Question

Pressure over an ideal binary liquid solution containing $10$ moles of each of liquid $A$ and $B$ is gradually decreased isothermally. At what pressure (in torr), half of the total amount of liquid will get converted into vapour? $\left(P_A^{\circ }=400torr,P_B^{\circ }=100torr\right)$

Answer 1

Answer: 200

Let the final composition, liquid ( $10$ mole) $A=x$ mole, $B=(10-x)$ mole Vapour ( $10$ moles), $A=10-x$ mole; $B=x$ mole
Now, $\frac{Y_A}{Y_B}=\frac{X_A}{X_B}\frac{P_A^0}{P_B^o}\Rightarrow \frac{10-x}{x}=\frac{x}{10-x}\times \frac{400}{100}$
$x=\frac{10}{3}$
Now, $P=X_A{P}_A^o+X_B{P}_B^o$
$=\frac{x}{10}\times 400+\frac{10-x}{10}\times 100$
$=200.00$