pH & pOH
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Uses pH = −log[H⁺] and Kw = 1.0×10⁻¹⁴ at 25 °C. Methodology & sources →
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View on Amazon →The pH and pOH Formulas
Water self-ionises so that [H⁺][OH⁻] = Kw = 1.0×10⁻¹⁴ at 25 °C. A solution is acidic when pH < 7, neutral at pH 7, and basic when pH > 7. Strong acids and bases dissociate completely, so [H⁺] (or [OH⁻]) equals the concentration times the number of ions released per formula unit. For the full method see Understanding pH and pOH.
Worked Example — pH of a Strong Acid and a Strong Base
Question: Find [H₃O⁺], [OH⁻], pH, and pOH for (a) 0.00165 M HNO₃, and (b) 5.8 × 10⁻⁴ M Ba(OH)₂.
(a) HNO₃ is a strong acid — it dissociates completely, so [H₃O⁺] = 0.00165 M directly.
pH = −log(0.00165) = 2.78. Since pH + pOH = 14.00 at 25°C, pOH = 11.22, and [OH⁻] = 10⁻¹¹·²² = 6.06 × 10⁻¹² M.
(b) Ba(OH)₂ provides 2 OH⁻ per formula unit, so [OH⁻] = 2 × 5.8 × 10⁻⁴ = 1.16 × 10⁻³ M.
pOH = −log(1.16×10⁻³) = 2.94, so pH = 14.00 − 2.94 = 11.06.
Answer: (a) pH = 2.78, pOH = 11.22. (b) pH = 11.06, pOH = 2.94.
Common Mistakes
- Forgetting the stoichiometric factor for bases like Ba(OH)₂ or Ca(OH)₂. Each formula unit releases 2 OH⁻ ions — the hydroxide concentration is double the salt concentration, not equal to it.
- Sign error in −log. pH = −log[H⁺] — for a concentration less than 1 M, log gives a negative number, and the leading minus sign makes pH positive. Dropping the minus sign gives a negative pH for an ordinary dilute acid.
- pH and pOH swapped. A high [H⁺] (strong acid) gives a low pH and a high pOH — they move in opposite directions.
Frequently Asked Questions
pH = −log₁₀[H⁺]. Take the base-10 log of the hydrogen-ion concentration in mol/L and change the sign. [H⁺] = 1.0×10⁻³ M gives pH = 3.00.
Because [H⁺][OH⁻] = Kw = 1.0×10⁻¹⁴ at 25 °C. Taking −log of both sides gives pH + pOH = 14. This only holds at 25 °C, where Kw has that value.
The pH + pOH = 14 relationship and the simple -log formula assume dilute solutions where activity ≈ concentration. For very concentrated strong acids (above ~1 M), [H+] exceeds 1 M, making -log[H+] negative — the formula is mathematically valid but the simple model becomes less physically accurate at high concentrations.
Only at 25°C, because it comes from Kw = [H+][OH-] = 1.0×10^-14, and Kw is temperature-dependent. At higher temperatures Kw increases, so pH + pOH is slightly less than 14; at lower temperatures it's slightly more. For introductory work, 25°C is the standard assumption.