Percent Ionization Calculator
Percent ionization measures how much of a weak acid has dissociated into ions at equilibrium. For a weak monoprotic acid it depends on both the acid dissociation constant Ka and the initial concentration: more dilute solutions ionize a larger fraction. This calculator solves the equilibrium expression exactly as a quadratic, avoiding the small-x approximation, and returns the hydrogen ion concentration, the percent ionization, and the resulting pH at 25 C. Enter Ka and the initial acid concentration in moles per liter to begin.
Percent ionization formula
equilibrium: x^2 / (C - x) = Ka
quadratic: x^2 + Ka*x - Ka*C = 0
x = [H+] = (-Ka + sqrt(Ka^2 + 4*Ka*C)) / 2
percent ionization = (x / C) * 100
pH = -log10(x)
Ka and the initial concentration must both be greater than zero. The quadratic is solved exactly, so the result holds for strongly ionizing or dilute weak acids.
Percent ionization context
- Percent ionization is the dissociated fraction expressed as a percentage.
- Diluting a weak acid increases its percent ionization.
- Ka is fixed for a given acid and temperature, unlike percent ionization.
- Strong acids approach 100 percent ionization; weak acids are far lower.
- This solver uses the exact quadratic rather than the small-x shortcut.
Percent ionization: frequently asked questions
What is percent ionization?
Percent ionization is the fraction of a weak acid or base that has dissociated into ions at equilibrium, expressed as a percentage. It equals the equilibrium concentration of hydrogen ions divided by the initial acid concentration, times 100.
How do I calculate percent ionization of a weak acid?
For a weak monoprotic acid with dissociation constant Ka and initial concentration C, solve x^2 / (C - x) = Ka for x, the hydrogen ion concentration. Percent ionization is x divided by C times 100. This calculator solves the quadratic exactly without the usual approximation.
Why does dilution increase percent ionization?
By Le Chatelier's principle, diluting a weak acid shifts its dissociation equilibrium toward more ions, so a larger fraction ionizes. The absolute hydrogen ion concentration still falls, but the percentage that has dissociated rises as concentration decreases.
What is the difference between Ka and percent ionization?
Ka is a fixed equilibrium constant that depends only on the acid and temperature. Percent ionization depends on both Ka and the concentration, so the same acid shows different percent ionization at different dilutions even though Ka is unchanged.
Does this use the small-x approximation?
No. This calculator solves the full quadratic x^2 + Ka x - Ka C = 0 exactly, so it stays accurate even for fairly strong weak acids or dilute solutions where the common small-x approximation would break down.
Official sources
- IUPAC Gold Book: acid dissociation and equilibrium constant terminology.
- NIST Chemistry WebBook: aqueous equilibrium reference data.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.