Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solution molecules ae added to get homogeneous solution. These are called colligative properties. Application 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 of water `(K_(f)^("water"))=1.86K kg "mol"^(-1)`
Freezing point depression constant of ethanol `(K_(f)^("ethanol")=2.0K kg "mol"^(-1)`
Boiling point elevation constant of water `(K_(b)^("water")=0.52K kg "mol"^(-1)`
Boiling point elevation constant of ethanol `(K_(b)^("ethanol")=1.2K kg "mol"^(-1)`
Standard freezing point of water`=273K`
Standard freezing point of ethanol`=155.7K`
Standard boiling point of water `=373K`
Stadndard boiling point of ethanol `=351.5K`
Vapour pressure of pure water `=32.8mm Hg `
Vapour pressure of pure ethanol`=40mm Hg`
Molecular weight of water `=18 g "mol"^(-1)`
Molecular weight of ethanol `=46g "mol"^(-1)`
In aswering the following questions, consider the solution to be ideal dilute solutions and solutes to be non volatile and non-dissociative.
The freezing point (in `.^(@)C`) of a solution containing `0.1g` of `K_(3)[Fe(CN)_(6)]` (Mol. Wt. `329`) in `100g` of water `(K_(f)=1.86K kg "mol"^(-1)` is :

Options

A. `-2.3xx10^(-2)`
B. `-5.7xx10^(-5)`
C. `-5.7xx10^(-3)`
D. `-1.2xx10^(-2)`

Answer

A

Explanation

`DeltaT_(f)=ixxK_(f)xxm`
`=4xx1.86xx(0.1)/(329xx0.1)=2.3xx10^(-2)`
`rArrT_(f)=0-2.3xx10^(-2)=-2.3xx10^(-2)^(@)C`.