A solution of \(6 \mathrm{~g}\) of solute in \(100 \mathrm{~g}\) of water boils at \(100.52^{\circ} \mathrm{C}\). The molal elevation constant of water is \(0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\). What is molar mass of solute?

\(\mathrm{W}_2=6 \mathrm{~g}, \mathrm{~W}_1=100 \mathrm{~g}, \mathrm{~K}_{\mathrm{b}}=0.52 \mathrm{Kg} \mathrm{mol}^{-1},\) \(\mathrm{~T}_{\mathrm{b}} 100.52^{\circ} \mathrm{C} \)
\( \therefore \Delta \mathrm{T}_{\mathrm{b}}=\mathrm{T}_{\mathrm{b}}-\mathrm{T}_{\mathrm{b}}^{\circ}=(100.52+273)\) \(-~(100+273) \)
\( =0.52 \mathrm{k}\)
Now, \(\mathrm{M}_2=\frac{1000 \cdot \mathrm{K}_{\mathrm{b}} \cdot \mathrm{W}_2}{\Delta \mathrm{T}_{\mathrm{b}} \cdot \mathrm{W}_1}=\)\(\frac{1000 \mathrm{~g} \mathrm{~kg}^{-1} \times 0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \times 6 \mathrm{~g}}{0.52 \mathrm{~K} \times 100 \mathrm{~g}}\)
\(
\therefore \mathrm{M}_2=60 \mathrm{~g} \mathrm{~mol}^{-1}
\)