An ideal solution is one in which the attraction between components of the solution is the same as the interaction between the molecules of each component. Heat is neither absorbed nor evolved during the formation of an ideal solution and the volume of the solution is equal to the sum of the volumes of the component liquids. Raoult’s law states that the partial vapour pressure of each component (say liquid A) of the solution is directly proportional to its mole fraction in the solution. The total vapour pressure over the solution is equal to the sum of the partial vapour pressures of the individual components.
A non-ideal solution is that solution (i) which does not obey Raoult’s law (ii) for which \(\Delta V_{mix}\) is not zero and (iii) for which \(\Delta H_{mix}\) is not zero. In non-ideal solutions, the solute–solvent interactions are weaker or stronger than the solute–solute and solvent–solvent interactions. The non-ideal solutions in which solute–solvent interactions are weaker than the solute–solute and solvent–solvent interactions show positive deviation from Raoult’s law, and those in which they are stronger show negative deviation.
Consider the following statements about solutions of two volatile liquids 1 and 2.
(A) For an ideal solution of liquids 1 and 2, the total vapour pressure over the solution varies linearly with the mole fraction of component 2.
(B) For an ideal solution of liquids 1 and 2 in which \( p_1^0 \lt p_2^0 \), the maximum value of the total vapour pressure is \( p_1^0 \).
(C) For an ideal solution of liquids 1 and 2, the total vapour pressure over the solution can be related to the mole fraction of any one component.
(D) A solution formed by adding carbon disulphide to acetone is nearly ideal in behaviour.
Which of the statements given above are correct? Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) and (C) only
For an ideal solution, Raoult’s law for each component and Dalton’s law of partial pressures together give the total vapour pressure in terms of the mole fraction of one component:
\( \displaystyle p_{total} = p_1^0 + (p_2^0 - p_1^0)\,x_2 \)
(A) For an ideal solution of liquids 1 and 2, the total vapour pressure over the solution varies linearly with the mole fraction of component 2. — True. The equation has the form y = c + mx, so the plot of ptotal against x2 is a straight line.
(B) For an ideal solution of liquids 1 and 2 in which \( p_1^0 \lt p_2^0 \), the maximum value of the total vapour pressure is \( p_1^0 \). — False. At x2 = 0 the total vapour pressure is \( p_1^0 \) and at x2 = 1 it is \( p_2^0 \). Since component 1 is the less volatile one, \( p_1^0 \) is the minimum value; the maximum is \( p_2^0 \).
(C) For an ideal solution of liquids 1 and 2, the total vapour pressure over the solution can be related to the mole fraction of any one component. — True. Since x1 + x2 = 1, the same equation can be written with x1 or with x2, so one mole fraction is enough.
(D) A solution formed by adding carbon disulphide to acetone is nearly ideal in behaviour. — False. In this solution the dipolar interactions between unlike molecules are weaker than those among like molecules, so it shows positive deviation from Raoult’s law.
NCERT (2026-27 edition):
1.4.1 Vapour Pressure of Liquid-Liquid Solutions – “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. (ii) Total vapour pressure over the solution varies linearly with the mole fraction of component 2. …”
\( \displaystyle p_{total} = p_1^0 + (p_2^0 - p_1^0)\,x_2 \qquad (1.16) \)
“…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.”
1.5.2 Non-ideal Solutions – “In a solution formed by adding carbon disulphide to acetone, the dipolar interactions between solute-solvent molecules are weaker than the respective interactions among the solute-solute and solvent-solvent molecules. This solution also shows positive deviation.”