Question

The boiling point of water in a $0.1$ molal silver nitrate solution (solution $A$ ) is $x ^{\circ} C$. To this solution $A$, an equal volume of $0.1$ molal aqueous barium chloride solution is added to make a new solution $B$. The difference in the boiling points of water in the two solutions $A$ and $B$ is $y \times 10^{-2}{ }^{\circ} C$.
(Assume: Densities of the solutions $A$ and $B$ are the same as that of water and the soluble salts dissociate completely.
Use: Molal elevation constant (Ebullioscopic Constant), $K _{ b }=0.5 \,K \,kg\, mol ^{-1}$;
Boiling point of pure water as $100^{\circ} C$.)
The value of $x$ is ______$^{\circ}C$.

Answer 1

$0.1$ molal $AgNO _{3}$ (aq) solution
$ AgNO _{3} \longrightarrow Ag ^{+}( aq )+ NO _{3}{ }^{-}( aq )$
$ i =1+(2-1) \times 1=2(\alpha=1,$ given )
$\Delta T _{ b }= i \times k _{ b } \times m $
$\Delta T _{ b }=2 \times 0.5 \times 0.1=0.1$
So, boiling point of solution ' $A$ ' is $=100.10^{\circ} C = x$