Explain the van't Hoff factor and provide its formula.

(N/A) The van't Hoff factor,denoted by $i$,was introduced to account for the extent of dissociation or association of solute particles in a solution. It is defined as:
$i = \frac{\text{Normal molar mass}}{\text{Abnormal molar mass}} = \frac{\text{Observed colligative property}}{\text{Calculated colligative property}}$
Alternatively,it can be expressed as:
$i = \frac{\text{Total number of moles of particles after association/dissociation}}{\text{Number of moles of particles before association/dissociation}}$
Here,the abnormal molar mass is the experimentally determined molar mass,and the calculated colligative properties are obtained by assuming that the non-volatile solute is neither associated nor dissociated.
In the case of association,the value of $i$ is less than unity $(i < 1)$,while for dissociation,it is greater than unity $(i > 1)$. When there is no association or dissociation,$i = 1$.
For example,the value of $i$ for an aqueous $KCl$ solution is close to $2$,while the value for ethanoic acid in benzene is nearly $0.5$.
Inclusion of the van't Hoff factor modifies the equations for colligative properties as follows:
$1$. Relative lowering of vapour pressure: $\frac{P_1^0 - P_1}{P_1^0} = i \frac{n_2}{n_1}$
$2$. Elevation of boiling point: $\Delta T_b = i K_b m$
$3$. Depression of freezing point: $\Delta T_f = i K_f m$
$4$. Osmotic pressure: $\Pi = i CRT$ (where $C = n/V$)