pH calculator, acids and bases
Exact pH of strong and weak acids and bases, water autoionisation included, with the gap to the textbook approximation.
Result
1
- Calculation
- [H⁺] = (C + √(C² + 4·Kw)) / 2, exact balance, autoionisation included
- Textbook approximation
- pH 1 (gap 4.343 × 10⁻¹³)
- pOH
- 13
- [H₃O⁺]
- 0.1
- [OH⁻]
- 1 × 10⁻¹³
Notes (2)
Acidic solution: pH 1, below neutrality (7).
At 25 °C, pKw is 14.00 and neutral pH is 7.00. Neutral pH equals pKw/2: 6.15 at 100 °C.
Calculation, assumptions and sources
OverviewExact pH of an acid or a base, strong or weak.
Exact pH of an acid or a base, strong or weak. For a strong acid, water autoionisation is included: at 10⁻⁸ mol/L the pH is 6.98, not 8. For a weak acid, the exact quadratic is solved, with the degree of dissociation α and the gap to the √(Ka·C) approximation. pKw is editable; neutral pH is pKw/2.
Method & formulaspH = −log₁₀[H₃O⁺], pH + pOH = pKw
Both textbook formulas are limiting cases of the exact calculation. For a strong acid, [H⁺] = C omits the protons supplied by water, 10⁻⁷ mol/L: negligible at 0.1 mol/L, they dominate at 10⁻⁸ mol/L, and the formula stops being usable near 10⁻⁶ mol/L. For a weak acid, √(Ka·C) assumes the undissociated acid concentration stays equal to C, which holds while α is small. The exact forms are the positive roots of the complete quadratic balances.
- Degree of dissociation α
- the fraction of acid dissociated, [H⁺]/C. The √(Ka·C) approximation is accepted for α < 5%. α grows on dilution (Ostwald’s dilution law).
- Neutrality
- the state where [H⁺] = [OH⁻], that is pH = pKw/2: 7.00 at 25 °C, 6.15 at 100 °C (pKw ≈ 12.3).
- Analytical concentration
- concentration of solute introduced, distinct from the equilibrium concentration; for a weak acid the latter is far smaller.
Validity domainThe model handles a single monoacid or monobase in aqueous solution.
The model handles a single monoacid or monobase in aqueous solution. Activities are taken equal to concentrations, ionic strength neglected; the error becomes significant beyond ~0.1 mol/L. For H₂SO₄, only the first acidity, which is complete, falls under the “strong acid” mode; polyprotic acids, mixtures, buffers and titrations are not covered. The pKa is entered from whichever table you use.