Solutions and Colligative Properties 1 Question 21
20. What weight of the non-volatile solute urea $\left(\mathrm{NH}{2}-\mathrm{CO}-\mathrm{NH}{2}\right)$ needs to be dissolved in $100 \mathrm{~g}$ of water, in order to decrease the vapour pressure of water by $25 %$ ? What will be the molality of the solution?
$(1993,3 \mathrm{M})$
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Solution:
- Vapour pressure of solution $=0.75 \times \mathrm{VP}$ of water
$\Rightarrow \quad 75=100 \chi_{1}: \chi_{1}=$ mole fraction of solute
$\Rightarrow \quad \chi_{1}=\frac{3}{4}$ and $\chi_{2}=1-\chi_{1}=\frac{1}{4}$
$\Rightarrow \quad \frac{\chi_{2}}{\chi_{1}}=\frac{n_{2}}{n_{1}}=\frac{1}{3}$
$\Rightarrow \quad n_{2}=\frac{n_{1}}{3}=\frac{100}{18 \times 3}=1.85$
$\Rightarrow$ Weight of urea $=1.85 \times 60=111 \mathrm{~g}$
Molality $=\frac{n_{2}}{n_{1}} \times \frac{1000}{M_{1}}$
$$ =\frac{1}{3} \times \frac{1000}{18}=18.5 $$
