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? $\left(P_{A} ^\circ = 400 torr , P_{B} ^\circ = 100 torr\right)$

Answer 1

Let the final composition, liquid ( $10$ mole) $A=x$ mole, $B=\left(\right.10-x\left.\right)$ 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, $P=X_{A}P_{A}^{o}+X_{B}P_{B}^{o}$
$=\frac{x}{10}\times 400+\frac{10 - x}{10}\times 100$
$=200.00$