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), $K_b=0.5Kkgmo{l}^{-1}$;
Boiling point of pure water as $100^{\circ }C$.)
The value of $|y|$ is ______.

Answer 1

Answer: 2.5

Let solution ' $B$ ' is prepared by mixing $1L$ ( $=1000g$ ) of solution '$A$' with $1L$ (= $1000g$ ) of solution of $BaC{l}_2$.

So, molality of new solution $=\left(\frac{i_1\times m_1+i_2\times m_2}{2}\right)$
$=\left(\frac{3\times 0.05+3\times 0.05}{2}\right)$
$=0.15$
Now, Elevation of boiling point of solution ' $B$ ' be $\left(\Delta T_b{}^1\right)$
$\Delta T_b^1=0.15\times k_b$
$=0.15\times \frac{1}{2}$
$=0.075$
Now, $T_b{}^1=100.075{}^{\circ }C$
So, difference of boiling point of ' $A$ ' and ' $B$ '
$=100.10-100.075=0.025=y\times 10^{-2}$ (given)
So, $y=2.5$