Van't Hoff Factor Calculator

The Van’t Hoff factor (i) accounts for the fact that some solutes dissociate or associate when dissolved, changing the number of particles in solution.

Definition:

i = (actual number of particles in solution) / (number of formula units dissolved)

For non-electrolytes (glucose, sucrose, urea): i = 1

For electrolytes (theoretical, complete dissociation):

• NaCl → Na⁺ + Cl⁻: i = 2
• MgCl₂ → Mg²⁺ + 2Cl⁻: i = 3
• AlCl₃ → Al³⁺ + 3Cl⁻: i = 4
• K₂SO₄ → 2K⁺ + SO₄²⁻: i = 3

Experimental determination from colligative properties:

From freezing point depression: i = ΔTf_observed / (Kf × m)

From boiling point elevation: i = ΔTb_observed / (Kb × m)

From osmotic pressure: i = π_observed / (MRT)

Relationship to degree of dissociation α:

For a compound that dissociates into n ions: i = 1 + α(n - 1)

Solving for α: α = (i - 1) / (n - 1)

Why i < theoretical for electrolytes? At higher concentrations, oppositely charged ions tend to cluster (ion pairing), reducing the effective number of particles. This is why the experimental i is always ≤ the theoretical value.

Example — 0.1 m NaCl:

• Theoretical i = 2 (complete dissociation)
• Experimental i ≈ 1.87 (some ion pairing)
• α = (1.87 - 1)/(2 - 1) = 0.87 (87% dissociated effectively)

Colligative property formulas with i:

• Freezing point depression: ΔTf = i × Kf × m
• Boiling point elevation: ΔTb = i × Kb × m
• Osmotic pressure: π = i × MRT
• Vapor pressure lowering: ΔP = i × x_solute × P°