Question

The vapour pressure of solution containing $6.69g$ of $Mg(N{O}_3{)}_2$ dissolved in $100g$ of water is $747torr$ at $373K$. Calculate the degree of dissociation of the salt in the solution.

• A. $0.38$
• B. $0.46$
• C. $0.56$
• D. $0.26$

Answer 1

Answer: (C)

$0.56$

The molar mass of magnesium nitrate is $148.3$ g/mol.

$6.69$ g of magnesium nitrate $=\frac{6.69}{148.3}=0.045$ moles.

The molar mass of water is 18 g/mol.

100 g of water $=\frac{100}{18}=5.56$ moles

The mole fraction of magnesium nitrate $=X=\frac{0.045}{0.045+5.56}=0.008028$

The relative lowering in the freezing point $\frac{P^o-P}{P^o}=iX$

$\frac{760-747}{760}=i\times 0.008028$

$i=2.13$

The degree of dissociation $\alpha =\frac{i-1}{n^{\prime }-1}$

$\alpha =\frac{2.13-1}{3-1}=0.565$