A solution is made by mixing one mole of volatile liquid \(A\) with 3 moles of volatile liquid \(B\). The…

A solution is made by mixing one mole of volatile liquid \(A\) with 3 moles of volatile liquid \(B\). The vapour pressure of pure A is 200 mm Hg and that of the solution is 500 mm Hg. The vapour pressure of pure \(B\) and the least volatile component of the solution, respectively, are :
  1. \(1400 \mathrm{~mm} \mathrm{Hg}, \mathrm{A}\)
  2. \(1400 \mathrm{~mm} \mathrm{Hg}, \mathrm{B}\)
  3. \(600 \mathrm{~mm} \mathrm{Hg}, \mathrm{B}\)
  4. \(600 \mathrm{~mm} \mathrm{Hg}, \mathrm{A}\)

Solution

\(\begin{aligned}
& \mathrm{P}_{\mathrm{S}}=\mathrm{P}_{\mathrm{A}}^{\mathrm{o}} \cdot \mathrm{X}_{\mathrm{A}}+\mathrm{P}_{\mathrm{B}}^{\mathrm{o}} \cdot \mathrm{X}_{\mathrm{B}} \\
& 500=200 \times \frac{1}{4}+\mathrm{P}_{\mathrm{B}}^{\mathrm{o}} \cdot \frac{3}{4} \\
& \mathrm{P}_{\mathrm{B}}^{\mathrm{o}}=600 \mathrm{~mm} \mathrm{Hg}
\end{aligned}\)
As \(\mathrm{P}_{\mathrm{A}}^{\mathrm{o}} \lt \mathrm{P}_{\mathrm{B}}^{\mathrm{o}} \Rightarrow \mathrm{A}\) is least volatile.

Asked in: JEE Main 2025 (02 Apr Shift 1)

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