In 2003, AstraZeneca's analytical chemistry team used titration curve analysis to confirm the pKa of the drug candidate rosuvastatin as 4.58 — critical data for determining its bioavailability and formulation pH. The team read the half-equivalence point directly from the curve's buffer region, identified the equivalence point inflection, and selected phenolphthalein as the quality control indicator — all four decisions made from one graph. Every feature of a titration curve is quantitative data, and this lesson teaches you to read all of it.
Four printable worksheets that build from the foundations up to exam-style questions — start at whatever level suits you.
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?
Four diagnostic checks uniquely identify any curve type
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.
Four curve types: SA+SB (EP = 7, no buffer, largest jump); WA+SB (EP > 7, buffer before EP); SA+WB (EP < 7, buffer after EP); WA+WB (no sharp jump — no reliable indicator). Four diagnostic checks: (1) starting pH low/intermediate; (2) buffer before EP yes/no; (3) EP pH above/at/below 7; (4) jump size. Starting pH ≠ EP pH.
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A titration curve starts at pH 3, has a flat plateau before the EP, and the EP pH is above 7. Which combination is this?
The richest curve — contains pKa, EP, buffer region, and more
We just saw the four diagnostic checks that identify any titration curve type. That raises a question: What specific information can be extracted from each region of the weak acid + strong base curve — the most information-rich of the four? This card answers it → five regions: start (ICE), buffer (H-H), half-EP (pH = pKa), EP (Kb calculation), post-EP (excess NaOH).
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 |
Five regions of WA+SB curve: start (ICE table: [H⁺] = √(Ka×c)); buffer (H-H: pH = pKa + log(n(A⁻)/n(HA))); half-EP at V_EP/2 (pH = pKa); EP (Kb = Kw/Ka; [OH⁻] = √(Kb×[A⁻]); pH = 14 − pOH; EP pH > 7); post-EP ([OH⁻] = n(excess)/V(total)). Each region requires a different calculation method — identify region first.
Add the highlighted point to your notes before the check below.
At the half-equivalence point of a weak acid + strong base titration, which is true?
Buffer capacity determines jump size — not reaction extent
We just saw the five-region structure of the weak acid + strong base curve — a buffer region flattens the rise before the EP. That raises a question: Why does the strong acid + strong base titration produce a jump 6–8 units high while weak acid + strong base produces only 4–6 units? This card answers it → jump size is determined entirely by buffer capacity near the EP, not by reaction extent or reactivity.
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.
Strong/strong jump (~6–8 units) is largest because zero buffer capacity exists near the EP — only H⁺ and spectator ions present. WA+SB jump (~4–6 units) is smaller because the HA/A⁻ buffer region moderates pH change even immediately before the EP. Jump size is NOT about reactivity — it is about buffer capacity near the EP. WA+WB: no measurable jump — overlapping dual buffer regions resist all change.
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The strong acid + strong base titration has the largest pH jump because strong acids are more reactive than weak acids.
V_EP, EP pH, and pKa — three standalone HSC skills
We just saw that buffer capacity determines jump size. That raises a question: Given a titration curve on an HSC paper, what are the exact techniques for reading V_EP, EP pH, and pKa from the graph? This card answers it → V_EP = midpoint of steepest section; EP pH = y-reading at V_EP; pKa = pH at V_EP/2 (weak acid curves only).
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.
V_EP = midpoint of steepest section on the VOLUME axis (not where curve crosses pH 7). EP pH = y-axis reading at V_EP (above 7 for WA+SB; exactly 7 for SA+SB; below 7 for SA+WB). pKa = pH at V_EP/2 — only for weak acid curves; never confused with EP pH or starting pH. State BOTH volume and pH when identifying the EP.
Add the highlighted point to your notes before the check below.
