Understanding pH and pOH
pH is just a compact way of writing the hydrogen-ion concentration. Because that concentration spans many orders of magnitude, we take its negative logarithm so the numbers stay manageable — turning values like 0.0000001 M into a tidy 7.
The definitions
[H⁺] = 10⁻ᵖᴴ · [OH⁻] = 10⁻ᵖᴼᴴ
A low pH means a high [H⁺] and an acidic solution. A high pH means a low [H⁺] and a basic solution. The negative sign and the logarithm work together so the everyday scale runs roughly 0 to 14, with 7 neutral at 25 °C.
Each unit is a factor of ten
Because the scale is logarithmic, every whole number is a tenfold change in [H⁺]. A solution at pH 3 has ten times the hydrogen-ion concentration of pH 4, and one hundred times that of pH 5. This is why a small pH change can represent a large chemical change.
| pH | [H⁺] (M) | Nature |
|---|---|---|
| 1 | 1 × 10⁻¹ | Strongly acidic |
| 3 | 1 × 10⁻³ | Acidic |
| 7 | 1 × 10⁻⁷ | Neutral (25 °C) |
| 11 | 1 × 10⁻¹¹ | Basic |
| 13 | 1 × 10⁻¹³ | Strongly basic |
Why pH + pOH = 14
Water self-ionises slightly, and at 25 °C the product of the ion concentrations is fixed:
Taking the negative log of both sides gives pH + pOH = 14. This relationship only holds at 25 °C, because Kₙ rises with temperature — at 50 °C neutral water sits closer to pH 6.6, even though it is still neutral.
Strong acids and bases
Strong acids (HCl, HBr, HI, HNO₃, HClO₄, and the first proton of H₂SO₄) dissociate completely, so [H⁺] equals the acid concentration. Strong bases (LiOH, NaOH, KOH, Ca(OH)₂, Ba(OH)₂) dissociate completely too — but Ca(OH)₂ and Ba(OH)₂ release two hydroxide ions per formula unit, so [OH⁻] is twice the concentration.
Worked example
For 0.00165 M HNO₃: [H⁺] = 0.00165 M, so pH = −log(0.00165) = 2.78, and pOH = 14 − 2.78 = 11.22.
For 0.0200 M Ba(OH)₂: each formula unit gives two OH⁻, so [OH⁻] = 0.0400 M, pOH = −log(0.0400) = 1.40, and pH = 14 − 1.40 = 12.60 — the factor of two is easy to miss.
Common mistakes
- Forgetting the factor of two for Ca(OH)₂ and Ba(OH)₂.
- Applying pH + pOH = 14 away from 25 °C, where it no longer holds exactly.
- Treating a weak acid like a strong one — for a weak acid, [H⁺] is much less than the concentration, so the equilibrium constant Ka is needed.
Try it on the pH & pOH Calculator, which converts between [H⁺], [OH⁻], pH and pOH and handles strong acids and bases directly. To see why some acids cannot be treated this way, read Strong vs Weak Acids and Bases.
The General Chemistry Workbook covers strong and weak acids, buffers and titrations with worked examples.
Frequently Asked Questions
pH measures the hydrogen-ion concentration of a solution, written as pH = −log[H⁺]. A lower pH means more hydrogen ions and a more acidic solution, while a higher pH means fewer and a more basic solution.
At 25 °C the product [H⁺][OH⁻] equals Kw = 1.0 × 10⁻¹⁴. Taking the negative logarithm of both sides gives pH + pOH = 14. The relationship shifts at other temperatures because Kw changes.
A strong acid dissociates completely, so the hydrogen-ion concentration equals the acid concentration. Take pH = −log of that concentration directly, with no equilibrium calculation needed.
Each formula unit of Ba(OH)₂ releases two hydroxide ions, so the hydroxide concentration is twice the stated concentration. Forgetting this factor of two is one of the most common pH errors.
Yes. Because the scale is logarithmic, each whole pH unit is a tenfold change in hydrogen-ion concentration. A drop from pH 5 to pH 3 is a hundredfold increase in acidity.