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GATE 2021 CY – Question 50

Physical Chemistry · Solutions: Ideal and non-ideal solutions, Raoult’s Law and Henry’s Law. · 2 marks · Multiple choice

Hexane and heptane are completely miscible. At 25 °C, the vapor pressures of hexane and heptane are 0.198 atm and 0.06 atm, respectively. The mole fractions of hexane and heptane in the vapor phase for a solution containing 4 M hexane and 6 M heptane, respectively, are:

  1. 0.688 and 0.312
  2. 0.400 and 0.600
  3. 0.312 and 0.688
  4. 0.600 and 0.400

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Correct answer: (A) 0.688 and 0.312

Explanation

The liquid mole fractions are xhexane=4/(4+6)=0.4 and xheptane=0.6. Raoult’s law gives partial pressures 0.4×0.198=0.0792 atm and 0.6×0.060=0.0360 atm. Divide each by the total 0.1152 atm: yhexane=0.6875 and yheptane=0.3125.

Thus **0.688 and 0.312, A**.