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GATE 2024 CH – Question 18

Thermodynamics · Phase equilibria and vapour-liquid equilibrium · 1 mark · Multiple choice

Consider a vapour-liquid mixture of components $A$ and $B$ that obeys Raoult's law. The vapour pressure of $A$ is half that of $B$. The vapour phase concentrations of $A$ and $B$ are 3 mol m$^{-3}$ and 6 mol m$^{-3}$, respectively. At equilibrium, the ratio of the liquid phase concentration of $A$ to that of $B$ is

  1. 1.0
  2. 0.5
  3. 2.0
  4. 1.5

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Correct answer: (A) 1.0

Explanation

By Raoult's law $y_AP = x_AP_A^{sat}$ and $y_BP = x_BP_B^{sat}$, so $\frac{y_A}{y_B} = \frac{x_AP_A^{sat}}{x_BP_B^{sat}}$. The vapour ratio is $\frac{3}{6} = 0.5$ and $\frac{P_A^{sat}}{P_B^{sat}} = 0.5$. So $\frac{x_A}{x_B} = \frac{0.5}{0.5} = 1.0$.