the 1.68 per cent layer should be refluxed. For compositions between 1.68 and 33.1 per cent phenol, décantation is a more efficient method of separation than distillation.

This two-tower system can be used to separate a number of binary systems, such as isobutanol-water, aniline-water, or benzene-water. In the last system the solubility of water in benzene is so low that a single-tower system is usually used for the dehydration of benzene, and the water layer is discarded without treating it in a stripping tower.

Some partially miscible mixtures cannot be separated directly by this method. For example, methyl ethyl ketone and water are partially miscible and form an azeotrope at atmospheric pressure, but

the compositions of the two liquid phases do not bracket the constant-boiling mixture composition. Cooling and décantation will not take the composition across the azeotrope. In this case, if salt is added to the décantation system, the solubility limits can be made to overlap the azeotrope and the fractionating-decantation system will make the separation.

2. Modification of Relative Volatility. The two most common methods of modifying the relative volatility bf azeotropic mixtures involve (1) changing the total pressure and (2) adding other components to the mixture. The effect of pressure on the azeotropic composition will be considered in the following section and the second method will be analyzed in Chap. 10.

The effect of pressure on the azeotropic composition is the result of (1) the change in the ratio of the vapor pressures and (2) the change in the activity coefficients. At a given composition the change in the activity coefficients is usually small in comparison to the effect of the vapor-pressure ratio. Thus, the qualitative effect of pressure on the azeotropic composition can be predicted from the vapor-pressure ratio. In the case of ethanol and water mixtures at atmospheric pressure, ethanol is the more volatile component for mixtures containing less than 89.5 mol per cent alcohol, and the less volatile component for more concentrated solutions. The ratio of the vapor pressure of ethanol to water decreases with increasing temperature and, assuming that the activity coefficients do not change, the azeotropic composition should decrease in alcohol content as the total pressure increases. This conclusion is in agreement with the experimental data.

A more quantitative prediction can be obtained by combining the Margules equation for the activity coefficients with equations for the vapor pressures.

At the azeotropic composition,

and Eq. (3-34a) becomes r°-26(In * - In PO - x\(b' + c'a*) (8-1)

The variation of the azeotrope composition with temperature can be obtained by subtracting Eq. (8-1) from Eq. (8-2).

ro.26 ln gi « br(2x! - 1) - c'(l - Zxi + 1.6XÎ) (8-3) * 2

If d and b' have been determined for one temperature, the value of Xt can be calculated as a function of the ratio of the vapor pressures. The total pressure can then be calculated by either Eq. (8-1) or (8-2).

Equations (8-1) and (8-2) can be combined with empirical equations for the vapor pressure as a function of the temperature to give a relation between the total pressure and the azeotropic composition, but the procedure outlined in the preceding paragraph will be found simpler in general.

Equation (8-3) was applied to the system ethanol-water, using T as degree Kelvin, V = 0.605, and c' = 6.01. These values were obtained by fitting Eq. (8-1) and (8-2) to the azeotrope data for atmospheric pressure. The calculated results are compared with the experimental data (Ref. 2) in Fig. 8-9. Some of the difference shown in this figure is due to the fact that the constants used in the equation were based on

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