Titration Curves: Interpreting & Analysing All Four Types

Q1 — Sample Band 6 response (8 marks), annotated

Solution X — identification: Strong acid. Evidence: (1) starting pH = 1.0 = –log(0.1000) — exactly consistent with 100% ionisation of 0.1000 mol/L strong acid; (2) no buffer region before EP — no HA/A– pair present; (3) EP pH = 7.00, consistent with a neutral salt (strong acid + strong base forms a salt that does not hydrolyse); (4) jump size ~7 pH units — largest possible, only achievable with no buffer capacity. [1 mark for correct identification with ≥ 3 pieces of evidence]

Solution Y — identification: Weak acid. Evidence: (1) starting pH = 2.87 ≫ 1.00 (expected for strong acid at 0.1 mol/L) — partial ionisation; (2) buffer region present (flat plateau pH 4–5) — HA and A– coexist; (3) EP pH = 8.72 > 7 — conjugate base hydrolyses to produce OH–; (4) jump size ~4 pH units — buffer capacity near EP reduces the jump. [1 mark for correct identification with ≥ 3 pieces of evidence]

pK_a of Y: At V_EP/2 = 12.50 mL, pH = 4.74. Therefore pK_a = 4.74. K_a = 10^–4.74 = 1.8 × 10^–5. This is consistent with acetic acid (CH₃COOH). [1 mark for pK_a = 4.74 and K_a = 1.8 × 10^–5]

Concentrations: For both X and Y: n(NaOH at EP) = 0.1000 × 0.02500 = 2.500 × 10^–3 mol = n(acid). c(acid) = 2.500 × 10^–3 / 0.02500 = 0.1000 mol/L for both. [1 mark]

Indicators: X (strong/strong, EP = pH 7.00): any indicator transitioning between pH 4–10 is suitable; bromothymol blue (pH 6.0–7.6) is ideal, centred at 7.00. Y (weak acid/strong base, EP = pH 8.72): phenolphthalein (pH 8.3–10.0) — transitions within the jump above pH 7. Methyl orange (3.1–4.4) would be entirely unsuitable for Y — it transitions in the buffer region. [1 mark for both indicators with justification]

pH meter justification: A NATA laboratory would use a pH meter (potentiometric method) because: (1) it detects the equivalence point for any acid type, including weak/weak where no indicator is usable; (2) it provides a complete titration curve, revealing not just concentration but also acid identity (strong vs weak) and pK_a — confirming what contaminants are present; (3) it eliminates subjective colour-change interpretation; (4) it provides traceable, digital data required for NATA accreditation records. [1 mark for at least two valid reasons]

Marking criteria summary.

• 1 mark — Correctly identifies Solution X as strong acid with ≥ 3 pieces of evidence from the table.
• 1 mark — Correctly identifies Solution Y as weak acid with ≥ 3 pieces of evidence.
• 1 mark — Correctly reads pK_a = 4.74 from the half-EP (V = 12.50 mL) and calculates K_a = 1.8 × 10^–5.
• 1 mark — Correctly calculates c = 0.1000 mol/L for both (with correct working).
• 1 mark — Names a suitable indicator for X with justification (EP pH 7, any mid-range indicator acceptable).
• 1 mark — Names phenolphthalein for Y and justifies using EP pH 8.72 vs transition range.
• 1 mark — Explains why a pH meter is preferred, citing at least two specific advantages relevant to NATA laboratory practice.
• 1 mark — Response is structured clearly with explicit region identification or equivalent analytical framework throughout (award for overall quality of analysis).

Q2 — Sample Band 6 response (7 marks), annotated

Overall judgement: The claim is almost entirely incorrect. It contains one partially defensible element but commits two major scientific errors that would cause systematic failures in real titrations.

What is partially defensible: Methyl orange is indeed useful for certain strong acid + strong base titrations (such as HCl + NaOH), where the equivalence point jump covers pH ~4–10, passing through methyl orange’s range (3.1–4.4). However, this is incidental — not because 4 is the “average pK_a” of weak acids. [1 mark]

Error 1 — Confusing pK_a with equivalence point pH: The claim states that the equivalence point of a weak acid + strong base titration “occurs near pH 4–5.” This is false. The equivalence point is determined by the hydrolysis of the conjugate base A–, which produces OH– and drives the EP above pH 7. Specific example: acetic acid (pK_a = 4.74) + NaOH has EP pH = 8.72 (calculated in the lesson using K_b of CH₃COO–). Lactic acid (pK_a = 3.85) + NaOH has EP pH = 8.43. In neither case is the EP near pH 4–5 — these pH values are in the buffer region, not at the equivalence point. Methyl orange (3.1–4.4) would change colour at approximately 18–25% neutralisation, not at equivalence — a catastrophic underestimate of acid concentration. [2 marks]

