Question:
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 \(\text{s}^{-1}\). It is desired to obtain 92 mol% DEA as distillate. The rate of withdrawal of the distillate from the column is 10 mol \(\text{s}^{-1}\). The equilibrium curve for the conditions in the column is given below. The latent heat of vaporization of the reboiler contents is 35 kJ \(\text{mol}^{-1}\). Neglect heat loss to the surroundings and assume constant molal overflow. Which one of the following is the minimum reboiler heat duty (in kW)?
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 \(\text{s}^{-1}\). It is desired to obtain 92 mol% DEA as distillate. The rate of withdrawal of the distillate from the column is 10 mol \(\text{s}^{-1}\). The equilibrium curve for the conditions in the column is given below. The latent heat of vaporization of the reboiler contents is 35 kJ \(\text{mol}^{-1}\). Neglect heat loss to the surroundings and assume constant molal overflow. Which one of the following is the minimum reboiler heat duty (in kW)?
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Find the pinch point where the vertical q-line at $x=x_F$ meets the equilibrium curve, get $R_{min}$ from the rectifying line through $(x_D,x_D)$ and the pinch, then $Q_r=(R_{min}+1)D\lambda$.
Updated On: Jul 17, 2026
- 350
- 700
- 1120
- 1470
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The Correct Option is D
Solution and Explanation
Step 1: Mass balance.
F=30, xF=0.5, D=10, xD=0.92, B=20, xB=0.29.
Step 2: Feed line.
q=1, vertical q-line at x=0.5.
Step 3: Pinch point.
Reading the equilibrium curve at x1=0.5, y*~0.6, pinch (0.5, 0.6).
Step 4: Minimum reflux ratio.
\[ \frac{R_{min}}{R_{min}+1} = \frac{0.92-0.6}{0.92-0.5} = 0.7619 \Rightarrow R_{min}=3.20 \]
Step 5: Boilup vapor rate.
\[ \bar V = (R_{min}+1)D = 4.20\times10=42\ \text{mol/s} \]
Step 6: Minimum reboiler duty.
\[ Q_{r,min} = 42\times35=1470\ \text{kW} \]
\[ \boxed{Q_{r,min} = 1470\ \text{kW}} \]Was this answer helpful?
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