Calculate van't Hoff factor of 0.15 M solution of electrolyte if it freezes at -0.5 K.…

Calculate van't Hoff factor of 0.15 M solution of electrolyte if it freezes at -0.5 K. $\left[\mathrm{K}_{\mathrm{f}}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right]$
  1. 1.12
  2. 1.25
  3. 1.45
  4. 1.79

Solution

$\begin{array}{ll} & \Delta \mathrm{T}_{\mathrm{f}}=\mathrm{T}_{\mathrm{f}}^0-\mathrm{T}_{\mathrm{f}}=0-(-0.5 \mathrm{~K})=0.5 \mathrm{~K} \\ & \Delta \mathrm{~T}_{\mathrm{f}}=\mathrm{i} \mathrm{K}_{\mathrm{f}} \mathrm{m} \\ \therefore \quad & \mathrm{i}=\frac{\Delta \mathrm{T}}{\mathrm{K}_{\mathrm{f}} \mathrm{m}}=\frac{0.5 \mathrm{~K}}{1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \times 0.15 \mathrm{~mol} \mathrm{~kg}^{-1}}=1.79\end{array}$

Asked in: MHT CET 2024 (16 May Shift 1)

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