Properties such as boiling point, freezing point, and vapor pressure of a pure solvent change when solute molecules are added to get a 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 an 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, the freezing point depression constant of water
$\left(K_f^{\text{water}}\right)=1.86\mathrm{K}\mathrm{kg}{\mathrm{mol}}^{-1}$
Freezing point depression constant of ethanol
$\left(K_f^{\text{ethanol }}\right)=2.0\mathrm{K}\mathrm{kg}{\mathrm{mol}}^{-1}$
Boiling point elevation constant of water
$\left(K_b^{\text{water }}\right)=0.52\mathrm{K}\mathrm{kg}{\mathrm{mol}}^{-1}$
Boiling point elevation constant of ethanol
$\left(K_b^{\text{ethanol }}\right)=1.2\mathrm{K}\mathrm{kg}{\mathrm{mol}}^{-1}$
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.