GATE 2025 CH – Question 57
Components $A$ and $B$ form an azeotrope. The saturation vapour pressures of $A$ and $B$ at the boiling temperature of the azeotrope are 87 kPa and 72.7 kPa, respectively. The azeotrope composition is ____ mol% $A$ (rounded off to the nearest integer).
GIVEN: $\ln\frac{\gamma_A}{\gamma_B} = 0.9(x_B^2 - x_A^2)$ where $x_i$ and $\gamma_i$ are the liquid phase mole fraction and activity coefficient of component $i$, respectively.
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Correct answer: 60
Explanation
At an azeotrope $y_i = x_i$, so $\gamma_AP_A^{sat} = \gamma_BP_B^{sat} = P$. Then $\ln\frac{\gamma_A}{\gamma_B} = \ln\frac{P_B^{sat}}{P_A^{sat}} = \ln\frac{72.7}{87} = -0.1796$. With $x_B^2 - x_A^2 = (x_B - x_A)(x_B + x_A) = 1 - 2x_A$, we get $0.9(1 - 2x_A) = -0.1796$, so $1 - 2x_A = -0.1996$ and $x_A = 0.600$, which is 60 mol% A.