GATE 2020 CH – Question 57

Mass Transfer · Leaching, liquid-liquid extraction, drying, humidification and adsorption · 2 marks · Numerical answer

Two ideal cross-current extraction stages treat a feed of P and Q. Stage 1 receives P = 1000 kg/h and Q = 10000 kg/h; fresh pure solvent S enters stages 1 and 2 at 5000 and 15000 kg/h. Q and S are immiscible. Equilibrium is Y* = 1.5X, where X is kg P/kg Q and Y is kg P/kg S. Find P remaining in stage-2 raffinate in kg/h, rounded to the nearest integer.

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Correct answer: 171 to 181

Explanation

For one ideal stage with solute-free solvent, $P_{in}=QX+SY=QX+1.5SX$, so the fraction retained in raffinate is $1/[1+1.5S/Q]$. Stage 1 retains $1000/[1+1.5(5000/10000)]=571.4286$ kg/h. Stage 2 retains $571.4286/[1+1.5(15000/10000)]=175.824$ kg/h. The final amount rounds to 176 kg/h.

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