Percent Ionization Calculator
Enter the ionized concentration (e.g. equilibrium [H⁺]) and the initial concentration C₀; using % = ionized/C₀ × 100 the tool instantly computes the percent ionization of a weak acid or weak base.
Input Data
Results
At a glance:Percent ionization (also degree of ionization or dissociation) describes how much a 'weak electrolyte' ionizes in solution: the percentage of the initial concentration that has ionized: % = (ionized concentration / initial concentration C₀) × 100%. Strong electrolytes (strong acids like HCl, strong bases like NaOH, strong salts) ionize almost completely in water, so percent ionization is near 100%; but weak electrolytes (weak acid CH₃COOH acetic acid, weak base NH₃ ammonia) only have a small fraction of molecules ionized into ions, with most remaining as unionized molecules, reaching an ionization equilibrium. Percent ionization measures 'how much ionized'. Take weak acid HA: HA ⇌ H⁺ + A⁻. If initial concentration is C₀ and x mol/L of HA ionizes at equilibrium, it produces x mol/L of H⁺ (ionized concentration = [H⁺] = x), so percent ionization = (x / C₀) × 100%. Using this tool's default: a weak acid with initial C₀ = 0.1 mol/L, equilibrium [H⁺] = 1.3×10⁻³ mol/L, percent ionization = (1.3×10⁻³ / 0.1) × 100% = 1.3% — a fairly weak acid, only about 1.3% of molecules ionized. The relation between percent ionization and acid/base strength / Ka: the lower the percent ionization, the weaker the acid (or base) and the smaller Ka. For dilute solutions, Ka ≈ (percent ionization)² × C₀ (when percent ionization is small), consistent with Ostwald's dilution law. An important and counter-intuitive phenomenon: 'dilution raises percent ionization' — when you dilute a weak acid (C₀ gets smaller), although the absolute [H⁺] falls, the 'proportion' ionized rises (equilibrium shifts toward ionization to keep Ka constant). This explains why very dilute weak acids can have a fairly high percent ionization. Applications: (1) comparing strengths of different weak acids/bases (higher percent ionization at the same concentration means stronger); (2) from percent ionization and initial concentration back-calculating [H⁺] and pH; (3) acid-base equilibrium with Ka; (4) understanding buffering and indicator ionization. Notes: first, ionized and initial concentration must use the same unit (both mol/L), since they cancel to a percentage. Second, for a monoprotic weak acid, ionized concentration equals equilibrium [H⁺] (ignoring water's own ionization); for a monoprotic weak base it equals [OH⁻]. Third, C₀ is the analytical concentration before ionization, not the remaining unionized concentration at equilibrium. Fourth, percent ionization is between 0 (no ionization) and 100% (complete). Fifth, this calculator takes non-negative ionized concentration and initial concentration > 0.
Formula
Percent ionization: % = (ionized concentration / initial concentration C₀) × 100.
Monoprotic weak acid: ionized concentration = equilibrium [H⁺].
Approximation: Ka ≈ (percent ionization)² × C₀ (dilute solution).
Dilution (smaller C₀) raises percent ionization (Ostwald's dilution law).
$$\alpha\% = \dfrac{[\text{ionized}]}{C_0} \times 100$$How to Use
- Enter the equilibrium ionized concentration (for a weak acid, [H⁺], mol/L).
- Enter the initial concentration C₀ of the weak acid/base (mol/L).
- The right panel instantly shows the percent ionization (%).
Approximate percent ionization of common weak acids (~0.1 mol/L, 25 °C)
| Weak Acid | Approx % Ionization | Strength |
|---|---|---|
| Acetic acid CH₃COOH | ≈ 1.3% | Weak |
| Formic acid HCOOH | ≈ 4% | Moderately weak |
| Hydrofluoric acid HF | ≈ 8% | Moderately weak |
| Hydrochloric acid HCl (strong, reference) | ≈ 100% | Strong |
Percent ionization varies with concentration; dilution raises it. Strong acids ionize almost completely.
Case Studies
Percent ionization of a weak acid
0.1 mol/L weak acid, equilibrium [H⁺] = 1.3×10⁻³ mol/L.
% = (1.3×10⁻³ / 0.1) × 100 = 1.3%.
Only 1.3% of molecules ionized — a fairly weak acid.
Comparing two acid strengths
Both 0.1 mol/L: acid A ionizes 1.3%, acid B ionizes 4%.
Acid B has the higher percent ionization, so B is the stronger weak acid (larger Ka).
Percent ionization is the direct indicator of acid strength at the same concentration.
FAQ
What does percent ionization mean?
It is the percentage of ionized molecules relative to the initial molecules of a weak electrolyte: (ionized concentration / initial concentration) × 100%. The higher it is, the more complete the ionization, i.e. the stronger the acid or base.
How to take the ionized concentration of a weak acid?
For monoprotic weak acid HA ⇌ H⁺ + A⁻, the ionized concentration equals the equilibrium [H⁺] (ignoring water's own ionization). For monoprotic weak base, take the equilibrium [OH⁻].
Why does dilution raise percent ionization?
Dilution lowers the initial concentration; to keep Ka constant, equilibrium shifts toward ionization, raising the 'proportion' ionized (though the absolute [H⁺] falls). This is Ostwald's dilution law.
How is percent ionization related to Ka?
The lower the percent ionization, the smaller Ka and the weaker the acid. For dilute solutions there is the approximation Ka ≈ (percent ionization)² × C₀. Both measure weak-acid strength, but Ka does not change with concentration while percent ionization does.
What is the percent ionization of a strong acid?
Strong acids (HCl, HNO₃, H₂SO₄ first step) ionize almost completely in water, so percent ionization is near 100%. Thus the essence of 'strong vs weak acid' is exactly the level of percent ionization.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.