Question

Urea $(N{H}_2-CO-N{H}_2)$ 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, $P^0=x$ ]

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

$\therefore w=111.118$

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