Solutions and Colligative Properties - Result Question 22
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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Answer:
Correct Answer: 21. $(746.32$ $ mm)$
Solution:
$ \underset{1-\alpha}{\mathrm{Ca}(\mathrm{NO}_3)_2 }\rightleftharpoons \underset{ \alpha }{\mathrm{Ca}^{2+}}+ \underset{2 \alpha}{2 \mathrm{NO}_3^{-}} $
$ i=1+2 \alpha \text { where, } \alpha=0.7 $
$ \Rightarrow \quad i=1+2 \times 0.7=2.4 $
$ \Rightarrow \quad \text { Mole fraction of solvent }=\dfrac{n_1}{n_1+i n_2} $
$ = \quad\dfrac{\left(\dfrac{100}{18}\right)}{\left(\dfrac{100}{18}\right)+2.4 \times \dfrac{7}{164}}=0.982 $
$ \Rightarrow \quad p=p_0 \chi_1=760 \times 0.982 $
(VP of $\mathrm{H}_2 \mathrm{O}$ at $100^{\circ} \mathrm{C}=760 $ $\mathrm{mm}$ of Hg )
$ = \quad746.32 $ $\mathrm{mm} $
BETA
