Question

Let a mixture be prepared by mixing $n_A$ moles of liquid A and $n_B$ moles of liquid B. Let $P_A$ and $P_B$ be the partial pressures of the two constituents and $P_A^{\circ }$ and $P_B^{\circ }$ be the vapour pressures in their pure state respectively. P_T is the total pressure. Which of the following relations are true?

• A. $P_T=P_A+P_B$
• B. $P_T=P_A^{\circ }+P_B^{\circ }$
• C. $P_T=P_A^{\circ }.\frac{{\eta }_A}{{\eta }_A+{\eta }_B}+P_B^{\circ }.\frac{{\eta }_B}{{\eta }_A+{\eta }_B}$
• D. None of these

Answer 1

Answer: (A), (C)

$P_T=P_A^{\circ }.\frac{{\eta }_A}{{\eta }_A+{\eta }_B}+P_B^{\circ }.\frac{{\eta }_B}{{\eta }_A+{\eta }_B}$

According to Raoult's law,
$P_A=P_A^{\circ }\times \frac{{\eta }_A}{{\eta }_A+{\eta }_B}$
$P_B=P_B^{\circ }\times \frac{{\eta }_B}{{\eta }_A+{\eta }_B}$

The total pressure is nothing but the sum of the partial pressures of the components which is
$P_T=P_A+P_B=P_A^{\circ }\times \frac{{\eta }_A}{{\eta }_A+{\eta }_B}+P_B^{\circ }\times \frac{{\eta }_B}{{\eta }_A+{\eta }_B}$