Two volatile liquids \( A \) and \( B \) form an ideal solution. Consider a \( 5 \, \text{molal} \) solution of \( B \) in \( A \) inside a closed container having a total vapour pressure of \( 100 \, \text{mm Hg} \) at \( 300 \, \text{K} \). The vapour pressure of pure \( A \) at \( 300 \, \text{K} \) is \( 105 \, \text{mm Hg} \). Assume that \( A \) and \( B \) behave as ideal gases in the vapour phase.
Given:
The gas constant \( R = 0.08 \, \text{L atm K}^{-1} \text{ mol}^{-1} \)
Molar mass of \( A \) is \( 50 \, \text{g mol}^{-1} \)
Molar mass of \( B \) is \( 57 \, \text{g mol}^{-1} \)
Density of liquid \( B \) at \( 300 \, \text{K} \) is \( 0.5 \, \text{g/mL} \)
\( 1 \, \text{atm} = 760 \, \text{mm Hg} \)
The mole fraction of \( B \) in vapour phase which is in equilibrium with this solution is ________.
