Question

Mole fraction of component $A$ in the vapour phase is $X_1$ and mole fraction of component $A$ in liquid mixture is $X_2(P_A^o=$ vapour pressure of pure $A;P_B^o=$ vapour pressure of pure B) then total vapour pressure of the liquid mixture is:

• A. $\frac{P_A^o{X}_2}{X_1}$
• B. $\frac{P_A^o{X}_1}{X_2}$
• C. $\frac{P_B^o{X}_1}{X_2}$
• D.
  $\frac{P_B^o{X}_2}{X_1}$

Answer 1

The correct option is A $\frac{P_A^o{X}_2}{X_1}$

According to Dalton's law
$P_A=P.X_1$
Where, $P=\text{Total vapour pressure}$
Raoult's law state that the solvent's partial vapour pressure is a solution is equal to the vapour pressure of the pure solvent multiplied by its mole fraction in the solution.
$P_A=X_2{P}_A^o.....\left(2\right)$
By equating equation (1) and (2)
$P=\frac{P_A^o.X_2}{X_1}$
Therefore the correct answer is (A).