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GATE 2023 CY – Question 60

Physical Chemistry · Phase Equilibria: Phase rule. Clausius- Clapeyron equation. Phase diagram of one component system: CO2, H2O, S; two component systems: liquid-vapor, liquid-liquid and solid-liquid systems. Fractional distillation. Azeotropes and Eutectics. · 2 marks · Numerical answer

Naphthalene–benzene forms a simple eutectic solid–liquid system. For an ideal solution at 300 K and 1 bar, naphthalene mole fraction in benzene is ______ (two decimal places). Naphthalene freezing point is 353 K and fusion enthalpy 19.28 kJ/mol; $R=8.31$ J K$^{-1}$ mol$^{-1}$.

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Correct answer: 0.30 to 0.32

Explanation

For ideal solid–liquid equilibrium, ln x=−ΔHfus/R(1/T−1/Tfp). Substitution gives ln x=−19280/8.31(1/300−1/353)=−1.16114. Exponentiating gives x≈0.3131, rounded **0.31**. The temperature inverses must be in kelvin.