Solutions and Colligative Properties - Result Question 50
####21. The degree of dissociation of $Ca\left(NO _3\right) _2$ in a dilute aqueous solution, containing $7.0 g$ of the salt per $100 g$ of water at $100^{\circ} C$ is $70 %$. If the vapour-pressure of water at $100^{\circ} C$ is $760 mm$, calculate the vapour pressure of the solution.
$(1991,4 M)$
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Solution:
- $\begin{aligned} Ca\left(NO _3\right) _2 \ 1-\alpha\end{aligned} \rightleftharpoons \underset{\alpha}{Ca^{2+}+\underset{2 \alpha}{2 NO _3^{-}}}$
$$ \begin{array}{rlrl} & & i & =1+2 \alpha \text { where, } \alpha=0.7 \ \Rightarrow & i & =1+2 \times 0.7=2.4 \end{array} $$
$\Rightarrow$ Mole fraction of solvent $=\frac{n _1}{n _1+i n _2}$
$$ \begin{aligned} & =\frac{\left(\frac{100}{18}\right)}{\left(\frac{100}{18}\right)+2.4 \times \frac{7}{164}}=0.982 \ \Rightarrow \quad p & =p _0 \chi _1=760 \times 0.982 \ & \left.=746.32 mm \text { of } H _2 O \text { at } 100^{\circ} C=760 mm \text { of } Hg\right) \end{aligned} $$
