Solutions and Colligative Properties - Result Question 45
####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
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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 } & \
