Question

The degree of dissociation of $Ca{\left(N{O}_3\right)}_2$ in a dilute aqueous solution, containing 7.0 g of the salt per 100 g of water at ${100}^{o}C$ is 70%. If the vapour pressure of water at ${100}^{o}C$ is 760 mm, calculate the vapour pressure of the solution. Please report your answer as [vapour pressure/100]. ([] is greatest integer function)

Answer 1

$Ca{\left(N{O}_3\right)}_2⟶{Ca}^{2+}+2N{O}_3^{\ominus }$
Initial 1 mol 0 0
Final 1-$\alpha$ $\alpha$ $\alpha$
Total moles at equilibrium =$1-\alpha +\alpha +2\alpha =1+2\alpha$
$\alpha$= 70%=0.7 (given)
$i=\frac{1+2\alpha }{1}=1+2\times 0.7=2.4$
$M{W}_{(Ca{\left(N{O}_3\right)}_2}=164g{mol}^{-1}$
$M{W}_{\left(H_{2}O\right)}=18g{mol}^{-1}$
Use the formula,
$\frac{P^o-P_S}{P^o}=i\frac{n_2}{n_1}$
$\frac{760-P_S}{760}=2.4\times \frac{7\times 18}{164\times 100}$
$\Rightarrow P_S=746$ mm Hg.