What this calculator does
A weak acid only partly dissociates, so its pH cannot be read off the concentration the way a strong acid can. A 0.1 mol/L solution with a Ka of 1.8×10⁻⁵, which is acetic acid, gives a pH of 2.88 and is only 1.33% ionised.
Dilution has a counterintuitive effect worth understanding. Diluting that solution tenfold to 0.01 mol/L raises the percent ionised from 1.33% to 4.15%, because there is more water available per acid molecule to accept a proton. The pH still rises, to 3.38, since the absolute ion concentration falls even as the fraction rises.
The formula
An ICE table gives Ka equal to x² over (C₀ − x), where x is the concentration ionised. Solving that quadratic exactly, rather than using the common approximation that x is negligible against C₀, gives x and hence the pH. The exact solution matters when the acid is not very weak or the solution is dilute, which is precisely where the approximation fails.
| Term | Meaning |
|---|---|
| Ka | The acid dissociation constant. Smaller means weaker. |
| ICE table | Initial, Change, Equilibrium: the bookkeeping method for equilibrium problems. |
| Percent ionised | The fraction of acid molecules that have donated a proton. |
| Ostwald dilution law | The result that percent ionisation rises as concentration falls. |
The inputs explained
| Field | What to enter |
|---|---|
| Type | Weak acid uses Ka and returns an acidic pH; weak base uses Kb and returns a basic one. |
| Ka or Kb | Ka or Kb. Acetic acid is 1.8e-5; ammonia as a base is 1.8e-5 for Kb. |
| Initial concentration C₀ (mol/L) | Starting concentration before any dissociation. |
When to use it
Predicting solution pH
A weak acid pH cannot be read from the concentration alone and needs the equilibrium solved.
Designing a buffer
Knowing how far a weak acid dissociates on its own informs the starting point for a buffer.
Teaching equilibrium
The ICE table for a weak acid is the standard first equilibrium calculation.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What does dilution do to ionisation?
The same acid at a range of starting concentrations.
| Starting concentration | pH | % ionised | [H⁺] or [OH⁻] ionised (x) |
|---|---|---|---|
| 0.01 mol/L | 3.38 | 4.15% | 0.00041536 mol/L |
| 0.1 mol/L | 2.88 | 1.33% | 0.00133267 mol/L |
| 1 mol/L | 2.37 | 0.423% | 0.00423365 mol/L |
Questions
Why can I not just take the negative log of the concentration?
Because a weak acid does not fully dissociate. A 0.1 mol/L strong acid gives pH 1 exactly; a 0.1 mol/L acetic acid gives pH 2.88, because only 1.33% of it has released a proton. The equilibrium must be solved to find the actual ion concentration.
Why does dilution increase the percent ionised?
Le Chatelier principle applied to dilution: adding water shifts the equilibrium toward the side with more particles, which is the dissociated side. This is Ostwald dilution law, and it means percent ionisation approaches 100% as concentration approaches zero.
When does the simple approximation fail?
When the ionised fraction is more than about 5% of the starting concentration, which happens for stronger weak acids and for dilute solutions. This calculator solves the quadratic exactly, so it stays correct in those regions where the textbook shortcut does not.
What is the difference between Ka and pKa?
pKa is the negative log of Ka, which puts the numbers on a convenient scale. Acetic acid has a Ka of 1.8×10⁻⁵ and a pKa of 4.74. Smaller Ka means a larger pKa and a weaker acid, so the two run in opposite directions.
For a buffer rather than a pure acid, see the Henderson-Hasselbalch calculator. For converting Ka to pKa, see the pKa calculator.