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.
Water is added to the solution M such lthat the molecules fraction of water in t he solution becomes `0.9`. The boiling point of this solution is :

Options

A. 380.4 K
B. 376.2 K
C. 375.5 K
D. 354.7 K

Answer

B

Explanation

1. Molality `m = (x_(B)xx1000)/((1-x_(B))m_(A))=(0.1xx1000)/(0.9xx46)`
`=2.415`
`DeltaT=K_(f)xxm`
`=2xx2.415=4.83`
Freezing point of solution `= 155.7 - 4.83 = 150.9 K`
2. `p=p^(0)x_(A)`
`=40xx0.9=36` mm Hg
3. When water becomes solvent, the molality of solution will be :
`m=(x_(B)xx100)/(x_(A)xxm_(A))=(0.1xx1000)/(0.9xx18)=6.172`
`DeltaT=K_(b)xxm=0.52xx6.172=3.209`
Boiling point of solution `= 373 + 3.209`
`=376.2 K`]