The solution containing $18 \mathrm{~g} \mathrm{dm}^{-3}$ glucose (molar mass 180) in water and another…

The solution containing $18 \mathrm{~g} \mathrm{dm}^{-3}$ glucose (molar mass 180) in water and another containing $6 \mathrm{~g} \mathrm{dm}^{-3}$ of solute A in water boils at same temperature. What is molar mass of A ?
  1. $54 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $90 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $120 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $60 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

As boiling points of both the solutions are same, they must have same molality. $\begin{aligned} \therefore \quad & \mathrm{m}_{\text {glucose }}=\mathrm{m}_{\mathrm{A}} \\ & \frac{\mathrm{~W}_{\text {glucose }}}{\mathrm{M}_{\text {glucose }} \times \mathrm{W}_{\text {solvent }}}=\frac{\mathrm{W}_{\mathrm{A}}}{\mathrm{M}_{\mathrm{A}} \times \mathrm{W}_{\text {solvent }}} \\ & \frac{18}{180 \times \mathrm{W}_{\text {water }}}=\frac{6}{\mathrm{M}_{\mathrm{A}} \times \mathrm{W}_{\text {water }}} \end{aligned}$
Considering weight of water is same in both solutions, $\therefore \quad M_A=60 \mathrm{~g} \mathrm{~mol}^{-1}$

Asked in: MHT CET 2024 (11 May Shift 2)

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