Discussion Forum

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 )

Answer:

Explanation:

Use the formula

$p_{total}= p_A^0\times X_A +P_B^0\times X_{B}$

  and for equimolar solutions  $X_{A}=X_{B}=\frac{1}{2}$

Given , p_total =45 torr for equimolar solution 

        $p_A^0=20torr$

So,        $45= p_A^0\times \frac{1}{2}+p_B^0\times\frac{1}{2}=\frac{1}{2}(p_A^0+p_B^0)$

or     $ p_A^0+p_B^0=90torr$               .............(i)

      But we know $ p_A^0=20torr$

So  $ p_B^0$= 90-20=70 torr         (From Eq. (i))

  Now , for the new solution from the same formula

     p_total  = 22.5 torr

   22.5 = 20 X_A+70 (1-X_A)  [X_A + X_B=1]

    Or,         22.5 =70-50 X_A

   So,$X_{A}=\frac{70-22.5}{50}=0.95$

Thus, X_B =1-0.95 =0.05     (as X_A+ X_B =1)

Hence, the ratio

        $\frac{X_{A}}{X_{B}}=\frac{0.95}{0.05}=19$