Question

If $ \chi_{1} $ and $ \chi_{2} $ represent the mole fractions of a component $ A $ in the vapour phase and liquid mixture respectively, and $ p^{\circ}_{A} $ and $ p^{\circ}_{B} $
represent vapour pressures of pure $A$ and pure $B$, then total vapour pressure of liquid mixture is

• A. $ \frac{\rho^{\circ}_{A}\chi_{1}}{\chi_{2}} $
• B. $ \frac{\rho^{\circ}_{A}\chi_{2}}{\chi_{1}} $
• C. $ \frac{\rho^{\circ}_{B}\chi_{1}}{\chi_{2}} $
• D. $ \frac{\rho^{\circ}_{B}\chi_{2}}{\chi_{1}} $

Answer 1

Answer: (B)

Mole fraction in the vapour phase $\left(\chi_{1}\right)=\frac{p_{A}}{p_{total}}$
But, $P_{A}\times\chi_{A}\times p_{A}^{\circ}=\chi_{2}p_{A}^{\circ}$
or $ \chi_{1}\times p_{A}^{\circ} = \chi_2 p^{\circ}_{A} \left(as \chi_{A}=\chi_{1}\right)$
$\therefore \chi_{1}=\frac{\chi_{2}p_{A}^{\circ}}{p_{total}}$
or $p_{total}=\frac{p^{\circ}_{A}\chi_{2}}{\chi_{1}}$