A binary solution of two volatile liquids and denote the two components as 1 and 2. When taken in a closed vessel, both the components would evaporate and eventually an equilibrium would be established between vapour phase and the liquid phase. Let the total vapour pressure at this stage be p_total and p₁ and p₂ be the partial vapour pressures of the two components 1 and 2 respectively. These partial pressures are related to the mole fractions x₁ and x₂ of the two components 1 and 2 respectively. The French chemist, Francois Marte Raoult (1886) gave the quantitative relationship between them. The relationship is known as the Raoult’s law which states that 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.

Which will show negative deviation from Raoult's law?

ΔV_mix < 0

The correct answer is option 2. \(\Delta V_{mix} < 0\).

Raoult's law states that the partial vapor pressure of each volatile component in an ideal solution is directly proportional to its mole fraction. Mathematically, for a component \(A\) in a solution:

\(P_A = X_A \cdot P_A^\circ\)

where:

\(P_A\) is the partial vapor pressure of component \(A\) in the solution.

\(X_A\) is the mole fraction of component \(A\) in the solution.

\(P_A^\circ\) is the vapor pressure of pure component \(A\).

For ideal solutions, the interactions between unlike molecules (A-B) are similar to those between like molecules (A-A and B-B). Therefore, the mixing process neither absorbs nor releases a significant amount of energy, and the volume change upon mixing is negligible.

However, in real solutions, deviations from Raoult's law can occur:

Positive deviation: When the interactions between unlike molecules (A-B) are weaker than those between like molecules (A-A and B-B). This causes the solution to have a higher vapor pressure than predicted by Raoult's law. It also often leads to an increase in volume upon mixing (\(\Delta V_{\text{mix}} > 0\)) because the molecules do not pack as tightly.

Negative deviation: When the interactions between unlike molecules (A-B) are stronger than those between like molecules (A-A and B-B). This causes the solution to have a lower vapor pressure than predicted by Raoult's law. It also often leads to a decrease in volume upon mixing (\(\Delta V_{\text{mix}} < 0\)) because the stronger interactions cause the molecules to pack more closely together.

For negative deviations, the stronger interactions between the different components result in a more exothermic mixing process, leading to a decrease in the overall volume of the solution. This is why: \(\Delta V_{\text{mix}} < 0\) (a negative change in volume upon mixing) indicates stronger intermolecular forces between the different components, leading to negative deviation from Raoult's law.