Q.
Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-today life. One of its examples is the use of ethylene glycol and water mixture as anti-freezing liquid in the radiator of automobiles.
A solution $M$ is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixture is $0.9$.
Given: Freezing point depression constant of water $\left( K _{ f }^{\text {water }}\right)=1.86 \,K \,kg\, mol ^{-1}$
Freezing point depression constant of ethanol $\left( K _{ f }^{\text{ ethanol }}\right)=2.0\, K \,kg \,mol ^{-1}$
Boiling point elevation constant of water $\left( K _{ b }^{ \text{water} }\right)=0.52 \,K\, kg\, mol ^{-1}$
Boiling point elevation constant of ethanol $\left( K _{ b }^{\text{ ethanol }}\right)=1.2 \,K \,kg\, mol ^{-1}$
Standard freezing point of water $=273 \,K$
Standard freezing point of ethanol $=155.7 \,K$
Standard boiling point of water $=373\, K$
Standard boiling point of ethanol $=351.5\, K$
Vapour pressure of pure water $=32.8 \,mm \,Hg$
Vapour pressure of pure ethanol $=40\, mm\, Hg$
Molecular weight of water $=18 \,g\, mol ^{-1}$
Molecular weight of ethanol $=46 \,g \,mol ^{-1}$
In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and nondissociative.
The vapour pressure of the solution $M$ is
JEE AdvancedJEE Advanced 2008
Solution: