Question

Let 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 two constituents and $P_A^{\circ }$ and $P_B^{\circ }$ are the vapour pressures in pure state. Which of the following relations are true?

• A. $P_A=P_A^{\circ }\times \frac{{\eta }_A}{{\eta }_B}{P}_B=P_B^{\circ }\times \frac{{\eta }_B}{{\eta }_A}$
• B. $P_A^{\circ }=P_A\frac{{\eta }_A}{{\eta }_A+{\eta }_B}{P}_B^{\circ }=P_B\frac{{\eta }_B}{{\eta }_A+{\eta }_B}$
• C. $P_A=P_A^{\circ }\times \frac{{\eta }_A}{{\eta }_A+{\eta }_B}{P}_B=P_B^{\circ }\times \frac{{\eta }_B}{{\eta }_A+{\eta }_B}$
• D. $P_A^{\circ }=P_A.n_B{P}_B^{\circ }=P_B.n_B$

Answer 1

The correct option is C $P_A=P_A^{\circ }\times \frac{{\eta }_A}{{\eta }_A+{\eta }_B}{P}_B=P_B^{\circ }\times \frac{{\eta }_B}{{\eta }_A+{\eta }_B}$

If two volatile liquids of vapor pressures $P_A^{\circ },P_B^{\circ }$ are mixed together to form a solution. The partial pressure of one component is equal to Vapour pressure of pure component multiplied by mole fraction.
So putting this definition in the equations
$P_A=P_A^{\circ }\times \frac{{\eta }_A}{{\eta }_A+{\eta }_B}{P}_B=P_B^{\circ }\times \frac{{\eta }_B}{{\eta }_A+{\eta }_B}$