How this calculator works
pH is defined by hydrogen-ion activity. This calculator uses the dilute ideal approximation activity = molar concentration divided by 1 mol/L. Direct ion modes use the entered ion concentration. Strong and weak solution modes solve electroneutrality, dissociation and water autoionization together, including very dilute solutions. Enter a known Ka or Kb and the correct molar mass instead of inferring a constant from an ambiguous chemical name. The default pKw = 14 approximates water at 25 C. Multi-step acid mode supports up to three successively weaker dissociations. Insoluble hydroxides, salts and activity corrections require a fuller model.
Formula
pH = -log10([H+]/1 mol/L); pOH = pKw - pH; [H+][OH-] = Kw. Weak acid: [A-] = C Ka/(Ka + [H+]); weak base: [BH+] = C [H+]/([H+] + Kw/Kb).
Worked example
Hydrogen-ion concentration 1e-6 mol/L gives pH 6 and pOH 8 at pKw 14. A pOH of 3 gives pH 11, hydroxide concentration 0.001 mol/L and hydrogen concentration 1e-11 mol/L.
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Frequently asked questions
Must pH stay between zero and fourteen?
No. That familiar range is not a mathematical limit. Concentrated solutions also need activity corrections.
What if the strong acid is extremely dilute?
The solution calculation includes water ionization, so an acid does not incorrectly become alkaline merely by dilution.
Can I model all dissociation steps of phosphoric acid?
Use multi-step acid mode with all three dissociation constants at the working temperature. The monoprotic model uses only one step.