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 pres sines 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)

$\frac{\rho^{\circ}_{A}\chi_{2}}{\chi_{1}}$

Answer 2

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 $\chi_{1}\times p_{A}^{\circ} \left(as \chi_{A}=\chi_{1}\right)$
$\therefore \chi_{1}=\frac{\chi_{2}p_{A}^{\circ}}{p_{total}}$
or $p_{total}=\frac{p^{\circ}_{A}\chi_{2}}{\chi_{1}}$