Acids, bases, and pH

Why this matters

pHA measure of acidity equal to −log10[H⁺]; below 7 is acidic and above 7 is basic at 25 °C. is one of the most measured numbers in science and industry. Blood must stay between about 7.35 and 7.45; drinking-water plants control pH to protect pipes; enzymes in a biotech process stop working outside a narrow range; concrete is strongly basic, which protects the steel inside it. Knowing what pH means, and how to calculate it, lets you read a lab result or a process sheet with confidence.

What acids and bases are

The most useful working definition for this course is Brønsted–LowryThe definition in which an acid donates a hydrogen ion (H⁺) and a base accepts one.:

• An acid donates a hydrogen ion (H⁺, a proton).
• A base accepts a hydrogen ion.

HCl + H2O  ->  H3O+ + Cl-        HCl is the acid (donates H+)
NH3 + H2O  <=> NH4+ + OH-        NH3 is the base (accepts H+)

In water, H⁺ is actually attached to a water molecule as H₃O⁺ (hydronium); chemists write [H⁺] and [H₃O⁺] interchangeably. Square brackets mean "concentration in mol/L".

Strong vs weak

• Strong acidsAcids that ionise completely in water, such as HCl, so [H⁺] equals the acid concentration. ionise completely in water: HCl, HNO₃, HBr, HI, HClO₄ and H₂SO₄ (first proton). For a strong acid, [H⁺] equals the acid concentration.
• Weak acidsAcids that ionise only partly in water, such as acetic acid, so [H⁺] is much lower than the acid concentration. ionise only partly: acetic acid (vinegar), citric acid, carbonic acid. Most molecules stay intact, so [H⁺] is much lower than the acid concentration.
• Strong bases such as NaOH and KOH release OH⁻ completely. Ammonia is a weak base.

"Strong" is about how completely it ionises, not how concentrated it is. A dilute strong acid can have a higher pH than a concentrated weak one.

The pH scale

pH  = −log10[H+]
[H+] = 10^(−pH)

Because it is a logarithm, each pH unit is a factor of 10. pH 3 has ten times more H⁺ than pH 4, and a thousand times more than pH 6.

Water itself ionises a tiny amount: H₂O ⇌ H⁺ + OH⁻. At 25 °C,

Kw = [H+][OH−] = 1.0 × 10^−14
pH + pOH = 14.00

In pure water [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ M, so pH = 7: neutral. Below 7 is acidic, above 7 is basic. (Kw changes with temperature, so "neutral = 7" is exact only at 25 °C.)

Worked examples

1. A strong acid. 0.010 M HCl ionises completely, so [H⁺] = 0.010 = 1.0 × 10⁻² M.

pH = −log10(0.010) = 2.00

2. A non-round concentration. [H⁺] = 2.5 × 10⁻⁴ M.

pH = −log10(2.5 × 10^−4) ≈ 3.60

Sanity check: 2.5 × 10⁻⁴ sits between 10⁻⁴ (pH 4) and 10⁻³ (pH 3), so 3.60 is sensible.

3. A strong base. 0.0010 M NaOH gives [OH⁻] = 1.0 × 10⁻³ M.

pOH = −log10(0.0010) = 3.00
pH  = 14.00 − 3.00  = 11.00

4. Going backwards. A sample reads pH 5.0. Then [H⁺] = 10⁻⁵ M = 0.00001 M.

5. Dilution and pH. Diluting 0.010 M HCl ten times gives 0.0010 M, so the pH rises from 2 to 3. Diluting only ever moves pH toward 7; no amount of water makes an acid basic.

Neutralisation

An acid and a base react to form water and a salt:

HCl + NaOH -> NaCl + H2O

This is the basis of a titrationAdding a base of known concentration to an acid until an indicator changes colour, to work out the acid's concentration., where a base of known concentration is added to an acid until an indicator changes colour, so you can calculate the acid's concentration. You will meet titrations in lab courses.

How pH is measured

• Indicator paper gives a rough colour reading.
• A pH meter with a glass electrode gives two decimal places, but only if it is calibrated against standard buffers first. Calibration is a routine lab task done under the lab's procedures.

Safety note

Strong acids and bases cause serious burns, and some household products react dangerously with each other (for example, mixing bleach with acids or with ammonia releases toxic gases). Never mix cleaning products. Working with acids and bases is learned in a lab under supervision with proper eye and skin protection; employer or institution training is required. See OSHA's laboratory safety guidance. Checked on 2026-10-23.

Common mistakes

• Forgetting the minus sign. log10(0.010) = −2, so pH = −(−2) = 2.
• Treating the scale as linear. pH 2 is 100 times more acidic than pH 4, not twice.
• Using pH directly for a base. Find pOH−log10[OH⁻]; at 25 °C, pH + pOH = 14. from [OH⁻] first, then pH = 14 − pOH.
• Using the acid concentration for a weak acid. That only works for strong acids.

Quick recap

• Acids donate H⁺; bases accept it. Strong means fully ionised.
• pH = −log10[H⁺]; each unit is a factor of 10.
• At 25 °C, pH + pOH = 14 and neutral is 7.

Try it

Open the Do tab: you will write the pH formula in a small Python calculator, then take the quiz.