Two solutions containing 0.75 g of urea (molecular weight 60) and 1.5 g of compound A in 100 g water, freeze at the same temperature. The molecular weight of A is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 120
The depression of freezing point of a dilute solution is proportional to its molality:
\( \displaystyle \Delta T_f=K_f\,m \)
Both solutions are made in water (same Kf) and freeze at the same temperature (same ΔTf). So they have the same molality. Both use 100 g of water, so they contain the same number of moles of solute (urea and A are taken as non-electrolytes).
Moles of urea:
\( \displaystyle n_{\text{urea}}=\frac{0.75\,\mathrm{g}}{60\,\mathrm{g\,mol^{-1}}}=0.0125\,\mathrm{mol} \)
Compound A must also be 0.0125 mol:
\( \displaystyle M_A=\frac{1.5\,\mathrm{g}}{0.0125\,\mathrm{mol}} \)
\( \displaystyle M_A=120\,\mathrm{g\,mol^{-1}} \)
The molecular weight of A is 120.
Shortcut: equal moles in equal masses of solvent means mass is proportional to molar mass. A has twice the mass of urea (1.5 g against 0.75 g), so its molar mass is twice 60, that is 120.