The Vant Hoff factor is:
The Vant Hoff factor is a measure of the degree of dissociation or association of solute particles in a solution. It is denoted by the symbol "i" and is defined as the ratio of the observed colligative property of the solution to the colligative property calculated based on the assumption of complete dissociation or association of the solute.

Less than one in case of dissociation:
In the case of dissociation, the Vant Hoff factor is less than one. This is because the solute particles dissociate into smaller particles or ions when dissolved in a solvent. Each dissociated particle contributes to the colligative properties of the solution, but the total number of particles is greater than the number of moles of the solute. Therefore, the observed colligative property is higher than what would be expected based on the assumption of complete dissociation. As a result, the Vant Hoff factor is less than one.

Greater than one in case of association:
In the case of association, the Vant Hoff factor is greater than one. This occurs when solute particles combine or associate with each other to form larger particles or aggregates in the solvent. The observed colligative property is lower than what would be expected based on the assumption of no association. Therefore, the Vant Hoff factor is greater than one to compensate for the decreased number of particles contributing to the colligative properties.

Example:
Let's consider an example to illustrate the concept of the Vant Hoff factor. Suppose we have a solution of sodium chloride (NaCl) in water. Sodium chloride dissociates into sodium ions (Na+) and chloride ions (Cl-) when dissolved in water. If we assume complete dissociation, the Vant Hoff factor would be 2 (one Na+ ion and one Cl- ion for every formula unit of NaCl).

Now, let's say we measure the boiling point elevation of this solution. The observed boiling point elevation would be higher than what would be expected based on the assumption of complete dissociation. This is because the solution contains more particles (Na+ and Cl-) than expected, resulting in a higher boiling point elevation. Therefore, the Vant Hoff factor in this case would be less than one.

On the other hand, if we had a solution of acetic acid (CH3COOH) in water, the acetic acid molecules can associate with each other through hydrogen bonding. This association decreases the number of particles in the solution, resulting in a lower observed colligative property. In this case, the Vant Hoff factor would be greater than one to account for the decreased number of particles.

In summary, the Vant Hoff factor is less than one in the case of dissociation and greater than one in the case of association. It is a useful concept in understanding the behavior of solutes in solutions and calculating colligative properties.