The solution containing $3 \mathrm{~g}$ urea (molar mass 60 ) per $\mathrm{dm}^3$ of water and another…
The solution containing $3 \mathrm{~g}$ urea (molar mass 60 ) per $\mathrm{dm}^3$ of water and another solution containing $4.5 \mathrm{~g}$ of solute A per $\mathrm{dm}^3$ boils at same temperature, then what is molar mass of A?
$54 \mathrm{~g} \mathrm{~mol}^{-1}$
$180 \mathrm{~g} \mathrm{~mol}^{-1}$
$120 \mathrm{~g} \mathrm{~mol}^{-1}$
$90 \mathrm{~g} \mathrm{~mol}^{-1}$
Solution
$\Delta \mathrm{T}_{\mathrm{b}}=\mathrm{K}_{\mathrm{b}} \cdot \mathrm{m}$
$\text { molality }(\mathrm{m})=\frac{\text { moles of solute }}{\text { mass of water }(\mathrm{kg})}$
1L $\mathrm{H}_2 \mathrm{O}=1 \mathrm{dm}^3 \mathrm{H}_2 \mathrm{O}=1 \mathrm{~kg} \mathrm{H}_2 \mathrm{O}$
Density of water $=1 \mathrm{~kg} / \mathrm{L}$
Boiling points are same for two solutions,
$\begin{aligned}
& \Delta \mathrm{T}_{\mathrm{b}_1}=\Delta \mathrm{T}_{\mathrm{b}_2} \\
& \mathrm{~m}_1=\mathrm{m}_2
\end{aligned}$
$\begin{aligned}
& \frac{3 / 60}{1}=\frac{4.5 / \mathrm{M}}{1} \\
& \mathrm{M}=\frac{60 \times 4.5}{3} \\
& =90 \mathrm{~g} / \mathrm{mol}
\end{aligned}$