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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-to-day 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 \( \mathrm{M} \) 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 \( \left(\mathrm{K}_{\mathrm{f}}{ }^{\text {water }}\right)=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \)
Freezing point depression constant of ethanol \( \left(\mathrm{K}_{\mathrm{f}}{ }^{\text {ethanol }}\right) \) \( =2.0 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \)

Boiling point elevation constant of water \( \left(\mathrm{K}_{\mathrm{b}}^{\text {water }}\right) \) \( =0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \)

Boiling point elevation constant of ethanol \( \left(\mathrm{K}_{\mathrm{b}}{ }^{\text {ethanol }}\right) \) \( =1.2 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \)
Standard freezing point of water \( =273 \mathrm{~K} \)
Standard freezing point of ethanol \( =155.7 \mathrm{~K} \)
Standard boiling point of water \( =373 \mathrm{~K} \)
Standard boiling point of ethanol \( =351.5 \mathrm{~K} \)
Vapour pressure of pure water \( =32.8 \mathrm{~mm} \mathrm{Hg} \)
Vapour pressure of pure ethanol \( =40 \mathrm{~mm} \mathrm{Hg} \)
Molecular weight of water \( =18 \mathrm{~g} \mathrm{~mol}^{-1} \)
Molecular weight of ethanol \( =46 \mathrm{~g} \mathrm{~mol}^{-1} \)
In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.
Water is added to the solution \( \mathrm{M} \) such that the mole fraction of water in the solution becomes 0.9 . The boiling point of this solution is
(a) \( 380.4 \mathrm{~K} \)
(b) \( 376.2 \mathrm{~K} \)
(c) \( 375.5 \mathrm{~K} \)
(d) \( 345.7 \mathrm{~K} \)
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