pH = power of Hydrogen • [H⁺] = hydrogen ion concentration in mol/L • pOH = 14 − pH
What is the pH Scale?
The pH scale was developed in 1909 by Danish chemist Søren Peter Lauritz Sørensen while working at the Carlsberg Laboratory in Copenhagen. He introduced it to measure the acidity of solutions used in brewing. The "p" stands for the German word Potenz (power/potency) and the "H" refers to hydrogen ions (H⁺).
The pH scale typically runs from 0 to 14, although values outside this range are possible for very concentrated acids or alkalis. Each unit change in pH represents a tenfold change in hydrogen ion concentration (the scale is logarithmic). A solution at pH 3 has 10 times more H⁺ ions than one at pH 4, and 100 times more than one at pH 5.
pH Scale Reference
| pH | Classification | Examples | [H⁺] mol/L |
|---|---|---|---|
| 0 | Very strong acid | Battery acid (H₂SO₄) | 1 |
| 1 | Strong acid | Hydrochloric acid (HCl) | 10⁻¹ |
| 2 | Strong acid | Stomach acid, lemon juice | 10⁻² |
| 3–4 | Weak acid | Vinegar, orange juice, wine | 10⁻³–10⁻⁴ |
| 5–6 | Weak acid | Coffee, acid rain, urine | 10⁻⁵–10⁻⁶ |
| 7 | Neutral | Pure water at 25°C | 10⁻⁷ |
| 8–9 | Weak alkali | Baking soda, seawater, blood | 10⁻⁸–10⁻⁹ |
| 10–11 | Moderate alkali | Soap, milk of magnesia | 10⁻¹⁰–10⁻¹¹ |
| 12–13 | Strong alkali | Bleach, oven cleaner | 10⁻¹²–10⁻¹³ |
| 14 | Very strong alkali | NaOH solution, drain cleaner | 10⁻¹⁴ |
Strong vs Weak Acids
The distinction between strong and weak acids is fundamental to understanding pH calculations:
- Strong acids completely dissociate in water. Every molecule of HCl gives one H⁺ and one Cl⁻ ion. So for 0.1 mol/L HCl: [H⁺] = 0.1 mol/L, pH = −log(0.1) = 1.
- Weak acids partially dissociate. Ethanoic acid (CH₃COOH) has Ka = 1.8 × 10⁻⁵. Only a small fraction of molecules release H⁺ at equilibrium. The pH is higher (less acidic) than a strong acid at the same concentration.
Calculating pH for Weak Acids
For a weak acid HA with dissociation constant Ka and initial concentration C (assuming Ka << C, the approximation is valid when less than 5% dissociates):
pH = ½(pKa − log[HA])
Weak Acid pH Example: Ethanoic Acid
Ethanoic acid (vinegar): Ka = 1.8 × 10⁻⁵, pKa = −log(1.8 × 10⁻⁵) = 4.74. Concentration = 0.1 mol/L.
pH = ½(4.74 − log(0.1)) = ½(4.74 + 1) = ½(5.74) = 2.87
Compare with 0.1 mol/L HCl (strong acid): pH = 1. The weak acid gives a significantly higher pH at the same concentration.
Buffer Solutions and Henderson-Hasselbalch
A buffer solution resists pH changes when small amounts of acid or alkali are added. It contains a weak acid and its conjugate base in comparable amounts. The pH of a buffer is given by the Henderson-Hasselbalch equation:
pH = pKa + log([A⁻]/[HA])
When [A⁻] = [HA], the log term equals zero and pH = pKa. A buffer works best within ±1 pH unit of its pKa. Blood is the most important biological buffer system — the bicarbonate buffer (H₂CO₃/HCO₃⁻) maintains blood pH between 7.35 and 7.45.
Buffer pH Example
Ethanoate buffer: pKa = 4.74, [CH₃COO⁻] = 0.15 mol/L, [CH₃COOH] = 0.10 mol/L
pH = 4.74 + log(0.15/0.10) = 4.74 + log(1.5) = 4.74 + 0.176 = 4.92
Kw, pOH and the Water Ionic Product
Water self-ionises according to the equilibrium: H₂O ⇌ H⁺ + OH⁻. The ionic product of water at 25°C is:
Kw = [H⁺][OH⁻] = 1 × 10⁻¹⁴ mol²/L² at 25°C
Taking −log of both sides: pH + pOH = 14 (at 25°C). This means if you know the pH, you instantly know the pOH (and vice versa). Note: Kw changes with temperature, so the neutral point is not always exactly 7 (it is 7 only at 25°C).
Acid-Base Indicators
Indicators are weak acids that change colour depending on pH. Different indicators suit different titration types:
| Indicator | Colour in Acid | Colour in Alkali | pH Range | Use |
|---|---|---|---|---|
| Litmus | Red | Blue | 5–8 | General acid/base test |
| Phenolphthalein | Colourless | Pink/Red | 8.2–10 | Strong base titrations |
| Methyl orange | Red | Yellow | 3.1–4.4 | Strong acid titrations |
| Universal indicator | Red (strong) → Yellow | Blue → Violet | 0–14 | Approximate pH measurement |
pH in Everyday Life
pH has practical importance well beyond the chemistry laboratory:
- Soil pH: Most plants grow best at pH 6–7. Acidic soils (pH < 6) can be limed with calcium carbonate to raise pH. Acid-loving plants like blueberries and heathers prefer pH 4.5–5.5.
- Swimming pools: Pool water should be maintained at pH 7.2–7.6. Too acidic (low pH) corrodes metal fittings and irritates eyes; too alkaline (high pH) reduces chlorine effectiveness and causes cloudy water.
- Brewing and winemaking: Yeast performs best at pH 4.5–5. Brewers often adjust wort pH to optimise enzyme activity during mashing.
- Food preservation: Pickling uses acetic acid (vinegar) to lower food pH below 4.6, inhibiting the growth of harmful bacteria including Clostridium botulinum.
Titrations and pH Curves
A titration is a technique for finding the concentration of an unknown acid or base by reacting it with a known amount of the other. The equivalence point is where moles of acid equal moles of base. The shape of the pH curve depends on whether the acid and base are strong or weak:
- Strong acid + Strong base (e.g. HCl + NaOH): Very steep pH change around equivalence point (pH 7). Use phenolphthalein or methyl orange.
- Weak acid + Strong base (e.g. CH₃COOH + NaOH): Equivalence point above pH 7 (around 8–9). Buffer region present. Use phenolphthalein.
- Strong acid + Weak base (e.g. HCl + NH₃): Equivalence point below pH 7. Use methyl orange.
GCSE and A-Level Chemistry pH Content
For GCSE Chemistry, you need to know: the pH scale, indicators (litmus, universal indicator), neutralisation reactions, and that pH <7 is acidic, pH = 7 is neutral, pH >7 is alkaline.
For A-Level Chemistry, the pH content is significantly more demanding: pH = −log[H⁺] and [H⁺] = 10⁻ᴸᵈ, Kw and pKw, Ka and pKa, weak acid pH calculations, buffer solutions and Henderson-Hasselbalch, indicators as weak acids, pH titration curves and their shapes.