ν is the theoretical particle count from stoichiometry; i is the effective particle count in solution and may be lower due to ion pairing or incomplete dissociation.

Van’t Hoff Factor (i) Calculator

Determine the van’t Hoff factor i—the effective number of particles a solute produces in solution. Use Simple mode (ideal dissociation with optional degree of dissociation) or Advanced mode (infer i from colligative data such as ΔT_f, ΔT_b, or osmotic pressure).

Background

The van’t Hoff factor i multiplies into colligative property equations and osmotic pressure to account for how many dissolved particles are present. For a fully dissociated electrolyte AB → A⁺ + B⁻, the theoretical particle count is 2; for CaCl₂ it is 3, etc. Real solutions can deviate: i may be lower than the theoretical value due to ion pairing or incomplete dissociation.

Choose a mode and enter values:

Mode:

Simple (ideal ν & degree of dissociation)

Advanced (from ΔT_f/ΔT_b or π)

Theoretical particles per formula unit (ν):

Optional degree of dissociation (α, 0–1):

Formula used: i = 1 + α(ν − 1)

Quick picks:

Advanced method:

From ΔT (freezing/boiling): i = ΔT / (K·m)

From osmotic pressure: i = π / (M R T)

Measured ΔT (°C):

Solvent constant (K):

Molality (m, mol/kg):

Optional ν (to estimate α):

If ν is provided, we estimate α from i via α = (i − 1)/(ν − 1).

Quick examples:

Result:

No results yet. Choose a mode and enter values.

How to use this calculator

Simple mode

Enter the theoretical particle count ν (e.g., glucose 1; NaCl 2; CaCl₂ 3; Al₂(SO₄)₃ 5).
Optionally enter a degree of dissociation α (0–1). Default is 1 (fully dissociated).
We compute i = 1 + α(ν − 1).

Advanced mode

From ΔT: Provide measured ΔT, the solvent constant K (Kf or Kb), and molality m. We compute i = ΔT / (K·m).
From π: Provide π, molarity M, and T (K or °C). We compute i = π / (M R T) using R = 0.082057 L·atm·mol⁻¹·K⁻¹ (or 8.314 J·mol⁻¹·K⁻¹ with Pa).
Optionally enter ν to estimate α via α = (i − 1)/(ν − 1).

Example Problems & Step-by-Step Solutions

Example 1 (Simple)

CaCl₂ (ν = 3) with α = 0.80. i = 1 + 0.80(3 − 1) = 1 + 1.6 = 2.6.

Example 2 (Advanced, ΔT method)

A 1.00 m solution in water (Kf = 1.86) shows ΔT_f = 3.72 °C. i = 3.72 / (1.86×1.00) = 2.00.

Example 3 (Advanced, π method)

A solution has π = 4.92 atm at 298 K and M = 0.200 mol/L. Using R = 0.082057 L·atm·mol⁻¹·K⁻¹:
i = 4.92 / (0.200 × 0.082057 × 298) ≈ 1.00.

Frequently Asked Questions

Q: What’s ν vs. i?

ν is the theoretical particle count from stoichiometry (e.g., CaCl₂ → 3 ions). i is the effective particle count in solution; it can be lower due to ion pairing or incomplete dissociation.

Q: When should I use ΔT vs. π?

Use ΔT when you have freezing/boiling data with a known solvent constant (Kf or Kb). Use π when you have osmotic pressure, molarity, and temperature.

Q: Can i be less than 1?

Yes—association (e.g., dimer formation) can reduce the effective particle count so i < 1.

Solutions