Question

Liquids A and B form ideal solution for all compositions of A and B at ${25}^{\circ }C$. Two such solutions with $0.25$ and $0.50$ mole fractions of A have the total vapor pressures of $0.3$ and $0.4$ $bar$, respectively. What is the vapor pressure of pure liquid B in $bar$?

Answer 1

When, $P_{Total}=0.3$, where $x_A=0.25$

So, $x_B=0.75$

$0.3=P_A^{\circ }{x}_A+P_B^{\circ }{x}_B$
$0.3=0.25P_A^{\circ }++0.75P_B^{\circ }........\left(i\right)$

When, $P_{Total}=0.4$, where $x_A=0.50$

So, $x_B=0.50$

$0.4=P_A^{\circ }{x}_A+P_B^{\circ }{x}_B$
$0.4=0.5P_A^{\circ }+0.5P_B^{\circ }........\left(ii\right)$
From $\text{eq.(i)}\text{and}\text{eq.(ii)}$, we get

$P_B^{\circ }=0.2bar$