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 to 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 anwering the following questions consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.
Water is added to the solution `M` such that the mole fraction of water in the 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

`chi_(H2O)=0.9 (solvent)`,`chi_C_(2)H_(5)OH=0.1 (solute)`
Molality of `C_(2)H_(5)OH (m_(C_(2)H_(5)OH))=(chi_(2) xx 1000)/(chi_1 xx Mw_(1))`
`(0.1 xx 1000)/(0.9 xx 18)`
`DeltaT_(b)=K_(b) xx m`
`=0.52 xx (0.1 xx 1000)/(0.9 xx 18) =3.2 K`
Boiling point =`373 + 3.2 =376.2 K`