A pharmaceutical chemist reads a titration curve for a new drug candidate and extracts four pieces of information in under a minute — the drug's pKa, its concentration, whether it is a weak acid or base, and which indicator to use for quality control. Every feature of the curve is quantitative data, not decoration.
Use the PDF for classwork, homework or revision. It includes key ideas, activities, questions, an extend task and success-criteria proof.
A research chemist is handed four unlabelled titration curves, each from a different acid-base combination. The curves show pH on the y-axis and volume of NaOH added on the x-axis.
Curve 1 starts at pH 1, has a dramatic vertical jump of nearly 8 pH units at exactly 25 mL, centred precisely on pH 7.
Curve 2 starts at pH 3, rises gradually through a plateau, then has a smaller sharp jump centred above pH 7.
Curve 3 starts at pH 1, has a sharp jump centred below pH 7, slightly smaller than Curve 1.
Curve 4 starts at pH 3 and rises gradually throughout with no discernible sharp jump.
Before reading on, write down: which curve corresponds to which acid-base combination (strong/strong, weak acid/strong base, strong acid/weak base, weak/weak)? What specific features are you using to make each identification?
Every titration curve is a pH-vs-volume graph — but the shape of that graph encodes the identity of the acid and base, the pKa of any weak species, the location of the equivalence point, and the suitability of any indicator, all readable without a calculation if you know what to look for.
Curve 1 — Strong acid + strong base (e.g. HCl + NaOH): starts at low pH (~1 for 0.1 mol/L HCl), no buffer region, then a dramatic near-vertical jump of 6–8 pH units centred precisely at pH 7.00. Symmetric S-shape.
Curve 2 — Weak acid + strong base (e.g. CH₃COOH + NaOH): starts at intermediate pH (~3). Rises gradually through a flat buffer region. At the half-equivalence point, pH = pKa — a horizontal inflection. The jump is smaller, centred at EP pH > 7 (≈ 8.7). Asymmetric.
Curve 3 — Strong acid + weak base (e.g. HCl + NH₃): starts at low pH (~1). No buffer region before EP. Jump centred at EP pH < 7 (≈ 5.3). A buffer region appears after the equivalence point (excess NH₃/NH₄⁺).
Curve 4 — Weak acid + weak base (e.g. CH₃COOH + NH₃): starts at intermediate pH. Rises gradually throughout with no discernible sharp jump — the two buffer regions overlap and blend. No indicator can reliably detect the EP.
The weak acid + strong base curve is the richest of the four — it contains extractable information at every point, and each region of the curve requires a different calculation method.
The curve has five distinct regions:
| Region | What's in solution | Calculation | Key feature |
|---|---|---|---|
| Before titrant | Only HA | [H⁺] = √(Ka × c) | Starting pH < 7 |
| Buffer region | HA + A⁻ | Henderson-Hasselbalch | Gradual rise; flat plateau |
| Half-EP (V_EP/2) | HA = A⁻ (equal moles) | pH = pKa | Read pKa from graph here |
| Equivalence point | Only A⁻ | Kb = Kw/Ka; [OH⁻] = √(Kb × [A⁻]) | Sharp jump ends; pH > 7 |
| After equivalence | Excess NaOH + A⁻ | [OH⁻] = n(excess)/Vtotal | Levels off at high pH |
The dramatic near-vertical pH jump in a strong acid + strong base titration is a quantitative consequence of the mathematics of the pH scale and the complete absence of buffer capacity — understanding this explains why the jump is largest for strong species and absent for weak/weak.
At the equivalence point of a strong/strong titration, the pH changes from ~4 to ~10 across a single drop (~0.05 mL) of titrant. This occurs because: (1) the system has absolutely no buffer capacity — only H⁺ and spectator ions are present; (2) near equivalence, both H⁺ and OH⁻ approach their minimum simultaneously; (3) a tiny excess of either species (0.1%) produces a pH change of ~3 units due to the logarithmic nature of pH.
For a weak acid titration, the buffer region before the EP means that HA and A⁻ coexist all the way up to the equivalence point, resisting pH change. Even 0.1% before equivalence, the buffer is still active — the jump is smaller.
Weak acid + weak base has the smallest (undetectable) jump: both the acid and base buffer regions overlap throughout the titration, continuously resisting pH change.
Every titration curve can be read quantitatively — the equivalence point volume, the equivalence point pH, and the pKa are all extractable from the graph using specific techniques that constitute standalone HSC exam skills.
Reading the equivalence point (V_EP): identify the midpoint of the steepest section of the jump — the point of maximum |dpH/dV|. This is the point of inflection of the sigmoid curve, not the highest or lowest pH point.
