Percent Ionization Calculator
Inputs
| Acid Dissociation Constant | 1.8e-5 |
|---|---|
| Initial Concentration | 0.1 M |
Percent Ionization Calculator
Find the percent ionization of a weak monoprotic acid from its acid dissociation constant Ka and initial concentration. Solves Ka = x²/(c − x) exactly for the hydrogen-ion concentration, then reports the percent ionized along with [H⁺] and pH.
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What percent ionization tells you
A weak monoprotic acid does not dissociate completely in water. It sits at an equilibrium:
HA⇌H++A−Percent ionization measures how far that equilibrium lies to the right — what share of the dissolved acid molecules have actually released their proton. A strong acid is essentially 100% ionized; a weak acid usually ionizes only a fraction of a percent to a few percent.
| Symbol | Quantity | Unit |
|---|---|---|
| Ka | Acid dissociation constant | dimensionless |
| c | Initial concentration | mol/L |
| [H⁺] | Equilibrium hydrogen-ion concentration | mol/L |
| α | Percent ionization | % |
The exact equilibrium
Let at equilibrium, leaving of undissociated acid. The acid dissociation constant is:
Ka=c−xx2Rearranging into a quadratic and taking the physically meaningful (positive) root gives an exact expression for the hydrogen-ion concentration:
[H+]=2−Ka+Ka2+4KacThe percent ionization and pH then follow directly:
α=c[H+]×100pH=−log10[H+]This calculator solves the quadratic exactly, so it stays accurate even where the popular shortcut would drift off.
Worked example
Acetic acid has . Prepare a 0.10 mol/L solution. How ionized is it?
[H+]=2−1.8×10−5+(1.8×10−5)2+4(1.8×10−5)(0.10)≈1.33×10−3 mol/L α=0.101.33×10−3×100≈1.33%pH=−log10(1.33×10−3)≈2.87So only about 1.3% of the acetic acid molecules have dissociated; the rest remain intact in solution.
Why dilution raises percent ionization
It is a famous quirk of weak acids: diluting the solution increases the percent ionization, even though the absolute hydrogen-ion concentration drops. Adding water lowers the concentration of every dissolved species, and by Le Chatelier's principle the equilibrium shifts toward the side with more dissolved particles — the ionized side — to partly oppose the change.
The approximation captures the trend: percent ionization scales with . Cut the concentration tenfold and the percent ionized rises by about times. Lower the concentration in the calculator to watch the figure climb.
Stronger acids ionize more
At a fixed concentration, the larger an acid's , the larger its percent ionization. Formic acid () is roughly ten times the of acetic acid and ionizes noticeably more in the same dilution. Pushed far enough — to the strong acids like HCl, where dissociation is effectively complete — percent ionization simply approaches 100%, and the equilibrium treatment is no longer needed.
Frequently Asked Questions (FAQ)
How is percent ionization calculated?
For a weak monoprotic acid HA ⇌ H⁺ + A⁻, set up the equilibrium with x = [H⁺] = [A⁻] and undissociated acid c − x. The acid dissociation constant is Ka = x²/(c − x). Solving this quadratic exactly gives x = (−Ka + √(Ka² + 4·Ka·c)) / 2. The percent ionization is then α = ([H⁺]/c) × 100. This calculator uses the exact quadratic, so it stays accurate even when the common approximation x ≈ √(Ka·c) would fail. As an example, acetic acid (Ka = 1.8 × 10⁻⁵) at 0.10 mol/L is about 1.33% ionized.
What does percent ionization mean?
Percent ionization is the fraction of a weak acid’s molecules that have actually broken apart into ions at equilibrium, expressed as a percentage. A strong acid is effectively 100% ionized — every molecule donates its proton. A weak acid only partly dissociates, so a 0.10 mol/L acetic acid solution sits at roughly 1.33%: the great majority of the acetic acid remains as intact, undissociated molecules. The larger an acid’s Ka, the higher its percent ionization at a given concentration.
Why does percent ionization rise when you dilute a weak acid?
Diluting a weak acid increases its percent ionization, even though the absolute [H⁺] falls. The reason is Le Chatelier’s principle: adding water lowers the concentration of all the dissolved species, and the equilibrium HA ⇌ H⁺ + A⁻ shifts toward the side with more dissolved particles — the ionized side — to partly counteract the dilution. Mathematically, in the approximation α ≈ √(Ka/c), the percent ionized scales with 1/√c, so cutting the concentration tenfold raises the percent ionization by roughly √10 ≈ 3.2 times. Try lowering the concentration in the calculator to see the effect.
How do strong and weak acids differ in ionization?
A strong acid such as HCl or HNO₃ dissociates essentially completely in water, so its percent ionization is close to 100% and its [H⁺] equals its formal concentration. A weak acid such as acetic, formic, or hydrofluoric acid has a small Ka and only partly ionizes — often just a fraction of a percent to a few percent at typical concentrations. This calculator is built for weak monoprotic acids, where the exact equilibrium solution is needed; for a strong acid the percent ionization is simply taken as 100%.
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