Q3 / 90 · JEE Main 2022 (25 Jun Shift 2) · Chemistry

Solute A associates in water. When $0.7 g$ of solute $A$ is dissolved in $42.0 g$ of water, it depresses the freezing point by $0.2 ° C$ . The percentage association of solute $A$ in water, is
[Given: Molar mass of $A = 93 g {mol}^{- 1}$ . Molal depression constant of water is $1.86 K kg {mol}^{- 1}$ ]

Solution

Depression in freezing point, ${ΔT}_{f} = {iK}_{f} \times m$

$2.0 = ix 1.86 \times \frac{7 \times 1000}{93 \times 42}$

$2.0 = i [3.33]$

$i = 0.6$

$i = 1 + [\frac{1}{n} - 1] β$

$0.6 = 1 + [\frac{1}{2} - 1] β$

$β = 0.8$

$% β = 80$

Hence, the percentage association of solute A in water is 80.

Hence, the correct answer is option: 'D'.