Reading the EP pH: read the y-axis at V_EP. For strong/strong: 7.00. For weak acid/strong base: above 7. For strong acid/weak base: below 7.
Reading pKa (weak acid + strong base only): find V_EP, calculate V_EP/2, read pH at that volume. pH at V_EP/2 = pKa.
The five regions of a weak acid + strong base curve each require a different calculation method — identifying which region a given volume falls in, then applying the correct method, is the most comprehensive calculation skill in IQ3.
For a weak acid HA (initial concentration c₀, volume V₀) titrated with NaOH (concentration cb, volume Vb added):
"The equivalence point is always at pH 7." Only for strong acid + strong base. For weak acid + strong base, EP pH > 7 (conjugate base hydrolyses). For strong acid + weak base, EP pH < 7. For weak/weak, there is no sharp EP at all.
"The half-equivalence point is at pH 7." The half-EP is at pH = pKa of the specific weak acid. For acetic acid (pKa = 4.74), the half-EP is pH 4.74. The half-EP has nothing to do with pH 7.
"Strong acid + strong base produces a larger jump because strong acids are more reactive." The jump size is determined by buffer capacity near the EP, not reactivity. Weak acid titrations go to the same completion — the buffer region reduces the jump, not incomplete reaction.
(a) Equivalence point: Jump spans 24.5–26.5 mL. Midpoint = (24.5 + 26.5)/2 = V_EP = 25.00 mL. EP pH = 8.72 (given at 25.00 mL).
(b) pKa: Half-EP volume = V_EP/2 = 12.50 mL. At 12.50 mL, pH = 4.74. Therefore pKa = 4.74 (Ka = 10−4.74 = 1.8 × 10−5 — consistent with acetic acid).
(c) Strong or weak: The acid is weak. Evidence: (1) starting pH = 2.87 > pH 1.00 (expected for 0.1 mol/L strong acid) — partial ionisation; (2) a buffer plateau is present before the EP; (3) EP pH = 8.72 > 7 — conjugate base A⁻ hydrolyses to give OH⁻.
(d) Indicator: EP pH = 8.72. Phenolphthalein (range 8.3–10.0) encompasses this EP pH — changes colourless → faint pink within the sharp jump. Methyl orange (3.1–4.4) is in the buffer region — completely unsuitable. BTB (6.0–7.6) is below EP — unsuitable.
Answers: (a) V_EP = 25.00 mL; EP pH = 8.72. (b) pKa = 4.74 (Ka = 1.8 × 10⁻⁵). (c) Weak acid — starting pH, buffer plateau, EP pH > 7. (d) Phenolphthalein only.
Setup: n(HA) = 0.200 × 0.02500 = 5.00 × 10⁻³ mol. V_EP = 5.00 × 10⁻³/0.200 = 25.00 mL. Half-EP = 12.50 mL.
(a) Start (V = 0): Check Ka/c = 1.4 × 10⁻⁴/0.200 = 7.0 × 10⁻⁴ << 0.0025 ✓
[H⁺] = √(1.4 × 10⁻⁴ × 0.200) = √(2.8 × 10⁻⁵) = 5.29 × 10⁻³ mol/L → pH = 2.28
(b) After 12.50 mL (half-EP): n(OH⁻) = 0.200 × 0.01250 = 2.50 × 10⁻³ mol = n(HA)/2. This is the half-equivalence point. pH = pKa = 3.85
(c) After 18.75 mL (buffer region): n(OH⁻) = 0.200 × 0.01875 = 3.75 × 10⁻³ mol < 5.00 × 10⁻³ → buffer region.
n(HA)_rem = 5.00 × 10⁻³ − 3.75 × 10⁻³ = 1.25 × 10⁻³ mol; n(A⁻) = 3.75 × 10⁻³ mol
pH = 3.85 + log(3.75 × 10⁻³/1.25 × 10⁻³) = 3.85 + log(3.00) = 3.85 + 0.477 = 4.33
(d) Equivalence point (25.00 mL): n(OH⁻) = 5.00 × 10⁻³ mol = n(HA). All HA → A⁻. [A⁻] = 5.00 × 10⁻³/0.05000 = 0.100 mol/L.
Kb = 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 = 8.43 (> 7 ✓)
(e) After 30.00 mL (post-equivalence): n(OH⁻)_total = 0.200 × 0.03000 = 6.00 × 10⁻³ mol. n(excess) = 6.00 × 10⁻³ − 5.00 × 10⁻³ = 1.00 × 10⁻³ mol.
V_total = 55.00 mL = 0.05500 L. [OH⁻] = 1.00 × 10⁻³/0.05500 = 0.01818 mol/L → pOH = 1.74 → pH = 12.26
Answers: (a) 2.28 (b) 3.85 (half-EP = pKa) (c) 4.33 (d) 8.43 (e) 12.26 — tracing the complete curve from start through buffer, half-EP, EP, post-EP.
