The solution containing $6 \mathrm{~g}$ urea (molar mass 60 ) per $\mathrm{dm}^3$ of water and another…

The solution containing $6 \mathrm{~g}$ urea (molar mass 60 ) per $\mathrm{dm}^3$ of water and another solution containing $9 \mathrm{~g}$ of solute $\mathrm{A}$ per $\mathrm{dm}^3$ water freezes at same temperature. What is molar mass of A?
  1. 90
  2. 180
  3. 54
  4. 120

Solution

$\begin{aligned} & \left(\Delta \mathrm{T}_{\mathrm{i}}\right)_1=\left(\Delta \mathrm{T}_{\mathrm{f}}\right)_2 \\ & \mathrm{~m}_1=\mathrm{m}_2 \\ & \mathrm{~m}=\text { molality, } 1 \mathrm{dm}^3=1 \mathrm{~L}=1000 \mathrm{ml} \mathrm{H}_2 \mathrm{O} \\ & 1000 \mathrm{ml} \mathrm{H}_2 \mathrm{O}=1000 \mathrm{~g} \mathrm{H}_2 \mathrm{O} \\ & \mathrm{m}=\frac{\mathrm{mol} / \mathrm{M}}{\text { Mass of } \mathrm{H}_2 \mathrm{O}} \\ & \frac{6 / 60}{1}=\frac{9 / \mathrm{M}_{\mathrm{A}}}{1} \\ & \mathrm{M}_{\mathrm{A}}=\frac{60 \times 9}{6}=90\end{aligned}$

Asked in: MHT CET 2021 (24 Sep Shift 1)

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