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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.
Water is added to the solution $M$ such that the fraction of water in the solution becomes $0.9. $The boiling point of this solution is

JEE AdvancedJEE Advanced 2008

Solution:

$\Delta T _{ b }= K _{ b } \times m$
$=0.52 \times \frac{0.1}{0.9 \times 18} \times 1000=3.2\, K$
$T _{ b }=373+3.2=376.2 \,K$