Solutions and Colligative Properties - Result Question 21
####20. What weight of the non-volatile solute urea $\left(NH _2-CO-NH _2\right)$ needs to be dissolved in $100 g$ of water, in order to decrease the vapour pressure of water by $25 %$ ? What will be the molality of the solution?
$(1993,3 M)$
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Solution:
- Vapour pressure of solution $=0.75 \times VP$ 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 $=1.85 \times 60=111 g$
Molality $=\frac{n _2}{n _1} \times \frac{1000}{M _1}$
$$ =\frac{1}{3} \times \frac{1000}{18}=18.5 $$
