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 :

380.4

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376.35

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375.5

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354.7

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Solution

The correct option is A $376.35$ K
$χ_{e t h a n o l} = 0.1; χ_{w a t e r} = 0.9$

( Solute $\equiv$ B ) ( Solvent $\equiv$ A )

$Δ T_{b} = K_{b} \cdot m = K_{b} \cdot \frac{χ_{B}}{1 - χ_{B}} \times \frac{1000}{M w_{A}}$

$= 0.52 \times \frac{0.1}{0.9} \times \frac{1000}{18} = 3.2 K$

$T_{b} = T_{b}^{o} + Δ T_{b} = 373 + 3.2 = 376.35 K$

Hence, the correct option is $B$

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Q. A solution M is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixture is 0.9. Water is added to the solution M such that the fraction of water in the solution becomes 0.9. The boiling point of this solution is :

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-to - day life.
One of its examples 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
$(K_{f}^{w a t e r}) = 1.86 K k g m o l^{- 1}$
Freezing point depression constant of ethanol
$(K_{b}^{w a t e r}) = 2.0 K k g m o l^{- 1}$
Boiling point elevation constant of water
$(K_{b}^{w a t e r}) = 0.52 K k g m o l^{- 1}$
Boiling point elevation constant of ethanol
$(K_{b}^{e t h a n o l}) = 1.2 K k g m o l^{- 1}$
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 = 351.5K
Vapour pressure of pure water = 32.8 mm Hg
Vapour pressure of pure ethanol = 40 mm Hg
Molecular weight of water $= 18 g m o l^{- 1}$
Molecular weight of ethanol $= 46 g m o l^{- 1}$
In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.