Van't Hoff Factor

The van't Hoff factor $i$ accounts for the actual number of particles produced per formula unit of solute:

$i = \frac{\text{observed colligative property}}{\text{calculated colligative property (for non-electrolyte)}}$

Or equivalently:
$i = \frac{\text{actual moles of particles in solution}}{\text{moles of formula units dissolved}}$

Three cases:

• $i = 1$: Non-electrolyte, no dissociation (glucose, urea, sugar)
• $i > 1$: Electrolyte that dissociates (NaCl $\to$ 2 ions, CaCl₂ $\to$ 3 ions, AlCl₃ $\to$ 4 ions)
• $i < 1$: Association in solution (acetic acid in benzene dimerises: $2\ce{CH3COOH} \to (\ce{CH3COOH})_2$)

All four colligative property equations are modified by inserting $i$:

$\text{RLVP: } \frac{p^\circ - p_s}{p^\circ} = i \cdot x_2$

$\Delta T_b = i \cdot K_b \cdot m$

$\Delta T_f = i \cdot K_f \cdot m$

$\pi = i \cdot M \cdot R \cdot T$

Abnormal molar mass: When colligative properties are measured experimentally and molar mass calculated assuming $i = 1$, the result is the apparent (abnormal) molar mass — lower than true for electrolytes (more particles), higher than true for associating solutes.

Degree of dissociation ($\alpha$) and van't Hoff factor:

For an electrolyte $\ce{AB} \to \ce{A+} + \ce{B-}$ (splits into $n$ ions):
$i = 1 + (n-1)\alpha$

where $\alpha$ = degree of dissociation (fraction dissociated), $n$ = number of ions formed.

For association (dimerisation: $2A \to A_2$):
$i = 1 - \frac{\alpha}{2}$

These allow you to calculate the degree of dissociation from experimental colligative property data.