to the vapor-liquid curve of Fig. 4-13. It is apparent

Experimental data

Raoult*s and Henry's laws

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