Relative volatility

Relative volatility

Relative volatility is a measure comparing the vapor pressures of the components in a liquid mixture of chemicals. This quantity is widely used in designing large industrial distillation processes. In effect, it indicates the ease or difficulty of using distillation to separate the more volatile components from the less volatile components in a mixture. By convention, relative volatility is usually denoted as α.
Relative volatilities are used in the design of all types of distillation processes as well as other separation or absorption processes that involve the contacting of vapor and liquid phases in a series of equilibrium stages.
Relative volatilities are not used in separation or absorption processes that involve components reacting with each other (for example, the absorption of gaseous carbon dioxide in aqueous solutions of sodium hydroxide).
  
Definition

For a liquid mixture of two components (called a binary mixture) at a given temperature and pressure, the relative volatility is defined as

where:
α	= the relative volatility of the more volatile component i to the less volatile component j
yi	= the vapor-liquid equilibrium concentration of component i in the vapor phase
xi	= the vapor-liquid equilibrium concentration of component i in the liquid phase
yj	= the vapor-liquid equilibrium concentration of component j in the vapor phase
xj	= the vapor-liquid equilibrium concentration of component j in the liquid phase
(y / x)	= K   commonly called the K value or vapor-liquid distribution ratio of a component

When their liquid concentrations are equal, more volatile components have higher vapor pressures than less volatile components. Thus, a K value (= y / x) for a more volatile component is larger than a K value for a less volatile component. That means that α ≥ 1 since the larger K value of the more volatile component is in the numerator and the smaller K of the less volatile component is in the denominator.
α is a unit less quantity. When the volatilities of both key components are equal, α = 1 and separation of the two by distillation would be impossible under the given conditions because the compositions of the liquid and the vapor phase are the same (azeotrope). As the value of α increases above 1, separation by distillation becomes progressively easier.

Thus, for the distillation of any multi-component mixture, the relative volatility is often defined as