Match the solutions with their characteristics:

A-s, B-r & s, C-p, D-q

The correct answer is option 2. A-s, B-r & s, C-p, D-q.

(A) \(CH_3COOH\) in \(H_2O\) → (s) \(Δf_{(obs)} > Δf_{(calc)}\)

Explanation: When acetic acid \((CH_3COOH)\) is dissolved in water, it undergoes partial dissociation into ions (\(CH_3COO^-\) and \(H_3O^+\)). As a result, the observed freezing point depression (\(Δf_{obs}\)) may be greater than the calculated freezing point depression (\(Δf_{calc}\)). This discrepancy occurs because the solute-solvent interactions in the solution are stronger than those assumed in the calculation, resulting in a greater deviation from ideal behavior. Consequently, the observed molecular mass (or molar mass) calculated from freezing point depression measurements may appear greater than the actual molecular mass due to the influence of ion-pairing or other non-ideal behavior in the solution.

(B) \(CH_3COOH\) in benzene → Molecular mass observed greater than molecular mass actual and (s) \(Δf_{(obs)} > Δf_{(calc)}\)

Explanation:

(r) When \(CH_3COOH\) (acetic acid) dissolves in benzene, the observed molecular mass is greater than the actual molecular mass. This is due to a phenomenon called association.

Here's a breakdown of the concept:

• Acetic Acid \((CH_3COOH)\): This is a polar molecule due to the presence of a hydroxyl \((OH)\) group.
• Benzene: This is a non-polar solvent.
• Association: In this scenario, individual acetic acid molecules form hydrogen bonds with each other. Hydrogen bonding is a strong intermolecular force that occurs when a hydrogen atom bonded to a highly electronegative atom (like oxygen in \(CH_3COOH\)) is attracted to the lone pair of electrons on another electronegative atom.
• Dimers: Due to hydrogen bonding, acetic acid molecules in benzene tend to pair up to form dimers (structures with two \(CH_3COOH\) units linked by hydrogen bonds). This association leads to fewer individual molecules being present in the solution compared to what would be expected based on the actual number of \(CH_3COOH\) molecules dissolved.

Colligative Properties and Observed Molecular Mass:

• When we measure colligative properties (properties that depend on the number of solute particles in solution, like freezing point depression or boiling point elevation), the observed value reflects the total number of particles present.

• In the case of \(CH_3COOH\) in benzene, the association into dimers effectively doubles the number of particles compared to the solution containing only individual molecules.

Therefore, when using colligative properties to determine the molecular mass of \(CH_3COOH\) in benzene, the observed value will be higher than the actual molecular mass of a single \(CH_3COOH\) molecule because the measurement takes into account the dimers formed through hydrogen bonding.

(s) When acetic acid (CH3COOH) is dissolved in a non-polar solvent like benzene, it primarily remains in its molecular form due to the lack of strong polar interactions. However, the observed freezing point depression (\(Δf_{obs}\)) is greater than the calculated freezing point depression (\(Δf_{calc}\)). This discrepancy occurs because the solute-solvent interactions in the solution are weaker than those assumed in the calculation, resulting in a greater deviation from ideal behavior. As a result, the observed molecular mass (or molar mass) calculated from freezing point depression measurements may appear greater than the actual molecular mass. This is indicative of the non-ideal behavior of the solution.

(C) Polymer in water → (p) Neither association nor dissociation

Explanation:When a polymer is dissolved in water, it typically does not undergo significant association or dissociation. Unlike small molecules or ions, polymers tend to remain in their molecular form when dissolved in solvents like water. Therefore, there's neither significant association nor dissociation observed. Instead, the polymer molecules are dispersed throughout the solvent without undergoing any significant change in their molecular structure.

(D) Vapour pressure of a liquid decreases → (q) When a non-volatile solute is added

Explanation: When a non-volatile solute is added to a liquid solvent, it lowers the vapor pressure of the solution. This phenomenon is known as a colligative property. The presence of the non-volatile solute reduces the number of solvent molecules at the surface, thereby decreasing the rate of evaporation and leading to a decrease in vapor pressure compared to the pure solvent. So, the correct match for this characteristic is (r), not (q). Thank you for catching that mistake.