Calculate van't Hoff factor (i) of 0.2 m aqueous solution of an electrolyte if it freezes at $-0.660…

Calculate van't Hoff factor (i) of 0.2 m aqueous solution of an electrolyte if it freezes at $-0.660 \mathrm{~K} .\left(\mathrm{K}_{\mathrm{f}}=1.84 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$
  1. 1.97
  2. 1.79
  3. 0.242
  4. 0.557

Solution

$\begin{array}{rlrl} & & \Delta \mathrm{T}_{\mathrm{f}} & =\mathrm{imK}_{\mathrm{f}} \\ \therefore \quad & 0.66 & =\mathrm{i} \times 0.2 \times 1.84 \\ \therefore \quad & \mathrm{i} & =\frac{0.66 \mathrm{~K}}{0.2 \mathrm{~mol} \mathrm{~kg}^{-1} \times 1.84 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}} \\ & & =1.793 \approx 1.79\end{array}$

Asked in: MHT CET 2024 (11 May Shift 1)

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