Colligative properties, such as boiling point elevation and freezing point depression, depend on the number of dissolved particles rather than what those particles are. A substance that stays whole in solution contributes one particle per formula unit, but a substance that splits into ions contributes more.
The van’t Hoff factor accounts for this by giving the effective number of particles each formula unit releases.
For a nonelectrolyte such as glucose or sucrose, which dissolves without breaking apart, i is equal to 1. For an ionic compound, i is ideally equal to the number of ions in the formula. Sodium chloride, NaCl, breaks into one sodium ion and one chloride ion, so its ideal i is 2. Calcium chloride, CaCl2, breaks into three ions, giving an ideal i of 3.
The factor is included in colligative equations by multiplying the concentration by i. Freezing point depression becomes delta T equals i times Kf times molality, and boiling point elevation and osmotic pressure are adjusted the same way. This is why one mole of salt lowers the freezing point of water about twice as much as one mole of sugar.
In real solutions, the measured van’t Hoff factor is usually a little smaller than the ideal value. This happens because some oppositely charged ions attract each other and briefly travel together as ion pairs, which reduces the number of independent particles. The effect grows as concentration increases, so dilute solutions come closer to the ideal factor. Chemists use experimental i values to study how completely a substance dissociates in solution.