GATE 2025 CH – Question 54
A binary $AB$ 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 nearest integer).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 43
Explanation
Take 1 mol of feed with $x_F = 0.3$. Recovering 60 % of the A means the distillate carries $0.6 \times 0.3 = 0.18$ mol A and the residue $W$ keeps $0.12$ mol A, so $Wx_W = 0.12$. The Rayleigh equation for constant $\alpha$ is $\ln\frac{F}{W} = \frac{1}{\alpha - 1}\left[\ln\frac{x_F}{x_W} + \alpha\ln\frac{1 - x_W}{1 - x_F}\right]$. Solving this together with $Wx_W = 0.12$ by trial gives $x_W = 0.2063$ and $W = 0.5815$ mol. The distillate is $1 - 0.5815 = 0.4185$ mol, so its average composition is $\frac{0.18}{0.4185} = 0.430$, that is 43 mol% A.