The molar masses determined from the colligative properties of substances that associate or dissociate in solution are abnormal and are called abnormal molar masses. Ionic substances such as NaCl, BaCl2 and AlCl3 dissociate into ions in solution. Their colligative properties are higher than those of solutions of non-electrolytes such as glucose of the same concentration, because the number of particles in solution increases. When molecules of a substance such as ethanoic acid (acetic acid) associate in benzene to form dimers, the number of particles decreases and the colligative properties also decrease. The van’t Hoff factor, i, accounts for the extent of dissociation or association:
\(\displaystyle i = \frac{\text{Normal molar mass}}{\text{Abnormal molar mass}} = \frac{\text{Observed colligative property}}{\text{Calculated colligative property}}\)
\(\displaystyle i = \frac{\text{Total number of moles of particles after association/dissociation}}{\text{Number of moles of particles before association/dissociation}}\)
The value of i is greater than 1 for ionic substances and less than 1 for substances that associate in solution.
The depressions in freezing point of 0.1 M aqueous solutions of HCl, CuSO4 and K2SO4 (assuming complete dissociation) are:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → In the ratio 1:1:1.5
Depression of freezing point is a colligative property: it depends on the number of solute particles. For an electrolyte the van’t Hoff factor i counts the particles each formula unit gives on complete dissociation:
\( \displaystyle \Delta T_f=i\,K_f\,m \)
All three solutions have the same concentration in the same solvent, so ΔTf is in the ratio of the i values.
\( \ce{HCl} \) — \( \ce{HCl -> H^+ + Cl^-} \), so i = 2.
\( \ce{CuSO4} \) — \( \ce{CuSO4 -> Cu^2+ + SO4^2-} \), so i = 2.
\( \ce{K2SO4} \) — \( \ce{K2SO4 -> 2K^+ + SO4^2-} \), so i = 3.
ΔTf(HCl) : ΔTf(CuSO4) : ΔTf(K2SO4) = 2 : 2 : 3 = 1 : 1 : 1.5.
NCERT (2026-27 edition):
1.7 Abnormal Molar Masses – “Table 1.4 depicts values of the factor, i for several strong electrolytes. For KCl, NaCl and MgSO4, i values approach 2 as the solution becomes very dilute. As expected, the value of i gets close to 3 for K2SO4.”
Table 1.4: Values of van’t Hoff factor, i, at Various Concentrations for NaCl, KCl, MgSO4 and K2SO4.
