Liquids 1 and 2 form an ideal solution, and component 1 is less volatile than component 2 \( (p_1^0 \lt p_2^0) \). Match List-I with List-II.
| List-I (Quantity) | List-II (Expression) |
|---|---|
| (A) Partial vapour pressure of component 2 over the solution | (I) \( p_2^0 \) |
| (B) Mole fraction of component 2 in the vapour phase | (II) \( x_2\,p_2^0 \) |
| (C) Minimum value of the total vapour pressure | (III) \( p_1^0 \) |
| (D) Maximum value of the total vapour pressure | (IV) \( x_2\,p_2^0 / p_{total} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-II, B-IV, C-III, D-I
Raoult’s law gives the partial vapour pressure of each component, and Dalton’s law of partial pressures gives the total vapour pressure and the composition of the vapour:
\( \displaystyle p_2 = x_2\,p_2^0 \)
\( \displaystyle p_{total} = p_1^0 + (p_2^0 - p_1^0)\,x_2 \)
\( \displaystyle y_2 = \frac{p_2}{p_{total}} = \frac{x_2\,p_2^0}{p_{total}} \)
(A) Partial vapour pressure of component 2 over the solution — This matches (II) \( x_2\,p_2^0 \), by Raoult’s law: the partial vapour pressure is proportional to the mole fraction in the liquid.
(B) Mole fraction of component 2 in the vapour phase — This matches (IV) \( x_2\,p_2^0 / p_{total} \). By Dalton’s law, y2 is the partial pressure of component 2 divided by the total pressure.
(C) Minimum value of the total vapour pressure — This matches (III) \( p_1^0 \). ptotal is lowest at x2 = 0, that is, for pure component 1, the less volatile liquid.
(D) Maximum value of the total vapour pressure — This matches (I) \( p_2^0 \). ptotal is highest at x2 = 1, for pure component 2.
NCERT (2026-27 edition):
1.4.1 Vapour Pressure of Liquid-Liquid Solutions – “…for a solution of volatile liquids, the partial vapour pressure of each component of the solution is directly proportional to its mole fraction present in solution.” … “Similarly, for component 2”
\( \displaystyle p_2 = p_2^0\,x_2 \qquad (1.13) \)
“…The minimum value of ptotal is p10 and the maximum value is p20, assuming that component 1 is less volatile than component 2, i.e., p10 < p20.”
“…If y1 and y2 are the mole fractions of the components 1 and 2 respectively in the vapour phase then, using Dalton’s law of partial pressures: p1 = y1 ptotal, p2 = y2 ptotal”