The vapour pressure of a pure liquid A is 70 torr at 27 °C. It forms an ideal solution with another liquid B. The mole fraction of B in the solution is 0.2 and the total vapour pressure of the solution is 84 torr at 27 °C. What is the vapour pressure of pure liquid B at 27 °C?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 140 torr
For an ideal solution of two volatile liquids, Raoult’s law holds for each component, and the total vapour pressure is the sum of the partial pressures. With xB = 0.2, xA = 1 − 0.2 = 0.8:
\( \displaystyle p_{\text{total}}=p_A^{\circ}x_A+p_B^{\circ}x_B \)
\( \displaystyle 84=70\times0.8+p_B^{\circ}\times0.2=56+0.2\,p_B^{\circ} \)
\( \displaystyle p_B^{\circ}=\frac{84-56}{0.2}=\frac{28}{0.2}=140\,\mathrm{torr} \)