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-tөday life. One of the examples is the use of the mixture of ethylene glycol and water 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: 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)=2.52 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 = `315.5 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 solution `M` is

Options

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

Explanation

`chi_("Ethanol")=0.9`
` chi_("water")=0.1`
`("Solvent" =-B)`
`("Solvent" =-A)`
`DeltaT_(f)=K_(f) .m=K_(f) . (chi_(B))/(1-chi_(B)) xx (1000)/(Mw_(A))`
`=2 xx 0.1/0.9 xx 1000/46=4.86 K`
`T_(f)=T_(f)^(@)-DeltaT_(f)=155.7 + 4.83 =150.87 K`