Question

The degree of dissociation of $Ca(N{O}_3{)}_2$ in a dilute aqueous solution containing $16.4\text{g}$of the salt per $358.2\text{g}$ of water at ${100}^{\circ }C$ is $0.7$. If the vapour pressure of water at $100{}^{o}C$ is $760\text{mm Hg}$, calculate the vapour pressure of the solution in $\text{mm Hg}$

Answer 1

The molar mass of calcium nitrate$\left(Ca\right(N{O}_3{)}_2)$ is $164\text{g/mol}$.
$16.4\text{g}$ of calcium nitrate =$\frac{16.4}{164}=0.1$ moles.
The molar mass of water is $18\text{g/mol}$.
$358.2\text{g}$ of water $=\frac{358.2}{18}=19.9$ moles
The mole fraction of calcium nitrate
$\chi =\frac{0.1}{0.1+19.9}=0.005$
The degree of dissociation $\alpha =0.7$
The van't Hoff factor $i=[1+(n^{\prime }-1\left)\alpha \right]$
$\Rightarrow i=[1+(3-1)\times 0.7]$
$\Rightarrow i=2.4$

The relative lowering of the vapour pressure $\frac{P^{\circ }-P}{P^{\circ }}=iX$
$\Rightarrow \frac{760-P}{760}=2.4\times 0.005=0.012$
$\Rightarrow 760-P=9.12$
$\Rightarrow P=750.88\text{mm Hg}$