What the calculator does
- Strong acids and bases: complete dissociation, including bases that release two hydroxide ions, such as Ba(OH)₂.
- Weak acids and bases: the exact equilibrium pH from Ka or Kb (or pKa, pKb), with the percentage ionised.
- Buffers: Henderson–Hasselbalch, checked against an exact calculation.
- Conversions: between pH, pOH, [H⁺] and [OH⁻], and between Ka, pKa, Kb and pKb.
The formulas
Weak acids
For HA ⇌ H⁺ + A⁻ with starting concentration C and equilibrium [H⁺] = x:
If x is small compared with C, then x ≈ √(Ka·C). The calculator does not rely on this: it solves the equilibrium exactly, including the contribution of water, and reports whether the approximation would have been acceptable.
Buffers: the Henderson–Hasselbalch equation
This works best when the ratio [A⁻]/[HA] is between 0.1 and 10 and both concentrations are much larger than Ka.
Worked example: 0.10 M acetic acid
Acetic acid has Ka = 1.8 × 10⁻⁵.
- Approximation: x ≈ √(1.8 × 10⁻⁵ × 0.10) = 1.34 × 10⁻³ M, which is 1.3% of C. That is below 5%, so the approximation is valid.
- Exact solution: [H⁺] = 1.333 × 10⁻³ M.
- pH: −log(1.33 × 10⁻³) = 2.88.
- Percentage ionised: 1.33%. Most of the acid stays as HA molecules.
Common mistakes
- Treating a weak acid as strong. For 0.10 M acetic acid, assuming [H⁺] = 0.10 M gives pH 1, not the correct 2.88. (Textbooks often quote 2.87, from the square-root approximation; the exact value is 2.875.)
- Using the approximation when x is not small. For fairly strong weak acids or dilute solutions, x/C can exceed 5%.
- Confusing Ka and pKa when entering values. The calculator lets you choose which you are giving.
- Forgetting that pH + pOH = 14 only at 25 °C. Kw changes with temperature.
Practical applications
- Biology and medicine. Blood is held at pH 7.35–7.45 by the carbonic acid–bicarbonate buffer.
- Food and drink. Acidity affects taste, preservation and safety.
- Environmental science. Acid rain, ocean acidification and soil pH.
- Laboratory work. Preparing buffers for experiments and titrations.
Assumptions and limitations
All calculations are for water at 25 °C (Kw = 1.0 × 10⁻¹⁴) and use concentrations in place of activities. That is accurate for dilute solutions, roughly below 0.1 mol/L, and less so above. Polyprotic acids, such as phosphoric acid with its successive dissociations, are not yet supported. For sulfuric acid the second dissociation is not complete, so “2 H⁺ per formula” overestimates its acidity.