Definition of the van’t Hoff factor, i : It is defined as a ratio of the observed colligative property of the solution to the theoretically calculated colligative property of the solution without considering molecular change.

The van’t Hoff factor can be represented as,

\(i = \frac{\text{Observed value of colligative property}}{\text{Theoretical value of the colligative property}}\)

This colligative property may be the lowering of vapour pressure of a solution, the osmotic pressure, the elevation in the boiling point or the depression in the freezing point of the solution. Hence,

\(i = \frac{\text{Observed lowering of vapour pressure}}{\text{Theoretical lowering of vapour pressure}}\)

\(=\Delta\,P_\text{(ob)}/\Delta P_\text{(th)}\)

\(i = \frac{\text{Observed elevation in boiling point}}{\text{Theoretical elevation in boiling point}}\)

\(=\Delta\,T_\text{b(ob)}/\Delta T_\text{b(th)}\)

\(i = \frac{\text{Observed depression in freezing point}}{\text{Theoretical depression in freezing point}}\)

\(=\Delta\,T_\text{f(ob)}/\Delta T_\text{f(th)}\)

\(i = \frac{\text{Observed osmotic pressure}}{\text{Theoretical osmotic pressure}}\)

\(=\frac{\pi_\text{(ob)}}{\pi_\text{(th)}}\)

• When the solute neither undergoes dissociation or association in the solution, then, i = 1
• When the solute undergoes dissociation in the solution, then, i > 1
• When the solute undergoes association in the solution, then i < 1

From the value of the van’t Hoff factor, the degree of dissociation of electrolytes, degree of association of nonelectrolytes can be obtained.

van’t Hoff factor gives the important information about the solute molecules in the solution and chemical bonding in them.