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 ?

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,
\(\therefore \quad M_A=60 \mathrm{~g} \mathrm{~mol}^{-1}\)