How to Calculate pH

The definition

pH = −log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in mol/L. Each step of 1 pH unit is a tenfold change in concentration. At 25 °C, pH + pOH = 14.

Strong acids and bases

Strong acids such as HCl ionize completely, so [H⁺] equals the acid concentration. 0.01 M HCl has pH −log(0.01) = 2.00. For a strong base, work out pOH from [OH⁻] and subtract it from 14: 0.01 M NaOH has pOH 2 and pH 12.

Weak acids

A weak acid ionizes only partly, set by its acid dissociation constant K_a. When the acid is not too dilute, [H⁺] ≈ √(K_a × C). For 0.1 M acetic acid, pK_a 4.76: √(10^−4.76 × 0.1) = 1.3 × 10⁻³ M, so pH is about 2.9.

Buffers

A buffer is a weak acid with its conjugate base. The Henderson-Hasselbalch equation gives its pH: pH = pK_a + log([A⁻] ÷ [HA]). For an acetate buffer at pH 5.0 the base-to-acid ratio is 10^{5.0 − 4.76} = 1.74. A buffer works best within about 1 unit of its pK_a.

Calculators

The pH Calculator handles [H⁺], pOH, [OH⁻] and strong or weak acids and bases. The Buffer Calculator gives the ratio and the amounts of acid and base for a buffer of a set concentration and volume.

More worked examples

• Mixing an acid and a base. 50 mL of 0.1 M HCl with 25 mL of 0.1 M NaOH: 5.0 mmol of acid minus 2.5 mmol of base leaves 2.5 mmol of acid in 75 mL, 0.0333 M. pH = −log(0.0333) = 1.48.
• A weak base. 0.1 M ammonia, pKb 4.75: [OH−] ≈ √(10^−4.75 × 0.1) = 1.3 × 10⁻³ M, pOH 2.88, so pH is about 11.1.
• A very dilute acid. 10⁻⁸ M HCl is not pH 8. Water itself gives 10⁻⁷ M H+, which outweighs the acid, so the pH is about 6.98, just below neutral.

Temperature

pH + pOH = 14 holds at 25 °C only. At 37 °C, the sum is about 13.6, so neutral water has a pH of about 6.8. It is still neutral, because [H+] still equals [OH−].

Common mistakes

• Forgetting the dilution after mixing. Concentrations change when two solutions are combined. Work in moles, then divide by the total volume.
• Using millimolar in the log. Convert to mol/L first. 1 mM is 10⁻³ M, pH 3 for a strong acid, not −log(1) = 0.
• An uncalibrated meter. Calibrate a pH meter with at least two buffers that bracket the expected value, such as pH 4 and 7 for acidic samples.