Error 2 — “Phenolphthalein is only needed for bases”: Phenolphthalein is the correct indicator for weak acid + strong base titrations (not just for bases). Because the EP pH is 8–9, phenolphthalein (range 8.3–10.0) transitions within the sharp pH jump. This is a standard HSC application. [1 mark]

Experimental detection: A student could record a full pH meter titration curve for acetic acid + NaOH. The curve would show: (a) the sharp jump centred at pH 8.72 (not 4–5); (b) methyl orange changing colour at approximately 5 mL of NaOH in a 25 mL EP titration — far before the sharp jump; (c) phenolphthalein changing at approximately 24.5–25.5 mL, within the sharp jump. Overlaying the indicator transition ranges on the derivative (dpH/dV) plot would confirm which indicator matches the EP. [1 mark]

Defensible reformulation: “Indicator selection for acid-base titrations must be based on the equivalence point pH, not the pK_a of the acid. For a weak acid + strong base titration, the equivalence point pH is above 7 (typically 8–9) because the conjugate base undergoes hydrolysis to produce OH–. Phenolphthalein (pH 8.3–10.0) is therefore the appropriate indicator; methyl orange (pH 3.1–4.4) changes colour in the buffer region, far from the equivalence point, and is unsuitable. An indicator is appropriate when its transition range falls within the sharp pH jump centred at the equivalence point.” [2 marks for full, accurate reformulation]

Marking criteria.

• 1 mark — States an overall evaluative judgement (claim is largely/almost entirely incorrect).
• 1 mark — Identifies the one partially defensible element (methyl orange is usable for some strong/strong titrations where the jump includes pH 3–4).
• 1 mark — Correctly identifies Error 1 (EP of weak acid + SB is above 7, not 4–5), with a specific named example and pK_a/EP pH values.
• 1 mark — Correctly explains why using methyl orange would fail in practice (changes colour in buffer region, giving a wrong volume and underestimated concentration).
• 1 mark — Correctly identifies Error 2 (phenolphthalein is appropriate for weak acid + SB titrations because its range matches the EP pH > 7).
• 1 mark — Describes a credible experimental method (titration curve via pH meter) that would detect the error, citing specific evidence (indicator colour change vs EP location on the curve).
• 1 mark — Provides a chemically defensible reformulated statement linking indicator selection to equivalence point pH (not pK_a), including the general rule.

Q3 — Five-region method answers

(a) Setup: n(lactic acid) = 0.200 × 0.02000 = 4.00 × 10^–3 mol. V_EP = 4.00 × 10^–3 / 0.200 = 0.02000 L = 20.00 mL. [1 mark]

(b) Start (Region 1: only HA): [H⁺] = √(K_a × c) = √(1.4 × 10^–4 × 0.200) = √(2.8 × 10^–5) = 5.29 × 10^–3 mol/L. pH = –log(5.29 × 10^–3) = 2.28. [2 marks: 1 for correct formula/region identification; 1 for correct pH]

(c) EP (Region 4: only A–): n(A–) at EP = 4.00 × 10^–3 mol. V_total = 0.02000 + 0.02000 = 0.04000 L. [A–] = 4.00 × 10^–3/0.04000 = 0.100 mol/L. K_b = K_w/K_a = 1.0 × 10^–14/1.4 × 10^–4 = 7.14 × 10^–11. [OH^–] = √(7.14 × 10^–11 × 0.100) = 2.67 × 10^–6 mol/L. pOH = 5.57. pH = 14 – 5.57 = 8.43 (> 7, consistent with weak acid + SB). [2 marks: 1 for correct K_b/[A–] method; 1 for correct pH = 8.43]

(d) Post-EP at 25.00 mL NaOH (Region 5: excess NaOH): n(NaOH) total = 0.200 × 0.02500 = 5.00 × 10^–3 mol. n(excess NaOH) = 5.00 × 10^–3 – 4.00 × 10^–3 = 1.00 × 10^–3 mol. V_total = 0.02000 + 0.02500 = 0.04500 L. [OH^–] = 1.00 × 10^–3/0.04500 = 0.02222 mol/L. pOH = –log(0.02222) = 1.65. pH = 14 – 1.65 = 12.35. [2 marks: 1 for correct excess OH^– calculation; 1 for correct pH = 12.35]