Percent Ionization Calculator
Shows the 5% rule failing instead of describing it.
Work out Percent Ionization. Shows the 5% rule failing instead of describing it. Solved exactly, with no shortcut applied.
Acetic acid is 0.000018, or 1.8 × 10⁻⁵
Ionised at equilibrium
1.333%
pH 2.875 · pKa 4.74
Ionisation is 1.33%, under the conventional 5% threshold, so the x ≪ C shortcut was acceptable here — and it still overstates [H⁺] by 0.67%.
How the Percent Ionization Calculator works
Percent ionisation and pH for a weak acid, solved exactly from the quadratic and shown alongside the √(Ka × C) shortcut so the error in the approximation is a number rather than a rule of thumb. The gap widens as the solution gets more dilute, which is the part that surprises people.
Also known as: percent ionisation calculator · percent dissociation of a weak acid · is the 5 percent rule valid · degree of dissociation from ka
The counterintuitive part: dilution raises percent ionisation
Diluting a weak acid raises the pH, because there is less acid. It also raises the fraction of that acid which has dissociated, which surprises people because the two seem to point in opposite directions.
Le Chatelier's principle explains it. Dissociation makes two particles from one, so it is the side favoured by dilution — spreading the same particles through more volume relieves the crowding on the side with fewer of them. Acetic acid at 1 M is about 0.42% ionised; at 0.001 M it is about 12.4%.
Both statements are true at once because they measure different things. Absolute [H⁺] falls with dilution, so pH rises. The fraction of acid molecules that have given up their proton rises. Percent ionisation is a property of the solution at that concentration, not a property of the acid — which is why quoting one without the other means nothing.
Why the shortcut always errs in the same direction
The exact treatment writes Ka = x²/(C − x). The shortcut writes Ka = x²/C, dropping the x from the denominator. Since x is positive, the shortcut's denominator is always too large, so its x is always too large — the approximation overstates [H⁺] every time, and therefore always reports a pH lower than the truth.
The size of the error tracks the size of x relative to C, which is exactly what percent ionisation measures. At 1% ionisation the shortcut is high by about half a percent, invisible against experimental scatter. At 10% it is high by about 5%; at 30% it is high by nearly 20% and the pH is off by most of a decimal place.
This page runs both and prints the gap, so the 5% rule is a measured quantity rather than a remembered threshold. It also means the rule can be seen doing its job: the error crosses into significance right about where the convention places it, which is not a coincidence.
Ka, pKa and what they do not tell you
Ka is an equilibrium constant, so it belongs to the acid and the temperature, not to the solution. pKa is its negative base-10 logarithm, which turns an awkward range — acetic acid at 1.8 × 10⁻⁵, hydrofluoric at 6.8 × 10⁻⁴ — into readable numbers, 4.75 and 3.17. A lower pKa means a stronger acid, and each unit is a factor of ten.
What Ka does not fix is pH, and this is the confusion worth clearing. Two acids with the same Ka at different concentrations have different pH values, and the same acid at two concentrations has two pH values and two percent ionisations. Only Ka stays put.
At the half-equivalence point of a titration, where exactly half the acid is neutralised, pH equals pKa. That is the practical route to measuring Ka: titrate, find the midpoint of the buffer region, read the pH. It is also why the Henderson–Hasselbalch equation reduces to pH = pKa when the acid and conjugate base concentrations match.
Where to go next
The Percent Ionization question rarely arrives on its own. These are the ones that usually come with it:
- Weak Acid pH Calculator — Solved exactly, without the x ≪ C approximation.
- pH Calculator — pH, pOH and both ion concentrations, on a log scale.
- ICE Table Calculator — Solved properly, with no assumption that x is small.
- Speed Distance Time Calculator — Any one of the three from the other two, in four units.
Frequently asked questions
What is percent ionization?
The fraction of the acid that has given up its proton at equilibrium, expressed as a percentage: [H⁺] divided by the initial acid concentration, times 100.
Why does dilution increase percent ionization?
Le Chatelier's principle. Dilution favours the side with more particles, and dissociation makes two ions from one molecule, so a weak acid ionises more completely the more you dilute it — even though the pH still rises.
What is the 5% rule?
The convention that the x ≪ C approximation is acceptable when ionisation stays under 5%. Above that the shortcut overstates [H⁺] enough to matter, which this page shows numerically for whatever values you enter.
Does a strong acid have a percent ionization?
It is effectively 100%. Strong acids dissociate completely in water, so [H⁺] equals the acid concentration and no equilibrium calculation is needed.
Why does the shortcut always overestimate [H⁺]?
Because it ignores the acid consumed by dissociation, leaving the denominator too large. The exact quadratic subtracts x from the initial concentration, and that always pulls the result down.
How do I get Ka from a measured pH?
Convert pH to [H⁺], which equals x. Then Ka = x²/(C − x), using the initial concentration you prepared. Doing it at the half-equivalence point of a titration is easier still, since pH equals pKa there directly.
What is the relationship between Ka and Kb?
Ka × Kb = Kw = 1.0 × 10⁻¹⁴ at 25 °C for a conjugate acid–base pair, so pKa + pKb = 14. A stronger acid necessarily has a weaker conjugate base, which is why the chloride ion is not basic at all.
Why does a buffer resist pH change?
It contains meaningful amounts of both a weak acid and its conjugate base, so added acid is absorbed by the base and added base by the acid. The Henderson–Hasselbalch equation describes the resulting pH, and buffering is strongest when the two are at similar concentrations — that is, near the pKa.
Does percent ionisation apply to weak bases too?
Yes, with Kb and [OH⁻] in place of Ka and [H⁺]. The same dilution behaviour holds: a weak base ionises more completely the more it is diluted, for exactly the same Le Chatelier reason.
What is the common ion effect?
Adding a product ion pushes the equilibrium back towards the undissociated acid, lowering percent ionisation. Adding sodium acetate to acetic acid suppresses its ionisation sharply — which is the mechanism a buffer runs on.
Does Ka change with temperature?
Yes, since it is an equilibrium constant. Published values are almost always for 25 °C, and using one at 37 °C introduces a small error. Kw changes too — water's neutral pH is 6.81 at 37 °C rather than 7.00, which matters in physiology.
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