pH of a Weak Acid from Ka

pH=−log⁡10Ka C\mathrm{pH} = -\log_{10}\sqrt{K_a\,C}

Worked example: 0.100 M acetic acid (Ka 1.8e-5) → pH 2.87236 — press Try an example to run it live, then adjust anything.

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Grade 12Grade 12 Chemistry

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pH of a Weak Acid from Ka explained

CKapH

For a weak acid HA the equilibrium expression Ka = x²/(C − x) is a quadratic, but when the acid barely dissociates the x in the denominator is negligible and it collapses to x = [H⁺] = √(Ka·C). Take 0.100 M acetic acid with Ka = 1.8 × 10⁻⁵: [H⁺] = √(1.8 × 10⁻⁶) = 1.34 × 10⁻³ M, so pH = 2.87. That is a thousand times less acidic than 0.100 M HCl at pH 1.00 — the whole difference between a weak acid and a strong one at the same concentration.

The approximation earns its keep but has a known failure mode. It assumes the dissociated fraction is under about 5%, which holds when C is at least a hundred times Ka. Push a fairly strong weak acid to low concentration — 0.0010 M chloroacetic acid, Ka = 1.4 × 10⁻³ — and the square-root shortcut overshoots badly; you must solve the quadratic. It also ignores water's own contribution to [H⁺], which starts to matter for very dilute or very weak acids where the predicted pH creeps above about 6.5.

pH of a Weak Acid from Ka formula

pH=−log⁡10Ka C\mathrm{pH} = -\log_{10}\sqrt{K_a\,C}
Where
  • pH\mathrm{pH}= pH of the solution
  • KaK_a= Acid dissociation constant
  • CC= Formal acid concentration (M)

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