A binary solution of components A and B obeys Raoult’s law. Which of the following is true?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A plot of the vapour pressure of each component against its mole fraction is linear
Raoult’s law states that the partial vapour pressure of each component is directly proportional to its mole fraction in the solution:
\( \displaystyle p_A=p_A^{\circ}\,x_A \qquad p_B=p_B^{\circ}\,x_B \)
Each equation has the form y = mx, so the plot of pA against xA (and of pB against xB) is a straight line through the origin, with slope equal to the pure vapour pressure.
Why the other options are incorrect
Option (1) The total vapour pressure cannot be related to the mole fraction of only one component — Incorrect. Putting \( x_A=1-x_B \) gives \( p_{\text{total}}=p_A^{\circ}+(p_B^{\circ}-p_A^{\circ})\,x_B \), so the total vapour pressure is related to the mole fraction of either one component.
Option (2) The vapour pressure of each component varies non-linearly with its mole fraction — Incorrect. Direct proportionality gives a linear variation, a straight line and not a curve.
Option (4) The total vapour pressure of the solution decreases with an increase in the mole fraction of either component — Incorrect. The total vapour pressure rises as the more volatile component is added and falls as the less volatile one is added; it cannot fall for both.
NCERT (2026-27 edition):
1.4.1 Vapour Pressure of Liquid-Liquid Solutions – “
\( \displaystyle p_{\text{total}}=p_1^0+(p_2^0-p_1^0)\,x_2 \qquad (1.16) \)
Following conclusions can be drawn from equation (1.16). (i) Total vapour pressure over the solution can be related to the mole fraction of any one component. … (iii) Depending on the vapour pressures of the pure components 1 and 2, total vapour pressure over the solution decreases or increases with the increase of the mole fraction of component 1. A plot of p1 or p2 versus the mole fractions x1 and x2 for a solution gives a linear plot as shown in Fig. 1.3.”
Fig. 1.3: The plot of vapour pressure and mole fraction of an ideal solution at constant temperature.