The properties of solutions which depend on the number of solute particles and are independent of their chemical identity are called colligative properties. These are lowering of vapour pressure, elevation of boiling point, depression of freezing point and osmotic pressure. The process of osmosis can be reversed if a pressure higher than the osmotic pressure is applied to the solution. Colligative properties have been used to determine the molar mass of solutes. Solutes which dissociate in solution exhibit molar mass lower than the actual molar mass and those which associate show higher molar mass than their actual values. Quantitatively, the extent to which a solute is dissociated or associated can be expressed by van’t Hoff factor i. This factor has been defined as ratio of normal molar mass to experimentally determined molar mass or as the ratio of observed colligative property to the calculated colligative property.
Match List-I with List-II.
| List-I (Solute in solvent) | List-II (Molar mass found from a colligative property, compared with the normal molar mass) |
|---|---|
| (A) KCl in water | (I) About one-half |
| (B) K2SO4 in a very dilute aqueous solution | (II) About one-third |
| (C) Ethanoic acid in benzene | (III) About twice |
| (D) Urea in water | (IV) The same |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A-I, B-II, C-III, D-IV
The van’t Hoff factor links the two molar masses. Rearranging its definition:
\( \displaystyle i = \frac{\text{Normal molar mass}}{\text{Abnormal molar mass}} \)
\( \displaystyle \text{Abnormal molar mass} = \frac{\text{Normal molar mass}}{i} \)
(A) KCl in water — This matches (I) About one-half. KCl gives two ions, i is close to 2, so the molar mass found is about half (about 37.25 g mol−1 in place of 74.5 g mol−1).
(B) K2SO4 in a very dilute aqueous solution — This matches (II) About one-third. K2SO4 gives three ions (2K+ and SO42−), so i is close to 3.
(C) Ethanoic acid in benzene — This matches (III) About twice. The molecules associate into dimers, i is nearly 0.5, and dividing by 0.5 doubles the molar mass.
\( \displaystyle \ce{2CH3COOH <=> (CH3COOH)2} \)
(D) Urea in water — This matches (IV) The same. Urea neither associates nor dissociates, so i = 1 and the molar mass found is the normal one.
NCERT (2026-27 edition):
1.7 Abnormal Molar Masses – “…one mole of KCl in one kg of water would be expected to increase the boiling point by 2 × 0.52 K = 1.04 K. Now if we did not know about the degree of dissociation, we could be led to conclude that the mass of 2 mol particles is 74.5 g and the mass of one mole of KCl would be 37.25 g.”
“It can be undoubtedly stated here that if all the molecules of ethanoic acid associate in benzene, then ΔTb or ΔTf for ethanoic acid will be half of the normal value. The molar mass calculated on the basis of this ΔTb or ΔTf will, therefore, be twice the expected value.”
“…calculated colligative properties are obtained by assuming that the non-volatile solute is neither associated nor dissociated. … For example, the value of i for aqueous KCl solution is close to 2, while the value for ethanoic acid in benzene is nearly 0.5.”
“…As expected, the value of i gets close to 3 for K2SO4.”