(a) V_EP and EP pH: The sharpest pH change occurs between 15–25 mL. Midpoint ≈ V_EP = 20.00 mL. EP pH ≈ 7.52 (above 7 — consistent with weak acid + strong base).
(b) Concentration of HA: n(NaOH) at EP = 0.1000 × 0.02000 = 2.000 × 10⁻³ mol = n(HA). c(HA) = 2.000 × 10⁻³/0.02000 = 0.1000 mol/L
(c) pKa and acid identity: Half-EP = V_EP/2 = 10.00 mL. At V = 10.00 mL, pH = 4.57. Therefore pKa ≈ 4.57 (Ka ≈ 2.7 × 10⁻⁵). Comparing: formic (pKa 3.74) ✗; lactic (pKa 3.85) ✗; acetic (pKa 4.74) — closest, within graphical reading uncertainty. Most likely acetic acid.
(d) Indicator: EP pH ≈ 7.5–8.0 (above 7). Phenolphthalein (8.3–10.0) transitions within the sharp jump. BTB (6.0–7.6) marginally possible but phenolphthalein is safer for a basic EP. Methyl orange (3.1–4.4) — completely unsuitable (transitions in the buffer region).
(e) Why pH 3.52 indicates a weak acid: For a strong acid at 0.1000 mol/L, pH = −log(0.1000) = 1.00. The observed starting pH = 3.52 is far above this. [H⁺] = 10⁻³·⁵² = 3.02 × 10⁻⁴ mol/L — only 0.30% ionisation. This partial ionisation is the defining characteristic of a weak acid; a strong acid at this concentration would produce pH 1.00, not 3.52.
Answers: (a) V_EP = 20.00 mL; EP pH ≈ 7.52. (b) c(HA) = 0.1000 mol/L. (c) pKa ≈ 4.57 — closest to acetic acid (pKa 4.74). (d) Phenolphthalein. (e) pH 3.52 >> pH 1.00 expected for strong acid at 0.1 mol/L → only 0.30% ionisation → confirmed weak acid.
| Curve type | Start pH | Buffer before EP | EP pH | Jump size |
|---|---|---|---|---|
| Strong/Strong | Low (~1) | None | = 7.00 | Largest |
| Weak acid/SB | Intermediate | Yes | > 7 | Moderate |
| SA/Weak base | Low | None before EP | < 7 | Moderate |
| Weak/Weak | Intermediate | Yes — throughout | ≈ 7 (no jump) | Absent |
pKa rule: read pH at V_EP/2 → that pH = pKa (weak acid + strong base only)
EP identification: midpoint of steepest section (NOT highest pH; NOT pH 7)
For each description below, identify the curve type and justify using the four diagnostic features.
Curve description 1: starts at pH 1.0; no plateau before the jump; sharp jump centred at pH 5.3 at 25 mL; the pH levels off gradually after the jump rather than reaching a high plateau.
Curve description 2: starts at pH 2.5; clear buffer plateau; at half the EP volume, pH = 3.75; jump ends above pH 9; curve levels off above pH 12.
Curve description 3: starts at pH 3; rises very gradually throughout the entire titration; no region with a gradient clearly steeper than the rest; ends around pH 9.
Use the five-region method and the half-EP rule to answer each problem.
Problem 1: A titration curve for propanoic acid (CH₃CH₂COOH) + NaOH shows an equivalence point at 20.00 mL and pH = 4.89 at 10.00 mL. State the pKa, identify the acid, and name the correct indicator.
Problem 2: 25.00 mL of 0.100 mol/L weak acid HA (Ka = 1.8 × 10⁻⁵) is titrated with 0.100 mol/L NaOH. Calculate the pH after 20.00 mL of NaOH has been added. Show which region this falls in.
Look back at what you wrote in the Think First section. What has changed? What did you get right? What surprised you?
Question 1. A titration curve starts at pH 2.5, has a gradual buffer plateau, pH = 3.75 at the half-equivalence point, and EP at pH 9.2. Which statement correctly identifies all features?
Question 2. A student titrates 25.00 mL of weak acid HA with 0.1000 mol/L NaOH. V_EP = 30.00 mL; pH at 15.00 mL = 5.20. They conclude pKa = 5.20, Ka = 6.3 × 10⁻⁶. Which statement best evaluates this?
Question 3. Under identical conditions, Curve X is for HNO₃ + NaOH; Curve Y is for HNO₂ (Ka = 4.5 × 10⁻⁴) + NaOH. Both reach EP at the same volume. Which correctly describes the differences?
