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GATE 2024 Chemical Engineering, Q40 · Mass Transfer

The correct answer is B, 0.0126.

Question

A gas stream containing 95 mol% CO2CO₂ and 5 mol% ethanol is to be scrubbed with pure water in a counter-current, isothermal absorption column to remove ethanol. The desired composition of ethanol in the exit gas stream is 0.5 mol%. The equilibrium mole fraction of ethanol in the gas phase, y*, is related to that in the liquid phase, x, as y* = 2x. Assume CO2CO₂ is insoluble in water and neglect evaporation of water. If the water flow rate is twice the minimum, the mole fraction of ethanol in the spent water is

  • A. 0.0225
  • B. 0.0126
  • C. 0.0428
  • D. 0.0316

Official answer: 0.0126

Why

GATE 2024 official key: (B). In mole-ratio terms, Yin=0.05/0.95=0.0526,Yout=0.005/0.995=0.00503.Y_{in}=0.05/0.95=0.0526, Y_{out}=0.005/0.995=0.00503. At minimum water rate, exit liquid equilibrates with inlet gas: Xmax=Yin/2=0.0263,X_{max}=Y_{in}/2=0.0263, giving (L/Gs)min≈1.809.(L/Gs)_{min}\approx 1.809. At L/Gs=2×1.809=3.618,Xout=(Yin−Yout)/(L/Gs)≈0.01316,L/Gs=2 \times 1.809=3.618, X_{out}=(Y_{in}−Y_{out})/(L/Gs)\approx 0.01316, so xout=Xout/(1+Xout)≈0.0126.x_{out}=X_{out}/(1+X_{out})\approx 0.0126.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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