Question

Urea $\left(\right.NH_{2}-CO-NH_{2}\left.\right)$ needs to be dissolved in 100g of water, in order to decrease the vapour pressure of water by 25%. What will be the molality of the solution?

• A. 18.52 m
• B. 62.45 m
• C. 28.52 m
• D. 35.64 m

Answer 1

Answer: (A)

$\frac{\text{p}_{\text{0}} - \text{p}_{\text{S}}}{\text{p}^{\text{0}}} \, \text{=} \, \text{x}_{\text{Solute}}$

$\text{=} \frac{\frac{\text{W}_{\text{Solute}}}{\text{M}_{\text{Solute}}}}{\frac{\text{W}_{\text{Solute}}}{\text{M}_{\text{Solute}}} \text{+} \frac{\text{W}_{\text{Solvent}}}{\text{M}_{\text{Solvent}}}}$

$\frac{P^{0} - P_{S}}{P_{0}}=\frac{w_{A}}{m_{A}}\times \frac{m_{B}}{W_{B}}$ (A stands for solute and B for solvent)

$\frac{x - x \times \frac{75}{100}}{x \times \frac{75}{100}}=\frac{w}{60}\times \frac{18}{100}$

[Let the vapour pressure of pure water, $P^{0}=x$ ]

$\frac{0.25 x}{0.75 x}=\frac{w}{60}\times \frac{18}{100}$

$\therefore w=111.118$

$\text{Molality} = \frac{111.11}{60} \times \frac{1000}{100} = 18.52$