GATE 2024 CY – Question 65

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

The following figure shows an experimental liquid-liquid phase diagram of phenol and water at the vapor pressure of the system. The total amount of phenol and water (in mol) present in the phenol-rich phase when 5 mol of water was shaken with 5 mol of phenol at 40 °C is ______. (rounded off to one decimal place)

Phenol–water liquid–liquid phase boundary plotted against mole fraction of phenol.

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Correct answer: 7.8 to 8.2

Explanation

Use the tie line at 40 °C and the lever rule. With overall phenol mole fraction 0.5 and total amount 10 mol, $n_{rich}=10(0.5-x_{poor})/(x_{rich}-x_{poor})$. Reading the actual graph gives approximately 8.0 mol; the accepted interval is 7.8–8.2 mol. The earlier endpoint estimates 0.1 and 0.7 were too inaccurate and led to 6.7 mol.

Official GATE 2024 answer key: https://gate2026.iitg.ac.in/doc/download/2024/CYFinalAnswerKey.pdf