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Q.

Water and chlorobenzene are immiscible liquids. Their mixture boils at 89oC under a reduced pressure of 7.7 x 104 Pa. The vapour pressure of pure water at 89oC is 
7 x 104 pa. Weight per cent of chlorobenzene in the distillate is :

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a

60

b

78.3

c

50

d

38.46

answer is D.

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Detailed Solution

Given:

  • Boiling point of the mixture: 89°C
  • Total pressure (boiling point pressure of the mixture): Ptotal = 7.7 × 104 Pa
  • Vapor pressure of pure water at 89°C:Pwater = 7 × 104 Pa
  • Vapor pressure of chlorobenzene: To be calculated

We know that the total vapor pressure of the mixture is the sum of the individual vapor pressures:

Ptotal = Pwater + Pchlorobenzene

Substituting the given values:

7.7 × 104 = 7 × 104 + Pchlorobenzene

Therefore:

Pchlorobenzene = 7.7 × 104 - 7 × 104 = 0.7 × 104 Pa

From Raoult's Law, we know that:

χchlorobenzene = Pchlorobenzene / Ptotal

Substituting the values:

χchlorobenzene = (0.7 × 104) / (7.7 × 104) = 0.0909

Using the formula for weight percent:

Weight percent of chlorobenzene = (χchlorobenzene × Mchlorobenzene) / [(χchlorobenzene × Mchlorobenzene) + (χwater × Mwater)] × 100

Where:

  • Mchlorobenzene: Molar mass of chlorobenzene = 112 g/mol
  • Mwater: Molar mass of water = 18 g/mol
  • χwater: Mole fraction of water = 1 - 0.0909 = 0.9091

Substituting the values:

Weight percent of chlorobenzene = (0.0909 × 112) / [(0.0909 × 112) + (0.9091 × 18)] × 100Weight percent of chlorobenzene = 38.46%

Final Answer: Option (d) 38.46%

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