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 molar mass of sodium chloride determined by the osmotic pressure method will be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Lower than the theoretical value
The molar mass found from a colligative property is calculated as if the solute did not dissociate. By the osmotic pressure method:
\( \displaystyle M_2=\frac{w_2\,R\,T}{\Pi\,V} \)
In water \( \ce{NaCl -> Na^+ + Cl^-} \): each formula unit gives two particles, so i is close to 2 and the observed Π is nearly twice the value expected for undissociated NaCl. A larger Π in the denominator gives a smaller M2. In terms of the van’t Hoff factor:
\( \displaystyle i=\frac{\text{Normal molar mass}}{\text{Abnormal molar mass}}\gt 1\quad\Rightarrow\quad\text{Abnormal molar mass}\lt\text{Normal molar mass} \)
So the molar mass found (about 58.5/2 ≈ 29 g mol−1 if dissociation were complete) is lower than the theoretical value of 58.5 g mol−1.
Why the other options are incorrect
Option (1) The same as the theoretical value — Incorrect. That would need i = 1, which holds for a non-electrolyte such as glucose, not for NaCl.
Option (2) Higher than the theoretical value — Incorrect. A higher molar mass is found when the solute associates (i < 1), as ethanoic acid does in benzene.
Option (4) Twice the theoretical value — Incorrect. Dissociation into two ions makes the observed Π nearly twice the expected value, so the molar mass found is nearly half the theoretical value, not twice.
NCERT (2026-27 edition):
1.7 Abnormal Molar Masses – “… 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. This brings into light the rule that, when there is dissociation of solute into ions, the experimentally determined molar mass is always lower than the true value.”