Liquid A and B form an ideal solution. The vapour pressure of pure liquids A and B are 350 and 750 mm Hg…

Liquid A and B form an ideal solution. The vapour pressure of pure liquids A and B are 350 and 750 mm Hg respectively at the same temperature. If $\mathrm{x}_{\mathrm{A}}$ and $x_B$ are the mole fraction of $A$ and $B$ in solution while $y_A$ and $y_B$ are the mole fraction of A and B in vapour phase then :
  1. $\frac{\mathrm{x}_{\mathrm{A}}}{\mathrm{x}_{\mathrm{B}}} \lt \frac{\mathrm{y}_{\mathrm{A}}}{\mathrm{y}_{\mathrm{B}}}$
  2. $\frac{\mathrm{x}_{\mathrm{A}}}{\mathrm{x}_{\mathrm{B}}}=\frac{\mathrm{y}_{\mathrm{A}}}{\mathrm{y}_{\mathrm{B}}}$
  3. $\frac{\mathrm{x}_{\mathrm{A}}}{\mathrm{x}_{\mathrm{B}}} \gt \frac{\mathrm{y}_{\mathrm{A}}}{\mathrm{y}_{\mathrm{B}}}$
  4. $\left(\mathrm{x}_{\mathrm{A}}-\mathrm{y}_{\mathrm{A}}\right) \lt \left(\mathrm{x}_{\mathrm{B}}-\mathrm{y}_{\mathrm{B}}\right)$

Solution

$\begin{aligned} & \mathrm{P}_{\mathrm{A}}^{\mathrm{o}} \lt \mathrm{P}_{\mathrm{B}}^{\mathrm{o}} \\ & \frac{\mathrm{P}_{\mathrm{A}}^o}{\mathrm{P}_{\mathrm{B}}^o} \lt 1 \\ & \frac{\mathrm{y}_{\mathrm{A}}}{\mathrm{y}_{\mathrm{B}}}=\frac{\mathrm{P}_{\mathrm{A}}^o}{\mathrm{P}_{\mathrm{B}}^o} \frac{\mathrm{x}_{\mathrm{A}}}{\mathrm{x}_{\mathrm{B}}} \\ & \frac{\mathrm{y}_{\mathrm{A}}}{\mathrm{y}_{\mathrm{B}}} \\ & \frac{\mathrm{x}_{\mathrm{A}}}{\mathrm{x}_{\mathrm{B}}}\end{aligned}$

Asked in: JEE Main 2025 (07 Apr Shift 2)

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