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GATE 2025 Chemical Engineering, Q57 · Distillation

The correct answer is 58 to 62.

Question

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(γA/γB)=0.9((xB)2−(xA))2),ln(γ_{A}/γ_{B}) = 0.9((x_{B})² − (x_{A}))²), where xix_{i} and γiγ_{i} are the liquid phase mole fraction and activity coefficient of component i, respectively.

Official answer: 58 to 62

Why

GATE 2025 official key: 58 to 62 mol% A. At the azeotrope, γA/γB=P°B/P°A=72.7/87≈0.836,γ_{A}/γ_{B} = P°_{B}/P°_{A} = 72.7/87 \approx 0.836, so ln(0.836) ≈−0.18=0.9(1−2xA),\approx −0.18 = 0.9(1−2x_{A}), giving xA≈0.60,x_{A} \approx 0.60, i.e., 60 mol% A.

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

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