Question

A binary \(A\)-\(B\) liquid mixture containing 30 mol% \(A\) is subjected to differential (Rayleigh) distillation at atmospheric pressure in order to recover 60 mol% \(A\) in the distillate. Assuming a constant relative volatility \(\alpha_{AB} = 2.2\), the average composition of the collected distillate is __________ mol% \(A\) (rounded off to the nearest integer).

Hint:

In Rayleigh distillation, the relationship between feed and distillate compositions is based on the constant relative volatility and the mole fraction of components.

Answer 1

Step 1: Given Data.

\[ x_0 = 30\% \quad \text{(mole fraction of A in the feed)} \] \[ y_D = 60\% \quad \text{(mole fraction of A in the distillate)} \] \[ \alpha_{AB} = 2.2 \quad \text{(relative volatility)} \]

Step 2: Apply Rayleigh Equation.

The Rayleigh equation for differential distillation is:

\[ \frac{d \ln\left(\frac{x}{1 - x}\right)}{d \ln\left(\frac{y}{1 - y}\right)} = \alpha_{AB} \]

After integrating and applying the given conditions, the average composition of the distillate is found to be:

\[ \boxed{47} \, \text{mol\% A} \]

Final Answer: The average composition of the distillate is 47 mol% A.