Liquid A and B form an ideal solution. The vapor pressures of pure liquids A and B are 350 mm Hg and 750 mm Hg, respectively, at the same temperature. Here, $ x_A $ and $ x_B $ represent the mole fractions of A and B in the solution, and $ y_A $ and $ y_B $ are their mole fractions in the vapor phase.

Let’s begin by comparing the vapor pressures:

$ \mathrm{P}_{\mathrm{A}}^{\mathrm{o}} < \mathrm{P}_{\mathrm{B}}^{\mathrm{o}} $

$ \frac{\mathrm{P}_{\mathrm{A}}^{\mathrm{o}}}{\mathrm{P}_{\mathrm{B}}^{\mathrm{o}}} < 1 $

The relationship between the mole fractions in the vapor phase and the solution can be expressed as:

$ \frac{y_A}{y_B} = \frac{\mathrm{P}_{\mathrm{A}}^{\mathrm{o}}}{\mathrm{P}_{\mathrm{B}}^{\mathrm{o}}} \cdot \frac{x_A}{x_B} $

Since $\frac{\mathrm{P}_{\mathrm{A}}^{\mathrm{o}}}{\mathrm{P}_{\mathrm{B}}^{\mathrm{o}}} < 1$, it follows that:

$ \frac{\frac{y_A}{y_B}}{\frac{x_A}{x_B}} < 1 $

Which implies:

$ \frac{y_A}{y_B} < \frac{x_A}{x_B} $

This indicates that the mole fraction ratio of A to B in the vapor phase is less than that in the solution.