Step 1: What it corrects.
Colligative properties depend on the actual number of solute particles. When a solute dissociates (like a salt) or associates (like a dimerising acid), the real particle count differs from the count assumed from moles taken. The factor \(i\) is introduced to bridge this gap.
Step 2: Formal expression.
\(i = \dfrac{\text{actual number of particles in solution}}{\text{number of particles if no dissociation/association}}\). It also equals the ratio of normal molar mass to the abnormally observed molar mass.
Step 3: Insert \(i\) into the four laws.
\(\dfrac{p^{\circ}-p_s}{p^{\circ}} = i\,x_2\), \(\ \Delta T_b = i\,K_b\,m\), \(\ \Delta T_f = i\,K_f\,m\), \(\ \pi = i\,CRT\).
Step 4: Interpretation.
\(i>1\) signals dissociation, \(i<1\) signals association, and \(i=1\) means the solute stays as taken.
\[\boxed{\Delta T_f = i\,K_f\,m,\quad \pi = i\,CRT}\]