What is the value of $\mathrm{K}_{\mathrm{f}}$ if $30 \mathrm{~g}$ urea (molar mass 60 ) dissolved in $0.5…

What is the value of $\mathrm{K}_{\mathrm{f}}$ if $30 \mathrm{~g}$ urea (molar mass 60 ) dissolved in $0.5 \mathrm{dm}^{3}$ of water decreases freezing point by $0 \cdot 15^{\circ} \mathrm{C}$ ?
  1. $0 \cdot 15 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
  2. $0.030 \mathrm{Kkg} \mathrm{mol}^{-1}$
  3. $0.30 \mathrm{Kkg} \mathrm{mol}^{-1}$
  4. $0.015 \mathrm{Kkg} \mathrm{mol}^{-1}$

Solution

Mass of water $=0.5 \mathrm{dm}^{3}=0.5 \mathrm{~kg}$ Moles of urea $=\frac{30}{60}=0.5$ mole Molality of urea $=\frac{0.5 \mathrm{~mol}}{0.5 \mathrm{~kg}}=1 \mathrm{~mol} / \mathrm{kg}$ $\Delta \mathrm{T}_{\mathrm{f}}=\mathrm{K}_{\mathrm{f}} \times \mathrm{m}$ $\mathrm{K}_{\mathrm{f}}=\frac{\Delta \mathrm{T}_{\mathrm{f}}}{\mathrm{m}}=\frac{0.15 \mathrm{~K}}{1 \mathrm{~mol} / \mathrm{kg}}=0.15 \mathrm{Kmol}^{-1} \mathrm{~kg}$

Asked in: MHT CET 2020 (14 Oct Shift 2)

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