Project ForgeMass Transfer
Mass Transfer Operations
GATE 2020
Hard
Two ideal cross-current extraction stages process a feed of P (1000 kg/h) and Q (10000 kg/h, carrier, immiscible with solvent S). Pure S is fed at 5000 kg/h to stage 1, 15000 kg/h to stage 2. Equilibrium: Y*=1.5X (X=mass P/mass Q in raffinate, Y*=mass P/mass S in extract). The mass flow rate of P (kg/h) in the raffinate from Stage 2 is (round off to nearest integer)
176 kg/h(± 6 accepted)
Explanation
Stage 1: Q·X0=Q·X1+S1·(1.5X1), X0=1000/10000=0.1: 1000=10000X1+7500X1 ⟹ X1=0.05714. Stage 2: Q·X1=Q·X2+S2·(1.5X2): 571.4=10000X2+22500X2 ⟹ X2=0.01758. Mass of P in Stage-2 raffinate=Q·X2=10000×0.01758=175.8 kg/h.
Source: GATE CH 2020 (2020)
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