Weak Acid pH Calculator
Calculate the pH of a weak monoprotic acid from its Ka and concentration, solved exactly with the equilibrium quadratic — no simplifying assumption.
How it works
[H⁺] = ( −Ka + √(Ka² + 4·Ka·C) ) / 2 · pH = −log₁₀[H⁺]
A weak acid only partially ionizes, so its hydrogen-ion concentration is much less than its formal concentration. Setting up the equilibrium Ka = x²/(C − x) and solving the resulting quadratic gives the exact [H⁺] without the common “x is negligible” shortcut, so the answer stays accurate even for dilute or moderately strong weak acids. Taking the negative logarithm of that concentration gives the pH.
Worked example
For 0.10 M acetic acid (Ka = 1.8 × 10⁻⁵): solving x² + 1.8e-5·x − 1.8e-6 = 0 gives [H⁺] = 1.33 × 10⁻³ M. So pH = −log₁₀(1.33 × 10⁻³) = 2.87, and the acid is about 1.3 % ionized.
Frequently asked questions
Why solve a quadratic instead of using √(Ka·C)?
The shortcut [H⁺] ≈ √(Ka·C) assumes the amount ionized is negligible versus the starting concentration. For dilute or stronger weak acids that assumption fails, so this calculator solves the full quadratic and stays exact.
Does this work for strong acids?
No. Strong acids ionize completely, so [H⁺] simply equals the acid concentration and pH = −log₁₀(C). Use this calculator only for weak, partially ionized acids.
What about polyprotic acids?
This treats a single ionization step (monoprotic). For diprotic or triprotic acids the first ionization usually dominates the pH, but a full treatment requires each successive Ka.
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This calculator is for educational purposes. Double-check important results before acting on them.