Solutions and Colligative Properties 1 Question 22
21. The degree of dissociation of $\mathrm{Ca}\left(\mathrm{NO}{3}\right){2}$ in a dilute aqueous solution, containing $7.0 \mathrm{~g}$ of the salt per $100 \mathrm{~g}$ of water at $100^{\circ} \mathrm{C}$ is $70 %$. If the vapour-pressure of water at $100^{\circ} \mathrm{C}$ is $760 \mathrm{~mm}$, calculate the vapour pressure of the solution.
$(1991,4 \mathrm{M})$
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Solution:
- $\begin{aligned} \mathrm{Ca}\left(\mathrm{NO}{3}\right){2} \ 1-\alpha\end{aligned} \rightleftharpoons \underset{\alpha}{\mathrm{Ca}^{2+}+\underset{2 \alpha}{2 \mathrm{NO}_{3}^{-}}}$
$$ \begin{array}{rlrl} & & i & =1+2 \alpha \text { where, } \alpha=0.7 \ \Rightarrow & i & =1+2 \times 0.7=2.4 \end{array} $$
$\Rightarrow$ Mole fraction of solvent $=\frac{n_{1}}{n_{1}+i n_{2}}$
$$ \begin{aligned} & =\frac{\left(\frac{100}{18}\right)}{\left(\frac{100}{18}\right)+2.4 \times \frac{7}{164}}=0.982 \ \Rightarrow \quad p & =p_{0} \chi_{1}=760 \times 0.982 \ & \left.=746.32 \mathrm{~mm} \text { of } \mathrm{H}_{2} \mathrm{O} \text { at } 100^{\circ} \mathrm{C}=760 \mathrm{~mm} \text { of } \mathrm{Hg}\right) \end{aligned} $$
