Degree of Ionization of Weak Acid/Base

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:

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.

Worked example

Acetic acid at 0.1 mol/L, Ka = 1.76 × 10⁻⁵:

α = (−Ka + √(Ka² + 4·Ka·C)) / (2C) = 0.01319

So 1.32% of the acid molecules have given up their proton at any moment. [H⁺] = α × C = 1.32 × 10⁻³, giving pH 2.88. The other 98.7% are sitting there intact, which is exactly what makes it a weak acid: not that it dissolves poorly, but that almost none of what dissolved has actually ionized.

Why dilution increases the degree of ionization

This is the part that feels wrong the first time you meet it. Dilute the acetic acid tenfold to 0.01 mol/L and α rises to about 4.15%. Dilute it again to 0.001 mol/L and α reaches roughly 12.5%. The solution is getting weaker in every ordinary sense, yet a larger fraction of it is ionized.

Ostwald’s dilution law is the formal statement of this, and Le Chatelier’s principle is the intuition. Ionization produces two particles from one, so it increases the number of dissolved species. Adding water gives those species more room, and the equilibrium shifts toward the side that makes more of them. The total amount of H⁺ still falls, because you have far less acid overall, but the proportion that has dissociated climbs.

Push this far enough and α approaches 1, which is why an extremely dilute weak acid behaves almost like a strong one in percentage terms while having almost no acidity in absolute terms.