JEE Main 2025 — Solutions Question with Solution

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.