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GATE 2024 CH – Question 42

Mass Transfer · Distillation · 2 marks · Multiple choice

A simple distillation column separates a binary mixture of $A$ and $B$. The relative volatility of $A$ with respect to $B$ is 2. The steady-state composition of $A$ in the vapour leaving the 1st, 2nd and 3rd trays in the rectifying section are 94, 90 and 85 mol%, respectively. For ideal trays and constant molal overflow, the reflux-to-distillate ratio is

  1. 1.9
  2. 2.7
  3. 1.2
  4. 1.1

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Correct answer: (B) 2.7

Explanation

For an ideal tray the liquid leaving a tray is in equilibrium with the vapour leaving it: $x = \frac{y}{\alpha - (\alpha - 1)y}$. So $x_1 = \frac{0.94}{2 - 0.94} = 0.8868$ and $x_2 = \frac{0.90}{2 - 0.90} = 0.8182$. The operating line relates the vapour from the tray below to the liquid on the tray above, so the slope $\frac{R}{R + 1}$ follows from two vapour compositions and the two liquid compositions: $\frac{y_2 - y_3}{x_1 - x_2} = \frac{0.90 - 0.85}{0.8868 - 0.8182} = 0.729$. Then $\frac{R}{R + 1} = 0.729$ gives $R = 2.69 \approx 2.7$.