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

Correct Answer: 41

Step 1: Given Data.
\[ x_0 = 30% \quad {(mole fraction of A in the feed)} \] \[ y_D = 60% \quad {(mole fraction of A in the distillate)} \] \[ \alpha_{AB} = 2.2 \quad {(relative volatility)} \] 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 \( 47 \) mol% \( A \). Final Answer: The average composition of the distillate is \( \boxed{47} \, {mol%} \, A \).