Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogenous solution. These are called colligative properties. Application of colligative properties are very useful in day-to-day life. One of its example 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 `(K_(f)^("water")) = 1.86 K "mol"^(-1)`
Freezing point depression constant of ethanol `(K_(f)^("ethonal")) = 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)^("ethonal")) = 1.2 K kg mol^(-1)`
Standard freezing point of water `= 273 K`
Standard freezing point of ethonal `= 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 ethonal `= 40 mm Hg`
Molecular weight of water `= 18 g "mol"^(-1)`
Molecular weight of ethonal `= 45 g"mol"^(-1)`
In answering the following questions, consider the solution to be ideal ideal solutions and solutes to be non-volatile and non-dissociative.
The freezing point of the solution M is :

Options

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

Answer

D

Explanation

Solution is `H_(2)O` and solvent is `C_(2)H_(5)OH`
`{:("let 0.9 moles of ethanol","0.1 mole of " H_(2)O),(41.4 gm,1.8 gm):}`
`Delta T_(f)=K_(f)xx M`
`Delta T_(f)=2xx[(1.8xx1000)/(1.8xx41.4)]`
`Delta T_(f)=4.83`
`T_(f)=155.7-4.83=150.9 K`