BioDeviceHub

pH Calculator (pH, pOH, Strong and Weak Acids)

Convert between pH, pOH, [H⁺] and [OH⁻], and calculate the pH of a strong acid or base, or a weak acid or base from its concentration and Ka or pKa, at 25 °C.

Formula

pH=−log⁡10[H+];pOH=−log⁡10[OH−]\mathrm{pH} = -\log_{10}[\mathrm{H}^+];\quad \mathrm{pOH} = -\log_{10}[\mathrm{OH}^-]
pH+pOH=14.00(25 ∘C)\mathrm{pH} + \mathrm{pOH} = 14.00\quad(25\,^\circ\mathrm{C})
weak acid:[H+]=[A−]+[OH−],[A−]=CKaKa+[H+]\text{weak acid:}\quad [\mathrm{H}^+] = [\mathrm{A}^-] + [\mathrm{OH}^-],\quad [\mathrm{A}^-] = \dfrac{C K_{\mathrm{a}}}{K_{\mathrm{a}} + [\mathrm{H}^+]}
CC
analytical (total) concentration of the acid or base
Ka, KbK_{\mathrm{a}},\ K_{\mathrm{b}}
acid and base dissociation constants
KwK_{\mathrm{w}}
ion product of water, 1.0 × 10⁻¹⁴ at 25 °C

How it works

pH is the negative logarithm of the hydrogen-ion concentration, and in water the product of [H⁺] and [OH⁻] is fixed at Kw, so pH and pOH add to 14.00 at 25 °C. A strong acid or base is fully dissociated, so its pH follows directly from its concentration, corrected for the water's own ions only when it is extremely dilute, which is why 10⁻⁸ M HCl has a pH of 6.98 and not 8.

A weak acid dissociates only partly. Rather than use the approximation [H⁺] ≈ √(Ka C), which fails for dilute solutions and strong-ish weak acids, the page solves the full charge balance numerically, which is exact for an ideal solution. The textbook approximation is shown for comparison.

Worked example

0.1 M acetic acid, pKa 4.76 (Ka = 1.74 × 10⁻⁵).

  1. Charge balance [H⁺] = [A⁻] + [OH⁻], solved numerically, gives [H⁺] = 1.31 × 10⁻³ M.
  2. pH = −log₁₀(1.31 × 10⁻³) = 2.88, and pOH = 11.12.

pH 2.88, acidic, which matches the standard textbook value for 0.1 M acetic acid.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • An ideal solution at 25 °C, where concentration stands in for activity.
  • Kw = 1.0 × 10⁻¹⁴, so neutral is pH 7.00. At 37 °C neutral is about 6.8.
  • Single-step dissociation (monoprotic acids and bases).

Common mistakes

  • Using pH + pOH = 14 at a temperature other than 25 °C.
  • Applying the √(Ka C) approximation to a dilute solution, or to an acid with a Ka near 10⁻²; use the full solution.
  • Treating a polyprotic acid as monoprotic, which misses the later dissociation steps.

Related tools

Henderson-Hasselbalch CalculatorBuffer pH, base-to-acid ratio, or pKaOpen calculatorpKa, Ka, pKb and Kb ConverterConvert between pKa, Ka, pKb and Kb of a conjugate pairOpen calculatorBuffer Capacity CalculatorBuffer capacity β, and the pH change after adding acid or baseOpen calculatorTitration Curve CalculatorpH against volume for a weak, strong or polyprotic acid titrated with baseOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.