Answer to Question #294927 in Physical Chemistry for Jen

Question

One component of an ideal binary solution has a pure component vapor pressure equal to one-fourth the total pressure of the vapor mixture. The component constitutes 20 mole % of liquid phase. What is its mole fraction in the vapor phase?

Answer 1

Using Raoult's law and Dalton law

$x_i=\frac{y_i\>p_{TOTAL}}{p_i^*}$

Where $x_i=$ Mole fraction of $i$ component in solution

$y_i=$ Mole fraction of component $i$ in gas phase

$p_{TOTAL}=$ Total vapor pressure

$p_i^*=$ Equilibrium vapor pressure of the pure component $i$

$\frac{20}{100}=\frac{y_i\>p_{TOTAL}}{\frac{1}{4}\>p_{TOTAL}}$

$y_i=\frac{1}{4}×\frac{1}{5}$

$=\frac{1}{20}$