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 adn water mixtures 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 `(K_(f)^(water)) = 1.86 K kg mol^(-1)`
Freezing point depression constant of ethanol `(K_(f)^("ethanol")) = 2.0 K kg mol^(-1)`
Boiling point elevation constant of water `(K_(b)^(water)) = 0.52 K kg mol^(-1)`
Boiling point elevation constant of ethanol `(K_(b)^("ethanol")) = 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 non-dissociative.
The freezing point of the solution M is

Options

A. `268.7K`
B. `268.5 K`
C. `234.2K`
D. `150.9 K`

Answer

D

Explanation

`(T_(f'))_(Alc.sol^(n)) = (T_(f))_(EtoH) - (K_(f))_(eton) m`
`= 115.7 - 2 xx (0.1)/(0.9 xx 46//1000)`
`= 155.7 - 2 xx 2.415 = 150.9 K`