Project ForgeA counter-current extraction column is designed to remove 99% of solute C from a solution of solvent A and solute C using pure solvent B. The initial concentration of solute in the solution of A+C is 20 wt%, and the total flow of solution is 1000 kg/h. If the equilibrium relationship is Y=2X, where Y=mass of C/mass of A and X=mass of C/mass of B. The minimum flow rate of solvent B required (in kg/h) is
- A1454
- 1584
- C1676
- D1874
Explanation
A=800 kg/h, C in feed=200 kg/h, Yin=200/800=0.25. After 99% removal, C remaining=2 kg/h, Yout=2/800=0.0025. At minimum solvent flow, the exiting extract is in equilibrium with the ENTERING feed (pinch): Xmax=Yin/2=0.125. Solute balance: A(Yin−Yout)=Bmin(Xmax−0) ⟹ 800×0.2475=Bmin×0.125 ⟹ Bmin=198/0.125=1584 kg/h.
Source: GATE CH 2012 (2012)
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