Separation by distillation is accomplished by partial vaporization and partial condensation.

  • Vapor-Liquid Equilibrium Relationship:

    • \(y = Kx\), where \(K\) is the equilibrium ratio.

    • The equilibrium ratio for any component depends on temperature, on pressure and on compositions of the liquid and vapor. Because higher temperatures favor vaporization and higher pressure retard it, equilibrium ratios generally become larger as the temperature is raised or as pressure is reduced.

    • First drop of liquid vaporizes at bubble point and last drop at dew point.

    • Because distillation conditions are usually close to isobaric, equilibrium diagrams are drawn for constant-pressure conditions.

Relative Volatility (\(\alpha\))

  • This is the ratio of components \(A\) and \(B\) in one phase to that in the other and is a measure of the separability. \[\alpha = \frac{y^*/(1 - y^*)}{x/(1 - x)}\]

  • If \(\alpha = 1\), no separation is possible.

  • For ideal solutions, \(\alpha\) stands in the simple ratio of the vapor pressure of the more volatile component (\(A\)) to that of its less-volatile counterpart (\(B\)). \[\alpha = \frac{P^{\text{sat}}_A}{P^{\text{sat}}_B}\] This ratio varies somewhat with temperature but the variation is not severe and is often accounted for by composing the arithmetic or geometric average of the two end values at \(x = 0\) and \(x = 1\).

  • The relative volatility and hence the separability usually becomes less at high pressures.

  • Volatility of different materials generally approach each other as temperature is raised. Because increasing the pressure on any system raises its boiling temperature, relative volatilities become smaller as pressures are raised.

  • Vapor pressure is related to temperature from the Clausius-Clapeyron equation as: \[\ln P^{\text{sat}} = A-\frac{B}{T}\] Using above, for binary system involving components 1 and 2, we get \[\ln\frac{P_1^{\text{sat}}}{P_2^{\text{sat}}} = \frac{B_2-B_1}{T} + (A_1-A_2)\] It is clearly seen from the latter that the vapor-pressure ratio and hence the separation factor both increase with a decrease in boiling point or total pressure. This result has sometimes been cast into a sweeping rule-of-thumb that low-pressure distillation leads to improved separation. Many nonideal systems follow this rule, but there are also numerous exceptions. Nevertheless, low-pressure distillation is a worthwhile alternative to explore, provided some low-pressure equilibrium data are available to confirm the expected results.

  • Equilibrium relation \[y^* = \frac{\alpha x}{1 + x(\alpha - 1)}\]

  • Relative volatility varies with the temperature.

  • As the pressure is increased, the relative volatility decreases.