Chemistry • Year 12 • Module 6 • Lesson 8
pH and pOH: Calculations for Strong Acids & Bases
Lock in the core formulas, the logarithmic meaning of pH, and the step-by-step methods for strong acid and strong base calculations before attempting multi-step problems.
1. Term–definition match
The ten definitions below are shuffled. In the right-hand column write the matching term from this list: pH, pOH, [H⁺], [OH⁻], K₩, strong acid, strong base, diprotic acid, pOH route, anti-log. 10 marks
| # | Definition (shuffled) | Matching term |
|---|---|---|
| 1.1 | The negative base-10 logarithm of the hydrogen ion concentration; decreases as [H⁺] increases. | |
| 1.2 | The negative base-10 logarithm of the hydroxide ion concentration; at 25°C: pH + this value = 14. | |
| 1.3 | An acid that donates two protons per formula unit in dilute aqueous solution (e.g. H₂SO₄). | |
| 1.4 | An acid or base that is assumed to be 100% ionised in dilute aqueous solution. | |
| 1.5 | The molar concentration of hydrogen ions in solution; equals 10−pH. | |
| 1.6 | The molar concentration of hydroxide ions in solution; equals 10−pOH. | |
| 1.7 | The ion-product constant of water equal to 1.0 × 10−14 mol²/L² at 25°C; equals [H⁺][OH⁻]. | |
| 1.8 | The calculation method used for strong bases: find [OH⁻], calculate pOH, then subtract from 14. | |
| 1.9 | A substance that fully dissociates in dilute aqueous solution to produce hydroxide ions (e.g. NaOH, Ca(OH)₂). | |
| 1.10 | The operation 10−pH that recovers [H⁺] from a known pH value. |
2. True or false — with correction
Circle T or F for each statement. If false, write the corrected version on the line provided. 10 marks (1 T/F + 1 correction where needed)
2.1 A solution at pH 3 has ten times more H⁺ ions than a solution at pH 4. T / F
2.2 For a 0.050 mol/L solution of H₂SO₄ (dilute), [H⁺] = 0.050 mol/L. T / F
2.3 pH + pOH = 14 is valid at all temperatures. T / F
2.4 For a strong base in aqueous solution, the pH must be greater than 7 at 25°C. T / F
2.5 Diluting a strong acid with water converts it into a weak acid. T / F
3. Function recall
Answer each question in 1–2 sentences using precise chemical terminology. 10 marks (2 each)
3.1 Why is the pH scale logarithmic rather than linear? What does a difference of 2 pH units mean in terms of [H⁺]?
3.2 Why must [H⁺] be multiplied by 2 when calculating the pH of a dilute H₂SO₄ solution?
3.3 Why must [OH⁻] be multiplied by 2 when calculating pH from a Ca(OH)₂ solution?
3.4 What is the physical reason that pH cannot rise above 7 when diluting a strong acid at 25°C?
3.5 In a mixing calculation, why must V(total) = V(acid) + V(base) be used rather than V(acid) alone?
4. Fill in the blanks
Complete the passage below using words from the word bank. Each word or phrase is used once. 8 marks
The pH scale is _____________ (1), which means each unit change in pH corresponds to a tenfold change in [H⁺]. A pH difference of 2 units corresponds to a _____________-fold (2) change in [H⁺]. The concentration of hydrogen ions can be recovered from a pH value using the expression [H⁺] = _____________ (3). At 25°C the relationship pH + _____________ (4) = _____________ (5) holds because K₩ = 1.0 × 10−14 mol²/L². Ca(OH)₂ is a strong diprotic base, releasing _____________ (6) OH⁻ ions per formula unit. When a strong acid and a strong base are mixed at equivalence, pH = 7.00 because the _____________ (7) present (e.g. Na⁺ and Cl⁻) do not hydrolyse. To correctly calculate the concentration of the excess species after mixing, divide by _____________ (8), the sum of both volumes.
5. Build a concept map
Draw labelled arrows between the six terms below to show how they connect. Each arrow must carry a linking phrase (e.g. “is calculated from”, “converts to”, “sums to”). Aim for at least 6 labelled arrows. 6 marks
Supplied terms: pH · [H⁺] · pOH · [OH⁻] · K₩ · strong acid concentration.
Q1 — Term–definition match
1.1 pH • 1.2 pOH • 1.3 diprotic acid • 1.4 strong acid (applies to strong base equally; accept either) • 1.5 [H⁺] • 1.6 [OH⁻] • 1.7 K₩ • 1.8 pOH route • 1.9 strong base • 1.10 anti-log.
Q2 — True / false
2.1 True. Each 1 pH unit = 10× change in [H⁺]; pH 3 has 10× more H⁺ than pH 4.
2.2 False. Correction: H₂SO₄ is a diprotic acid donating 2 H⁺ per formula unit in dilute solution, so [H⁺] = 2 × 0.050 = 0.10 mol/L.
2.3 False. Correction: pH + pOH = 14 applies only at 25°C where K₩ = 1.0 × 10−14. At different temperatures, pH + pOH = pK₩ at that temperature.
2.4 True. A strong base produces [OH⁻] > [H⁺], so [H⁺] < 10−7 mol/L, giving pH > 7.
2.5 False. Correction: dilution decreases concentration but does not change the strength of an acid. A diluted strong acid (e.g. HCl) is still 100% ionised at any dilution — it has lower concentration, not partial ionisation.
Q3.1 — Logarithmic scale
The range of [H⁺] in aqueous solution spans ~14 orders of magnitude (1 mol/L to 10−14 mol/L), so a logarithmic scale compresses this into a manageable 0–14 range. A difference of 2 pH units corresponds to a 102 = 100-fold difference in [H⁺].
Q3.2 — H₂SO₄ factor of 2
H₂SO₄ is a diprotic acid that donates 2 H⁺ ions per formula unit upon complete ionisation in dilute solution. Therefore [H⁺] = 2 × c(H₂SO₄), not c(H₂SO₄).
Q3.3 — Ca(OH)₂ factor of 2
Ca(OH)₂ is a strong diprotic base, releasing 2 OH⁻ ions per formula unit upon complete dissociation. Therefore [OH⁻] = 2 × c(Ca(OH)₂).
Q3.4 — Dilution limit
Water autoionises to produce [H⁺] = [OH⁻] = 1.0 × 10−7 mol/L at 25°C. As the acid is diluted, its contribution to [H⁺] decreases toward this background level. pH asymptotically approaches 7 but can never reach or exceed 7 because the water contribution sets a lower bound on [H⁺].
Q3.5 — V(total) in mixing
When two solutions are combined, the excess species is distributed throughout the combined volume. Using only V(acid) or only V(base) underestimates the volume and overestimates the concentration of the excess species, producing a pH that is too extreme.
Q4 — Fill in the blanks
(1) logarithmic • (2) 100 • (3) 10−pH • (4) pOH • (5) 14 • (6) two • (7) spectator ions • (8) V(total).
Q5 — Sample concept map
A correct map should include labelled arrows such as:
- pH — is calculated from → [H⁺] (pH = −log[H⁺])
- [H⁺] — is recovered from pH by → pH ([H⁺] = 10−pH)
- pH — sums with → pOH (pH + pOH = 14 at 25°C)
- [H⁺] — multiplied by [OH⁻] gives → K₩
- K₩ — links → [OH⁻] (K₩ / [H⁺] = [OH⁻])
- strong acid concentration — directly equals (for monoprotic) → [H⁺]
Accept any biologically valid linking phrases that respect causal/mathematical direction. Award 1 mark per correctly labelled arrow, max 6.