Calculate the molality of ethanol solution in which the mole fraction of water is $0.88$.

$7.57\text{ m}$

The correct answer is Option (2) → $7.57\text{ m}$ ##

Mole fraction of water $= 0.88$

$\text{Mole fraction of ethanol} = 1 - 0.88 = 0.12$

Therefore, $0.12\text{ moles}$ of ethanol are present in $0.88\text{ moles}$ of water.

$\text{Mass of water} = 0.88 \times 18 = 15.84\text{ g of water.} $

$\text{Molality} = \frac{\text{number of moles of solute (ethanol) present in}}{1000\text{ g of solvent (water)}}$

$= 0.12 \times \frac{1000}{15.84}$

$= 7.57\text{ m} $

$\text{Molality of ethanol } (\text{C}_2\text{H}_5\text{OH}) = 7.57\text{ m}$