pH calculations and pH in everyday life
If [H⁺] is 10⁻ⁿ, then the pH is n. For a base, find pOH first and subtract it from 14. pH matters in digestion, blood, teeth, soil and rain.
Worked example: pH of an acid
Find the pH of 1 × 10⁻⁵ M hydrochloric acid.
- HCl is a strong acid and ionises fully: [H⁺] = 1 × 10⁻⁵ mol L⁻¹
- Formula: pH = −log₁₀[H⁺]
- pH = −log(10⁻⁵) = 5
pH = 5 (acidic).
Worked example: pH of a base
Find the pH of 0.01 M sodium hydroxide solution.
- NaOH ionises fully: [OH⁻] = 0.01 mol L⁻¹ = 1 × 10⁻² mol L⁻¹
- pOH = −log₁₀[OH⁻] = −log(10⁻²) = 2
- pH = 14 − pOH = 14 − 2 = 12
pH = 12 (basic).
Worked example: from pH to concentrations
The pH of a solution is 6. Find [H⁺], pOH and [OH⁻].
- pH = 6 means −log[H⁺] = 6, so [H⁺] = 1 × 10⁻⁶ mol L⁻¹
- pOH = 14 − pH = 14 − 6 = 8
- pOH = 8 means [OH⁻] = 1 × 10⁻⁸ mol L⁻¹
- Check: [H⁺][OH⁻] = 10⁻⁶ × 10⁻⁸ = 10⁻¹⁴
[H⁺] = 1 × 10⁻⁶ mol L⁻¹, pOH = 8, [OH⁻] = 1 × 10⁻⁸ mol L⁻¹. The solution is acidic.
pH in everyday life
| Where | pH | Why it matters |
|---|---|---|
| Human blood | 7.35 to 7.45 | The body keeps blood in this narrow range; a large change is dangerous. |
| Stomach (gastric juice) | About 2 (strongly acidic) | Hydrochloric acid helps digestion. Too much acid causes acidity; antacids such as Mg(OH)₂ are bases that neutralise it. |
| Mouth and teeth | Enamel dissolves below 5.5 | Bacteria turn sugar left on teeth into acid. Toothpaste is basic and neutralises it. |
| Soil | Depends on the crop | Rice grows in acidic soil, sugarcane in neutral soil and citrus in slightly alkaline soil. Soil that is too acidic is treated with lime (CaO or Ca(OH)₂). |
| Rain | Acid rain is acidic | Gases such as sulphur dioxide and nitrogen oxides dissolve in rain and make it acidic. It harms lakes, plants and buildings, including marble monuments. |
Sweets like mysore pak leave sugar on teeth; mouth bacteria turn it into acid, and enamel starts dissolving below pH 5.5. Rinsing after sweets and brushing with toothpaste, a mild base, protects your teeth.
2 marks: “Calculate the pH of 1 × 10⁻⁶ M HNO₃.” HNO₃ ionises fully: [H⁺] = 10⁻⁶ mol L⁻¹. pH = −log(10⁻⁶) = 6.
4 marks: “The pH of a solution is 9. Find [H⁺], pOH and [OH⁻]. Is the solution acidic or basic?” [H⁺] = 10⁻⁹ mol L⁻¹; pOH = 14 − 9 = 5; [OH⁻] = 10⁻⁵ mol L⁻¹. pH above 7, so basic.
4 marks: “How does pH matter in our body, in farming and in the environment?” Blood 7.35 to 7.45; stomach acid (about pH 2) and antacids; tooth decay below 5.5; each crop needs a suitable soil pH, and lime treats acidic soil; acid rain harms plants and buildings.
Acid: read the power. Base: read the power, then take it from 14.