Discussion
Consider an ideal solution of two liquids A and B. If partial vapour pressures of both liquids are same, then total pressure of the solution is :
Answer: B
The total pressure is 2PA°PB°/(PA° + PB°).
By Raoult's law, pA = xAPA° and pB = xBPB°. Setting them equal, with xB = 1 − xA:
\[ \begin{aligned} x_{A}P_{A}^{o} &= (1-x_{A})P_{B}^{o} \\ x_{A} &= \frac{P_{B}^{o}}{P_{A}^{o}+P_{B}^{o}} \\ P &= 2x_{A}P_{A}^{o} = \frac{2P_{A}^{o}P_{B}^{o}}{P_{A}^{o}+P_{B}^{o}} \end{aligned} \]
The first option is the partial pressure of one component, half the total. The last two are ratios of pressures, dimensionless numbers, so they cannot be a pressure at all.
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