Liquids A and B form ideal solution over the entire range of comp… - Vidyadip

Question

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 . . . . . that the vapour pressure of pure liquid $A$ is $20$ Torr at temperature $T$ )

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Answer

The vapour pressure of pure liquid $A , P _{ A }=20$ torr

The vapour pressure of pure liquid $B , P _{ B }=$ ?

$P _{\text {Total }} = P _{ A }^{\prime} X _{ A }+ P _{ B }^{-} X _{ B }$

$45 =20\left(\frac{1}{2}\right)+ P _{ B }^{(}\left(\frac{1}{2}\right)$

$90 =20+ P _{ B }^{-} \quad \Rightarrow P _{ B }^{-}=70 \text { torr }$

For new solution, $P _{\text {Total }}=22.5= P _{ A }^0 X _{ A }+ P _{ B }^{ C } X _{ B }$

$22.5 =20 x +70(1- x )$

$x =0.95= X _{ A }$

$X _{ B } =1- x =0.05$

$\therefore \frac{ X _{ A }}{ X _{ B }}= \frac{0.95}{0.05}=19.00$

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