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GATE 2026 CH – Question 47

Mass Transfer · Distillation · 2 marks · Multiple choice

A continuous distillation column is used to separate an equimolar mixture of diethylamine (DEA) and methanol. The feed enters the column as saturated liquid at a flow rate of 30 mol s$^{-1}$. It is desired to obtain 92 mol% DEA as distillate. The rate of withdrawal of the distillate from the column is 10 mol s$^{-1}$. The equilibrium curve for the conditions in the column is given below. The latent heat of vaporization of the reboiler contents is 35 kJ mol$^{-1}$. Neglect heat loss to the surroundings and assume constant molal overflow. Which one of the following is the minimum reboiler heat duty (in kW)?

an equilibrium curve of the mole fraction of DEA in the vapour, $y_1$, against the mole fraction of DEA in the liquid, $x_1$, on a grid from 0 to 1. The curve passes through (0.2, 0.2), (0.5, 0.6), (0.7, 0.8) and (1, 1), above the diagonal in the middle region.
  1. 350
  2. 700
  3. 1120
  4. 1470

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Correct answer: (D) 1470

Explanation

The feed is a saturated liquid with $x_F = 0.5$, so the q-line is vertical and meets the equilibrium curve at $(0.5, 0.6)$. The minimum reflux line goes from $(x_D, x_D) = (0.92, 0.92)$ through $(0.5, 0.6)$ with slope $\frac{0.92 - 0.6}{0.92 - 0.5} = 0.762 = \frac{R_{min}}{R_{min} + 1}$, giving $R_{min} = 3.2$. The reflux is $L = 3.2 \times 10 = 32$ mol/s and the vapour in the rectifying section is $V = L + D = 42$ mol/s. With a saturated liquid feed the vapour in the stripping section is the same, $V' = 42$ mol/s. The minimum reboiler duty is $42 \times 35 = 1470$ kW.