The big idea: pH is just a convenient way to measure how acidic or basic a solution is, based on its hydrogen-ion concentration, [H+].
The more H+ ions a solution has, the more acidic it is — and the lower its pH.
The scale runs from about 0 to 14 at 25 °C: below 7 is acidic, exactly 7 is neutral, above 7 is basic (alkaline).
Each step of 1 pH unit is a ×10 change in [H⁺]. Below 7 is acidic, 7 is neutral, above 7 is basic (alkaline) — at 25 °C.
Interactive diagram
Explore the labelled diagram, charts and maps for this topic in full study mode.
Each step is ×10: Because pH uses a log scale, every change of 1 pH unit means [H+] changes by a factor of 10.
So a solution of pH 3 has ten times the [H+] of one at pH 4, and 100 times that of pH 5. A small pH change is a big concentration change.
Two given equations link pH and the hydrogen-ion concentration. Use the first to get pH from [H+], and the rearranged form to go back the other way.
- a measure of acidity (no units)
- hydrogen-ion concentration (mol dm⁻³)
- hydrogen-ion concentration (mol dm⁻³)
- the pH of the solution
Worked example — pH from concentration
A solution of hydrochloric acid has [H+] = 0.0100 mol dm⁻³. Calculate its pH.
Solution
- Formula first — take the negative log of [H+]:
- Substitute the value:
- Work it out:
Final answer
pH = 2.00.
Worked example — concentration from pH
A solution has a pH of 3.0. Calculate its hydrogen-ion concentration, [H+].
Solution
- Formula first — use the rearranged equation:
- Substitute the value:
- Work it out — keep the unit:
Final answer
[H⁺] = 1.0 × 10⁻³ mol dm⁻³.
Never wonder what to study next
Get a personalized daily plan based on your exam date, progress, and weak areas. We'll tell you exactly what to review each day.
Strength = degree of dissociation: 'Strong' and 'weak' describe how completely an acid or base splits into ions in water — not how concentrated it is.
- A strong acid (HCl, HNO3, H2SO4) is fully dissociated — virtually every molecule gives up its H+. - A weak acid (CH3COOH, HCN) is only partially dissociated — most molecules stay intact, so far fewer H+ ions form.
A strong acid shows full, one-way dissociation, so we write a single arrow:
A weak acid only partly dissociates and sits in equilibrium, so we use reversible (equilibrium) arrows:
Strong acid (e.g. HCl)
- Fully dissociates — every molecule splits into ions.
- High [H⁺] → lower pH.
- Better electrical conductor.
- Faster reaction (e.g. with a metal).
Weak acid (e.g. CH₃COOH)
- Partially dissociates — only a few molecules split.
- Lower [H⁺] → higher pH.
- Poorer electrical conductor.
- Slower reaction at the same concentration.
How to tell them apart at the same concentration: Take a strong and a weak acid at the same concentration. Because the strong acid produces more H_{+} ions, it has:
- a lower pH, - higher electrical conductivity (more ions carry the current), - a faster reaction with metals, carbonates, etc.
These are the three experimental signs the exam asks you to compare.
How this is tested: R3.1 mixes a quick calculation with a strength comparison.
- Paper 1A (MCQ): a one-step pH ↔ [H+] calculation, or 'which solution is acidic/basic?' from given [H+] or [OH-]. - Paper 2: write a weak-acid dissociation equation, then explain or outline how a weak acid differs from a strong one at equal concentration.
The favourite distinction is why a strong acid has a lower pH than a weak acid of the same concentration — answer in terms of degree of dissociation.
Score the marks: Never confuse strength (degree of dissociation) with concentration (amount dissolved). For the comparison, name a measurable difference: pH, conductivity, or reaction rate.
IB-style question — comparing two acids (a)
Hydrochloric acid (HCl) and ethanoic acid (CH3COOH) solutions both have a concentration of 0.10 mol dm⁻³. (a) Explain why the hydrochloric acid has the lower pH. [2]
How to score the marks
- Mark 1 — dissociation. HCl is a strong acid and is fully dissociated, whereas ethanoic acid is a weak acid and is only partially dissociated.
- Mark 2 — link to pH. The HCl therefore produces a higher [H_{+}], and since pH = −log[H+], a higher [H+] gives a lower pH.
Final answer
HCl fully dissociates (weak acid only partially), so it has a higher [H⁺]; a higher [H⁺] means a lower pH.
IB-style question — telling them apart (b)
(b) Other than measuring pH, outline two experimental ways to distinguish the 0.10 mol dm⁻³ ethanoic acid from the 0.10 mol dm⁻³ hydrochloric acid. [2]
How to score the marks
- Way 1 — conductivity. Measure the electrical conductivity: the HCl conducts better because it has more ions; the ethanoic acid conducts less well.
- Way 2 — reaction rate. Add a small piece of magnesium (or marble chip): the HCl reacts faster (more vigorous fizzing) because of its higher [H+]; the ethanoic acid reacts more slowly.
Final answer
(1) the HCl has a higher electrical conductivity; (2) the HCl reacts faster with a metal/carbonate — both because it has a higher [H⁺].