Question

Let mixture be prepared by mixing $n_A$ of liquid A and $n_B$ moles of liquid B. Let $P_A$ and $P_B$ be the partial pressures of two constituents and $P_A^{\circ }$ and $P_B^{\circ }$ are the vapour pressures in pure state. 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. $P_T=P_A^{\circ }.\frac{{\eta }_A}{{\eta }_A+{\eta }_B}+P_B^{\circ }.\frac{{\eta }_B}{{\eta }_A+{\eta }_B}$

Answer 1

Answer: (A), (C)

The correct options are
A $P_T=P_A+P_B$
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 Raoults law
$P_A=P_A^{\circ }\times \frac{{\eta }_A}{{\eta }_A+{\eta }_B}{P}_B=P_B^{\circ }\times \frac{{\eta }_B}{{\eta }_A+{\eta }_B}$
And total pressure is nothing but the sum of partial pressure of the components Which is
$P_T=P_A+P_B=P_A^{\circ }\times \frac{{\eta }_A}{{\eta }_A+{\eta }_B}{P}_B^{\circ }\times \frac{{\eta }_B}{{\eta }_A+{\eta }_B}$