A solution contains 50 g of a non-electrolytic solute per 100g of water at 25°C. The vapor pressure of water is 23.5 mmHg at this temperature. The molar mass of the solute is \( 250\, g\, mol^{-1} \). The vapor pressure of the solution at 25°C will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 22.67 mmHg
By Raoult’s law, a non-volatile solute lowers the vapour pressure of the solvent, and the relative lowering equals the mole fraction of the solute:
\( \displaystyle \frac{p_1^{\circ} - p_1}{p_1^{\circ}} = x_2 \Rightarrow p_1 = p_1^{\circ}\,(1 - x_2) \)
The amounts of solute and water:
\( \displaystyle n_2 = \frac{50}{250} = 0.20\ \mathrm{mol} \qquad n_1 = \frac{100}{18} = 5.556\ \mathrm{mol} \)
\( \displaystyle x_2 = \frac{0.20}{5.556 + 0.20} = \frac{0.20}{5.756} = 0.0347 \)
\( \displaystyle p_1 = 23.5 \times (1 - 0.0347) = 23.5 \times 0.9653 \approx 22.68\ \mathrm{mmHg} \)
This matches 22.67 mmHg within rounding.