Step 1: Explain the basic idea of distillation.
Distillation is a separation technique used for liquid mixtures.
It works by exploiting the fact that different components vaporize at different rates because they have different boiling points.
Step 2: Define relative volatility.
Relative volatility compares how readily one component vaporizes compared to another.
For two components A and B, it is defined as:
\[ \alpha_{AB} = \frac{(y_A/x_A)}{(y_B/x_B)} \]
Here, $x$ represents the mole fraction in the liquid phase and $y$ represents the mole fraction in the vapor phase.
For ideal mixtures, relative volatility can also be written as the ratio of pure-component vapor pressures:
\[ \alpha_{AB} = \frac{P_A^\circ}{P_B^\circ} \]
Step 3: Interpret what relative volatility indicates.
If $\alpha = 1$, both components behave identically in terms of volatility, making separation by distillation impossible.
When $\alpha > 1$, component A is more volatile than component B.
As the value of $\alpha$ increases, the difference in boiling behavior becomes more pronounced, and separation becomes easier.
Therefore, higher relative volatility means fewer stages and less energy are required in a distillation column.
Step 4: Final conclusion.
Relative volatility serves as a direct measure of how easily components in a mixture can be separated by distillation.