When 5 g of a non-volatile solute is dissolved in 50 g of water, the freezing point of water is lowered by 1.2 K. The molal depression constant (Kf) of water is 1.85 K kg mol−1. The molar mass of the solute is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 154.2 g mol−1
For a dilute solution of a non-volatile non-electrolyte, \( \Delta T_f = K_f\,m \), with molality \( m=\frac{w_2\times 1000}{M_2\times w_1} \). Solving for the molar mass:
\( \displaystyle M_2=\frac{K_f\times w_2\times 1000}{\Delta T_f\times w_1} \)
\( \displaystyle M_2=\frac{1.85\ \mathrm{K\,kg\,mol^{-1}}\times 5\ \mathrm{g}\times 1000\ \mathrm{g\,kg^{-1}}}{1.2\ \mathrm{K}\times 50\ \mathrm{g}}=\frac{9250}{60}\ \mathrm{g\,mol^{-1}} \)
\( \displaystyle M_2=154.2\ \mathrm{g\,mol^{-1}} \)