Why does tenfold dilution raise pH by one?

The concentration falls ten times, so its negative logarithm rises by one.

Why can a weak acid not use its concentration directly?

It ionises only partly, so find the hydrogen ion concentration from the pH first.

S4 Chemistry Acids and Alkalis, Paper 2: dilution, weak acids and titration sums

2026-11-02

Ten graded items on converting between pH and concentration, the Ka of a weak acid, and titration and enthalpy calculations.

Focus　Strong acids ionise fully so the concentration is the hydrogen ion concentration; for weak acids find the hydrogen ion concentration first, then use the Ka expression.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S4 Chemistry: Acids, Alkalis and Neutralisation
Level	Four basic, three advanced, two challenge and one error-repair item

02　Questions (10 items)

FoundationWhat is the hydrogen ion concentration, in mol dm^-3, of a solution with pH 4?
FoundationNitric acid is a strong acid that ionises completely. Find the pH of a 0.0010 mol dm^-3 solution.
FoundationFind the pH at 25 degrees of a 0.010 mol dm^-3 sodium hydroxide solution.
FoundationWhat colour is methyl orange in a solution of pH below 3.1?
Intermediate25.0 cm^3 of 0.200 mol dm^-3 sodium hydroxide is neutralised by 0.100 mol dm^-3 hydrochloric acid. What volume is needed?
IntermediateSulphuric acid is a strong diprotic acid. Find the pH of a 0.0050 mol dm^-3 solution.
IntermediateA 0.050 mol dm^-3 solution of a weak acid HA has pH 3.0. Find Ka.
Challenge0.250 g of calcium carbonate, molar mass 100 g mol^-1, dissolves completely in 0.100 mol dm^-3 hydrochloric acid. Find the volume of acid needed.
Challenge40.0 cm^3 of 1.00 mol dm^-3 hydrochloric acid is mixed with 40.0 cm^3 of 1.00 mol dm^-3 sodium hydroxide and the temperature rises by 6.8 degrees. Find the enthalpy of neutralisation, taking density 1.0 g cm^-3 and specific heat capacity 4.2 J g^-1 K^-1.
Error redoA student says diluting a pH 3 acid ten times gives pH 2. Give the correct answer.

03　Answers and one-line notes

#	Answer	One-line note
1	1 x 10^-4 mol dm^-3	pH four corresponds to a hydrogen ion concentration of one times ten to the minus four moles per cubic decimetre.
2	pH 3.0	The acid ionises completely, so the pH is the negative logarithm of 0.0010, which is 3.0.
3	pH 12.0	The pOH is 2.0 and pH plus pOH equals 14 at 25 degrees, so the pH is 12.0.
4	Red	Methyl orange is red in acid and yellow in alkali, changing over roughly pH 3.1 to 4.4.
5	50.0 cm^3	The alkali holds 0.0050 mol, so an equal amount of acid is needed, which takes 50.0 cm^3 of 0.100 mol dm^-3.
6	pH 2.0	Each molecule releases two hydrogen ions, so the concentration is 0.010 mol dm^-3 and the pH is 2.0.
7	About 2.0 x 10^-5 mol dm^-3	The hydrogen ion concentration is 10^-3, so dividing its square by the remaining 0.049 mol dm^-3 gives about 2.0 x 10^-5.
8	50.0 cm^3	The carbonate is 0.0025 mol and needs two moles of acid each, so 0.0050 mol of acid means 50.0 cm^3.
9	About 57.1 kJ mol^-1	The mixture of 80 grams releases 2 284.8 joules and 0.040 mol reacts, giving about 57.1 kilojoules per mole.
10	pH 4	Tenfold dilution cuts the hydrogen ion concentration to a tenth, raising the pH by one to 4.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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