Q.The Van't Hoff Factor

Molar mass calculated from a colligative property assumes a dilute solution with no association or dissociation of solute. In concentrated solutions, or when the solute associates (combines into dimers/trimers) or dissociates (splits into ions), the calculated molar mass differs from the true value -- called the abnormal molar mass.

Association reduces the true particle count, so the calculated molar mass comes out higher than actual. Example: acetic acid dimerises in benzene ($\mathrm{2CH_3COOH\rightarrow(CH_3COOH)_2}$), giving a measured molar mass (~120 g/mol) roughly double the true value (60 g/mol).

Dissociation increases the true particle count, so the calculated molar mass comes out lower than actual. Example: NaCl dissociates completely, $\mathrm{NaCl(s)\rightarrow Na^+(aq)+Cl^-(aq)}$ -- 1 mole of NaCl gives 2 moles of particles, roughly doubling the measured colligative property.

Van't Hoff factor (i) quantifies this: $i=\dfrac{\text{normal molar mass}}{\text{observed (abnormal) molar mass}}=\dfrac{\text{observed colligative property}}{\text{calculated colligative property}}$. Degree of dissociation (into $n$ species): $\alpha_{dissociation}=\dfrac{i-1}{n-1}$. Degree of association (of $n$ molecules): $\alpha_{association}=\dfrac{(1-i)n}{n-1}$. …