Solutions and Colligative Properties 1 Question 15
16. Liquids $A$ and $B$ form ideal solution over the entire range of composition. At temperature $T$, equimolar binary solution of liquids $A$ and $B$ has vapour pressure 45 torr. At the same temperature, a new solution of $A$ and $B$ having mole fractions $x_{A}$ and $x_{B}$, respectively, has vapour pressure of 22.5 torr. The value of $x_{A} / x_{B}$ in the new solution is
(Given that the vapour pressure of pure liquid $A$ is 20 Torr at temperature $T$ )
(2018 Adv. Paper-1)
True/False
Show Answer
Solution:
- Key Idea Use the formula
$$ p_{\text {Total }}=p_{A}^{\circ} \times \chi_{A}+p_{B}^{\circ} \times \chi_{B} $$
and for equimolar solutions $\chi_{A}=\chi_{B}=\frac{1}{2}$
Given, $p_{\text {Total }}=45$ torr for equimolar solution
$$ p_{A}^{\circ}=20 \text { torr } $$
So, $\quad 45=p_{A}^{\circ} \times \frac{1}{2}+p_{B}^{\circ} \times \frac{1}{2}=\frac{1}{2}\left(p_{A}^{\circ}+p_{B}^{\circ}\right)$
or $p_{A}^{\circ}+p_{B}^{\circ}=90$ torr
But we know $p_{A}^{\circ}=20$ torr
$$ \text { so, } \quad p_{B}^{\circ}=90-20=70 \text { torr } $$
Now, for the new solution from the same formula
Given,
$$ \begin{aligned} p_{\text {Total }}=22.5 \text { torr } & \
