pH: calculations, the pH scale and why pH matters
pH = −log[H⁺]. On the scale from 0 to 14, below 7 is acidic, 7 is neutral and above 7 is basic. At 25 °C, pH + pOH = 14.
What pH means
The concentration of H⁺ ions can range from about 1 mol L⁻¹ down to 10⁻¹⁴ mol L⁻¹. Such numbers are clumsy, so we use pH, which means power of hydrogen. A logarithm (log) gives the power of ten: log 10⁻³ = −3, and log 10 = 1. pH = −log[H⁺], so if [H⁺] = 10⁻ˣ mol L⁻¹, the pH is x. Because of the minus sign, more H⁺ means a lower pH. In the same way, pOH = −log[OH⁻], and at 25 °C pH + pOH = 14. These simple calculations are for strong acids and bases that are not extremely dilute (not below 10⁻⁶ mol L⁻¹).
Worked example: finding pH
Find the pH at 25 °C of: (a) 0.01 mol L⁻¹ nitric acid, HNO₃; (b) 5 × 10⁻⁴ mol L⁻¹ sulphuric acid, H₂SO₄; (c) 1 × 10⁻² mol L⁻¹ sodium hydroxide, NaOH.
- (a) HNO₃ is a strong acid: HNO₃ → H⁺ + NO₃⁻. One mole gives one mole of H⁺, so [H⁺] = 0.01 = 1 × 10⁻² mol L⁻¹.
- pH = −log(10⁻²) = −(−2) = 2.
- (b) H₂SO₄ → 2H⁺ + SO₄²⁻. One mole gives two moles of H⁺, so [H⁺] = 2 × 5 × 10⁻⁴ = 10 × 10⁻⁴ = 1 × 10⁻³ mol L⁻¹.
- pH = −log(10⁻³) = 3.
- (c) NaOH → Na⁺ + OH⁻, so [OH⁻] = 1 × 10⁻² mol L⁻¹ and pOH = −log(10⁻²) = 2.
- pH = 14 − pOH = 14 − 2 = 12.
(a) pH 2, acidic; (b) pH 3, acidic; (c) pH 12, basic
Worked example: working back from pH or pOH
(a) The pOH of a solution is 4.5. Find its pH and say whether it is acidic or basic. (b) The pH of a solution is 5. Find [H⁺].
- (a) pH + pOH = 14, so pH = 14 − 4.5 = 9.5.
- 9.5 is above 7, so the solution is basic.
- (b) pH = −log[H⁺] = 5, so log[H⁺] = −5.
- So [H⁺] = 10⁻⁵ mol L⁻¹. This is more than 10⁻⁷, so the solution is acidic.
(a) pH 9.5, basic; (b) [H⁺] = 1 × 10⁻⁵ mol L⁻¹
pH of some common substances (approximate; real samples vary)
| Substance | pH | Nature |
|---|---|---|
| Stomach acid | About 1 to 3 | Strongly acidic |
| Lemon juice | About 2 to 3 | Acidic |
| Vinegar | About 2.5 to 3.5 | Acidic |
| Orange juice | About 3 to 4 | Acidic |
| Sour milk | About 4 to 4.5 | Acidic |
| Pure water | 7 | Neutral |
| Blood plasma | About 7.4 (7.35 to 7.45) | Slightly basic |
| Sea water | About 8 | Slightly basic |
| Baking soda solution | About 8 to 9 | Mildly basic |
| Antacid (milk of magnesia) | About 10 | Basic |
| Lime water | About 12 | Strongly basic |
| Caustic soda (4% NaOH) | 14 | Strongly basic |
Activity: pH paper with lab solutions and fruit juices (practical)
- 1Take a little dilute HCl, acetic acid, ammonium hydroxide and sodium hydroxide solution in four test tubes.
- 2Dip a strip of pH paper in each. pH paper is soaked in universal indicator, a mixture of indicators.
- 3★Match the colour with the colour chart on the pack and note the pH.HCl and acetic acid are below 7 (HCl lower); ammonium hydroxide and NaOH are above 7 (NaOH higher)
- 4Crush and filter some apple, orange, tomato and carrot to get their juices. Test each in the same way.Most fruit and vegetable juices are acidic, below 7. Record the values you find
- 5Remember the limits.pH paper gives only an approximate value. A pH meter gives an accurate one
★ key step
Why pH matters in daily life
| Where | What happens |
|---|---|
| Our body | Most reactions in the body take place between pH 7.0 and 7.8. Even a small change upsets them. |
| Acid rain | Rain with pH below 5.6. It lowers the pH of rivers and lakes, so fish and other water life struggle to survive. |
| Soil and plants | Plants grow well only when the soil is neither too acidic nor too basic. |
| Digestion | The stomach makes hydrochloric acid. Too much acid after spicy food causes acidity; an antacid such as milk of magnesia, Mg(OH)₂, neutralises it. |
| Stings | A bee sting and the hairs of the nettle plant inject methanoic acid. Baking soda, a mild base, eases a bee sting; rubbing a dock leaf eases a nettle sting. |
| Tooth decay | Bacteria turn sugar left in the mouth into acid. Below pH 5.5, the acid attacks tooth enamel (calcium phosphate, the hardest substance in the body). |
Farmers and gardeners test soil pH before planting, and add lime if the soil is too acidic. Rinsing your mouth after eating sweets keeps the pH in your mouth above 5.5 and protects your teeth.
1 marks: “The pH of a solution is 3. Is it acidic, basic or neutral?” Acidic, because its pH is below 7.
3 marks: “Calculate the pH of a 1 × 10⁻³ mol L⁻¹ solution of KOH at 25 °C. Is the solution acidic or basic?” KOH is a strong base, so [OH⁻] = 10⁻³ mol L⁻¹. pOH = −log(10⁻³) = 3. pH = 14 − 3 = 11. The solution is basic, as its pH is above 7.
2 marks: “What is acid rain? How does it harm life in rivers?” Rain with a pH below 5.6. When it flows into rivers, the river water becomes acidic, and fish and other water life find it hard to survive.
Low pH, lots of H⁺. pH + pOH = 14 at 25 °C. Teeth suffer below 5.5; rain is acid below 5.6.