Question 4. A student calculates the pH at the equivalence point of a 0.100 mol/L acetic acid (Ka = 1.8 × 10⁻⁵) + 0.100 mol/L NaOH titration and gets pH = 7.00. What error have they made?
Question 5. A titration of weak acid HA with NaOH gives EP at 25.00 mL and pH = 4.74 at 12.50 mL. A student claims: "I can use methyl orange (range 3.1–4.4) as the indicator because it changes colour at pH 4.1, which is close to the pKa." Evaluate this claim.
Question 6. Explain why the equivalence point pH of an acetic acid + NaOH titration is above 7, and why the equivalence point pH of an HCl + ammonia titration is below 7. Use the term "hydrolysis" and identify the relevant species in each case.
Question 7. 20.00 mL of 0.150 mol/L formic acid (HCOOH, Ka = 1.8 × 10⁻⁴, pKa = 3.74) is titrated with 0.150 mol/L NaOH. Calculate the pH at: (a) the start; (b) the half-equivalence point; (c) the equivalence point.
Question 8. A titration curve for an unknown acid HA with 0.1000 mol/L NaOH shows: V_EP = 20.00 mL; at V = 10.00 mL, pH = 4.57; starting pH = 3.52. (a) Identify whether HA is strong or weak, with three pieces of evidence from the curve data. (b) Calculate the concentration of HA. (c) Determine pKa and Ka of HA from the curve. (d) Select and justify an appropriate indicator for this titration.
Acetic acid + NaOH: At the EP, CH₃COONa is formed. CH₃COO⁻ (conjugate base of weak acid) undergoes base hydrolysis: CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻. OH⁻ is produced → solution is basic → EP pH > 7. (2 marks)
HCl + NH₃: At the EP, NH₄Cl is formed. NH₄⁺ (conjugate acid of weak base) undergoes acid hydrolysis: NH₄⁺ ⇌ H⁺ + NH₃. H⁺ is produced → solution is acidic → EP pH < 7. (2 marks)
n(HCOOH) = 0.150 × 0.02000 = 3.00 × 10⁻³ mol. V_EP = 3.00 × 10⁻³/0.150 = 0.02000 L = 20.00 mL. Half-EP = 10.00 mL.
(a) Start: [H⁺] = √(Ka × c) = √(1.8 × 10⁻⁴ × 0.150) = √(2.7 × 10⁻⁵) = 5.20 × 10⁻³ mol/L → pH = −log(5.20 × 10⁻³) = 2.28 ✓ (1 mark)
(b) Half-EP: pH = pKa = 3.74 ✓ (1 mark)
(c) EP: [HCOO⁻] = 3.00 × 10⁻³/0.04000 = 0.0750 mol/L. Kb = 1.0 × 10⁻¹⁴/1.8 × 10⁻⁴ = 5.56 × 10⁻¹¹. [OH⁻] = √(5.56 × 10⁻¹¹ × 0.0750) = 2.04 × 10⁻⁶ mol/L. pOH = 5.69. pH = 8.31 ✓ (3 marks)
(a) HA is a weak acid — three pieces of evidence: ① Starting pH 3.52 >> pH 1.00 (expected for 0.1 mol/L strong acid) — partial ionisation only; ② a buffer region is implied (gradual rise to EP), absent in strong acids; ③ EP pH is above 7 (confirmed by the context of a 20 mL EP with 0.1 mol/L NaOH giving a basic salt). ✓ (3 marks)
(b) n(NaOH) at EP = 0.1000 × 0.02000 = 2.000 × 10⁻³ mol = n(HA). c(HA) = 2.000 × 10⁻³/0.02000 = 0.1000 mol/L ✓ (1 mark)
(c) Half-EP = V_EP/2 = 10.00 mL. At V = 10.00 mL, pH = 4.57. Therefore pKa = 4.57, Ka = 10⁻⁴·⁵⁷ = 2.7 × 10⁻⁵ ✓ (1 mark)
(d) EP pH is above 7 (weak acid + strong base — conjugate base hydrolyses to give OH⁻). Indicator: phenolphthalein (range 8.3–10.0) — the EP pH falls within the sharp jump above pH 7; phenolphthalein transitions from colourless to faint pink within this jump. Methyl orange (3.1–4.4) is unsuitable — transitions in the buffer region, far from the EP. ✓ (1 mark)
Go back and check your curve identifications. Curve 1 (starts pH 1, large jump at pH 7) = strong acid + strong base. Curve 2 (starts pH 3, buffer plateau, jump above pH 7) = weak acid + strong base. Curve 3 (starts pH 1, jump below pH 7) = strong acid + weak base. Curve 4 (starts pH 3, no sharp jump) = weak acid + weak base. The key diagnostic sequence: (1) starting pH → (2) buffer region before EP → (3) EP pH → (4) jump size.