Chemistry Q55 – JEE-MAIN 2025

Liquid A and B form an ideal solution. The vapour pressures of pure liquids A and B are

350

and

750

mm Hg respectively at the same temperature. If

x_{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,

Clue 1 of 3: Ideal Solutions and Vapor Pressure

Recall the fundamental laws governing the vapor pressure of components in an ideal solution and their distribution between liquid and vapor phases.

🥷

Ninja Strategy•Volatility Comparison

Identify the more volatile component (higher pure vapor pressure) and deduce its relative enrichment in the vapor phase to determine the direction of the inequality between the mole fraction ratios.

🧠 Full Solution Path

Step 1: Apply Raoult's Law and Dalton's Law✦ Active

For an ideal solution, the partial vapor pressures of components A and B are given by Raoult's Law:

P_{A} = x_{A} P_{A}^{0}

P_{B} = x_{B} P_{B}^{0}

The mole fractions in the vapor phase are given by Dalton's Law of Partial Pressures:

y_{A} = \frac{P_{A}}{P_{t o t a l}}

y_{B} = \frac{P_{B}}{P_{t o t a l}}

Step 2: Derive the relationship between liquid and vapor mole fraction ratios○ Expand

Substitute Raoult's Law expressions for $P_{A}$ and $P_{B}$ into the Dalton's Law expressions for $y_{A}$ and $y_{B}$ :

y_{A} = \frac{x_{A} P_{A}^{0}}{P_{t o t a l}}

y_{B} = \frac{x_{B} P_{B}^{0}}{P_{t o t a l}}

Now, form the ratio $\frac{y_{A}}{y_{B}}$ :

\frac{y_{A}}{y_{B}} = \frac{\frac{x_{A} P_{A}^{0}}{P_{t o t a l}}}{\frac{x_{B} P_{B}^{0}}{P_{t o t a l}}} = \frac{x_{A} P_{A}^{0}}{x_{B} P_{B}^{0}} = \frac{x_{A}}{x_{B}} \cdot \frac{P_{A}^{0}}{P_{B}^{0}}

💡 Teacher's Secret Hint

Remember that $P_{t o t a l}$ cancels out when taking the ratio of vapor phase mole fractions.

Step 3: Substitute given values and determine the inequality○ Expand

Given pure vapor pressures are $P_{A}^{0} = 350$ mm Hg and $P_{B}^{0} = 750$ mm Hg. Substitute these values into the derived ratio:

\frac{y_{A}}{y_{B}} = \frac{x_{A}}{x_{B}} \cdot \frac{350}{750} = \frac{x_{A}}{x_{B}} \cdot \frac{7}{15}

Since $\frac{7}{15} < 1$ , it implies that $\frac{y_{A}}{y_{B}} < \frac{x_{A}}{x_{B}}$ . Rearranging this inequality, we get $\frac{x_{A}}{x_{B}} > \frac{y_{A}}{y_{B}}$ . This matches option 1, which states $\frac{x_{A}}{x_{B}} \geq \frac{y_{A}}{y_{B}}$ (as $>$ is a subset of $\geq$ ). The component with higher vapor pressure (B) is relatively more abundant in the vapor phase.

💡 Teacher's Secret Hint

The component with the higher pure vapor pressure will be relatively more volatile and thus more enriched in the vapor phase.

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Chemistry Question 55 – JEE-MAIN 2025

Clue 1 of 3: Ideal Solutions and Vapor Pressure

🧠 Full Solution Path