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GATE 2023 CH – Question 40

Thermodynamics · Phase equilibria and vapour-liquid equilibrium · 2 marks · Multiple choice

Water in a container at 290 K is exposed to air containing 3% CO$_2$ by volume. Air behaves like an ideal gas and is maintained at 100 kPa pressure. The liquid phase comprising of dissolved CO$_2$ in water behaves like an ideal solution. Use Henry's constant of CO$_2$ dissolved in water at 290 K as 12 MPa. Under equilibrium conditions, which one of the following is the CORRECT value of the mole fraction of CO$_2$ dissolved in water?

  1. $2.9 \times 10^{-4}$
  2. $0.9 \times 10^{-4}$
  3. $2.5 \times 10^{-4}$
  4. $0.5 \times 10^{-4}$

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Correct answer: (C) $2.5 \times 10^{-4}$

Explanation

The partial pressure of CO₂ is $0.03 \times 100 = 3$ kPa. By Henry's law, $x = \frac{p}{H} = \frac{3}{12000} = 2.5 \times 10^{-4}$.