Q.In the case of dissociation, the abnormal molecular mass of the dissolved substance —

What is Abnormal Molar Mass?

Imagine you dissolve a spoonful of salt in water. You know the mass of salt you added, and you know its molecular formula is NaCl. So you expect the molar mass to be about 58.5 g/mol. But when you measure the colligative property — say, the freezing point depression — and work backwards to calculate the molar mass from that data, you get a number that is not 58.5. It might come out as roughly half that, around 29 g/mol.

That is an abnormal molar mass — a molar mass obtained from experiment that does not match the formula mass of the solute.

Why does this happen? Because the solute does not stay as individual molecules in solution. It either breaks apart into smaller particles (dissociation) or clumps together into larger ones (association). Colligative properties depend on the number of particles, not their identity. So if one NaCl formula unit splits into two ions (Na⁺ and Cl⁻), the solution behaves as if there are twice as many particles. The measured colligative effect is double what you'd expect for a non-electrolyte, and the calculated molar mass comes out half the true value.

The van't Hoff Factor — The Correction

To connect the observed (abnormal) molar mass to the true molar mass, we use the van't Hoff factor, denoted by $i$.

For a solute that dissociates, $i > 1$. For one that associates, $i < 1$. For an ideal non-electrolyte, $i = 1$.

The relationship between the observed molar mass ($M_{\text{obs}}$) and the theoretical molar mass ($M_{\text{theo}}$) is:

So if $i = 2$ (like NaCl fully dissociating), $M_{\text{obs}} = M_{\text{theo}} / 2$ — the observed molar mass is half the expected value. If $i = 0.5$ (like benzoic acid dimerising in benzene), $M_{\text{obs}} = M_{\text{theo}} / 0.5 = 2 M_{\text{theo}}$ — the observed molar mass is double.

A Concrete Example

Take acetic acid ($\text{CH}_3\text{COOH}$, molar mass 60 g/mol) dissolved in benzene. In benzene, acetic acid molecules form dimers through hydrogen bonding — two molecules stick together as one particle. …