Percent Ionization Calculator
Find how much of a weak acid dissociates by computing its percent ionization, hydrogen-ion concentration, and pH from Ka and initial concentration.
mol/L
Fraction of the weak acid that has dissociated
1.33%
ionizedIonized
1.3%
Un-ionized
98.7%
- 1
Discriminant (Ka² + 4·Ka·C0)
0.000018² + 4 × 0.000018 × 0.1 = 0.0000072 - 2
√(discriminant)
√(0.0000072) = 0.00268334 - 3
[H⁺] concentration (x)
(−0.000018 + 0.00268334) ÷ 2 = 0.001333Positive root of the quadratic Ka·(C0 − x) = x². - 4
Percent ionization
(0.001333 ÷ 0.1) × 100 = 1.333
How does this calculator work?
For a weak acid, solve x² + Ka·x − Ka·C0 = 0 for x = [H⁺] = (−Ka + √(Ka² + 4·Ka·C0)) / 2. Percent ionization is (x / C0) × 100 and pH = −log10(x). Larger Ka or lower initial concentration C0 gives a higher percent ionization.
Formula
How this is calculated
A weak acid HA partially dissociates in water: HA ⇌ H⁺ + A⁻. The equilibrium expression is Ka = x² / (C0 − x), where x is the equilibrium concentration of H⁺ (and of A⁻), Ka is the acid dissociation constant, and C0 is the initial acid concentration in mol/L. This calculator solves the full quadratic rather than using the simplifying assumption C0 − x ≈ C0, so it stays accurate even when ionization is significant.
Rearranging Ka·(C0 − x) = x² gives x² + Ka·x − Ka·C0 = 0, whose positive root is x = (−Ka + √(Ka² + 4·Ka·C0)) / 2. That root equals [H⁺]. Percent ionization is the dissociated fraction, (x / C0) × 100, and pH = −log10([H⁺]). The donut chart splits the initial concentration into ionized (x) and un-ionized (C0 − x) portions.
Assumptions: a single monoprotic weak acid in pure water at 25 °C, ideal behavior (activities ≈ concentrations), and autoionization of water neglected, which is valid when [H⁺] greatly exceeds 1×10⁻⁷ mol/L. Ka and C0 must both be positive. As C0 decreases or Ka increases, percent ionization rises toward 100%.
Frequently asked questions
The approximation assumes x is tiny compared with C0. When ionization exceeds about 5% (dilute solutions or larger Ka) that assumption fails, so this tool solves the exact quadratic for reliable results.
By Le Chatelier’s principle, dilution shifts the equilibrium toward more dissociation. Although [H⁺] drops, the fraction of acid molecules that ionize rises as C0 decreases.
No. Water autoionization is neglected, which is accurate when [H⁺] is well above 1×10⁻⁷ mol/L. For extremely dilute or very weak acids the true pH will be slightly closer to 7.
Also known as
TG we-Calculate Editorial Team. (2026). Percent Ionization Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/percent-ionization-calculator
TG we-Calculate Editorial Team. "Percent Ionization Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/percent-ionization-calculator.
TG we-Calculate Editorial Team, "Percent Ionization Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/percent-ionization-calculator
@misc{wecalculate_percent_ionization_calculator, title = {Percent Ionization Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/percent-ionization-calculator}}, year = {2026}, note = {TG we-Calculate} }
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