pH Calculator
Compute pH, pOH, and ion concentrations for strong or weak acids and bases. Enter concentration and either Ka/pKa (acid) or Kb/pKb (base). For weak species we use the quadratic solution and flag when the √(K·C) approximation would be reasonable.
Background
Strong acids/bases dissociate (nearly) completely: [H⁺] ≈ n·C or [OH⁻] ≈ n·C. Weak species require equilibrium: for a weak acid HA, Ka = x²/(C − x) ⇒ x = (−Ka + √(Ka² + 4KaC))/2 where x = [H⁺]. For a weak base B, Kb = x²/(C − x) with x = [OH⁻]. We report pH, pOH, and the dissociation fraction α = x/C.
How to use this calculator
- Strong acid/base: enter C and optionally n. We set [H⁺] = n·C or [OH⁻] = n·C.
- Weak acid: enter C and Ka (or pKa). We solve the quadratic exactly for [H⁺].
- Weak base: enter C and Kb (or pKb). We solve the quadratic exactly for [OH⁻].
- We report pH, pOH, [H⁺], [OH⁻], and the dissociation fraction α = x/C.
Assumes 25 °C so pH + pOH = 14.00. Activity effects ignored.
Example Problems & Step-by-Step Solutions
Example 1 (Strong acid)
0.100 M HCl (n=1): [H⁺] = 0.100 → pH = 1.000.
Example 2 (Weak acid)
Acetic acid, C = 0.10 M, pKa = 4.76. Ka ≈ 1.74×10⁻⁵. Solve quadratic for x = [H⁺]; pH ≈ 2.87.
Example 3 (Weak base)
NH₃, C = 0.10 M, pKb = 4.75. Kb ≈ 1.78×10⁻⁵. Solve quadratic for x = [OH⁻]; pOH ≈ 4.75 → pH ≈ 9.25.
Frequently Asked Questions
Q: When is √(K·C) valid?
If α = x/C ≲ 0.05. We always solve the quadratic and report α so you can judge.
Q: Can I handle polyprotic systems?
This tool treats strong species with a stoichiometric n. For true polyprotic equilibria, use a dedicated polyprotic calculator.
Q: Do temperature or activity matter?
At 25 °C we use pH + pOH = 14. Real solutions can deviate due to ionic strength (activity coefficients).
