Weak Acid pH Calculator
pH of a solution of a weak acid such as acetic, citric or formic acid from its pKa and concentration, solved exactly rather than by the usual shortcut.
Results
The dashed line marks the value you entered.
What this tool does
A weak acid only partly gives up its hydrogen ions, so its pH depends on both the pKa and the concentration. Solving the equilibrium exactly needs a quadratic, which is why textbooks use the shortcut ½(pKa − log C); it is fine while less than about 5 % of the acid dissociates and drifts off for dilute solutions or stronger acids — both values are shown so you can see the gap. Diluting a weak acid makes it dissociate more, which the chart shows. Water's own ions are ignored, so very dilute solutions (below about 10⁻⁶ mol/L) are not reliable.
Formula
Ka = x² ÷ (C − x) ⇒ [H⁺] = (−Ka + √(Ka² + 4 Ka C)) ÷ 2 · pH = −log₁₀[H⁺]
Variables
| Symbol | Meaning | Unit |
|---|---|---|
pk | pKa of the acid | — |
c | Weak acid concentration | mol/L |
PH | pH | — |
H | Hydrogen ion concentration [H⁺] | mol/L |
DS | Share of molecules dissociated | % |
AP | pH by the usual shortcut ½(pKa − log C) | — |
KA | Dissociation constant Ka | — |
Worked example
- pKa of the acid4.76
- Weak acid concentration0.1 mol/L
- pH2.883
- Hydrogen ion concentration [H⁺]0.0013096 mol/L
- Share of molecules dissociated1.310 %
- pH by the usual shortcut ½(pKa − log C)2.880
- Dissociation constant Ka0.000017378
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.