Degree of Ionization of Weak Acid/Base
Calculate the degree of ionization (α) of a weak acid or base from Ka/Kb and initial concentration.
Includes equilibrium concentrations and pH.
Weak acids and bases do not fully ionize in solution. The fraction that ionizes is called the degree of ionization (α).
For a weak acid HA ⇌ H⁺ + A⁻:
Ka = α²C / (1 - α)
Simplified (for small α < 5%):
α ≈ √(Ka/C)
Exact solution (quadratic formula):
Cα² + Kaα − Ka = 0
α = (-Ka + √(Ka² + 4KaC)) / (2C)
Equilibrium concentrations:
[H⁺] = [A⁻] = αC[HA] = C(1-α)pH = -log([H⁺]) = -log(αC)
For a weak base B + H₂O ⇌ BH⁺ + OH⁻: Replace Ka with Kb, and calculate pOH instead:
pOH = -log(αC)pH = 14 - pOH
Common Ka values:
| Acid | Ka |
|---|---|
| Acetic acid (vinegar) | 1.76 × 10⁻⁵ |
| Carbonic acid (H₂CO₃) | 4.3 × 10⁻⁷ |
| Hydrofluoric acid (HF) | 6.8 × 10⁻⁴ |
| Ammonium ion (NH₄⁺) | 5.6 × 10⁻¹⁰ |
When is the 5% approximation valid? If α < 0.05 (5%), the simplified formula is accurate to within 0.5%. If α > 0.05, use the quadratic formula (this calculator always uses the exact formula).
Percent ionization:
For weak acids: %α = α × 100%
Increases as concentration decreases — diluting a weak acid increases its ionization fraction.