To read the pKa from a weak acid + strong base titration curve, you should:
Identify the region first, then apply the right formula
We just saw how to read V_EP, EP pH, and pKa from a graph. That raises a question: When a question asks you to calculate the pH at a specific volume on a weak acid + strong base titration, what is the systematic method that prevents applying the wrong formula? This card answers it → five-region method: always identify the region first by comparing n(OH⁻) to n(HA), then apply the correct formula for that region only.
An exam question gives you a weak acid (pKa = 4.57, c = 0.1000 mol/L, V = 20.00 mL) titrated with 0.1000 mol/L NaOH and asks you to calculate pH at V = 0 mL, 10.00 mL, 20.00 mL, 25.00 mL, and 30.00 mL. Five volumes, five different regions, five different calculation methods. In 2003, AstraZeneca's analytical team used exactly this five-region logic to verify rosuvastatin's titration data. Identifying the region first is the skill that makes each calculation straightforward.
For a weak acid HA (initial concentration c₀, volume V₀) titrated with NaOH (concentration cb, volume Vb added):
Five-region method — always identify region by comparing n(OH⁻) vs n(HA): Start: [H⁺] = √(Ka×c₀). Buffer: pH = pKa + log(n(A⁻)/n(HA)). Half-EP: pH = pKa. EP: Kb = Kw/Ka; [OH⁻] = √(Kb×[A⁻]); pH = 14 − pOH; pH > 7. Post-EP: [OH⁻] = n(excess)/V(total). pH = 7 at EP is ONLY valid for strong/strong.
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At the equivalence point of a weak acid + strong base titration, which method correctly calculates the EP pH?
A titration curve shows: starting pH = 2.87; at 12.50 mL NaOH (0.100 mol/L), pH = 4.74; sharp jump between 24.5–26.5 mL; at 25.00 mL, pH = 8.72; levels above pH 12 after 30 mL. (a) V_EP and EP pH. (b) pKa. (c) Is the acid strong or weak? (d) Appropriate indicator.
(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.
25.00 mL of 0.200 mol/L lactic acid (Ka = 1.4 × 10⁻⁴, pKa = 3.85) is titrated with 0.200 mol/L NaOH. Calculate pH at: (a) start; (b) after 12.50 mL NaOH; (c) after 18.75 mL NaOH; (d) at equivalence point; (e) after 30.00 mL NaOH.
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 student titrates 20.00 mL of unknown acid HA with 0.1000 mol/L NaOH. Selected readings: V = 0 → pH 3.52; V = 5 → 4.18; V = 10 → 4.57; V = 15 → 4.93; V = 20 → 7.52 (approx. jump midpoint); V = 25 → 11.4; V = 30 → 12.2. (a) V_EP and EP pH. (b) Concentration of HA. (c) Extract pKa and identify acid (formic Ka = 1.8 × 10⁻⁴; lactic Ka = 1.4 × 10⁻⁴; acetic Ka = 1.8 × 10⁻⁵). (d) Suitable indicator. (e) Why does starting pH 3.52 indicate a weak acid?
(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.
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.
(a) SA + SB: pH = 7. Only Na⁺ and Cl⁻ remain — neither hydrolyses water, so the solution is neutral. (b) WA + SB: pH > 7 (typically 8–9). The conjugate base (e.g. CH₃COO⁻) undergoes hydrolysis: CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻, making the solution basic. (c) SA + WB: pH < 7 (typically 5–6). The conjugate acid (e.g. NH₄⁺) hydrolyses: NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺, making the solution acidic.
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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.
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?
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?
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?
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?
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.
1. B — Starting pH 2.5 > pH 1 → partial ionisation → weak acid. Buffer plateau present → confirmed weak acid. Half-EP pH = 3.75 → pKa = 3.75, Ka = 1.78 × 10⁻⁴. EP pH = 9.2 > 7 → conjugate base hydrolyses → consistent with weak acid + strong base.
2. B — The half-EP is correctly at V_EP/2 = 15.00 mL. At this point, n(A⁻) = n(HA); Henderson-Hasselbalch gives pH = pKa + log(1) = pKa. Therefore pKa = 5.20, Ka = 10⁻⁵·²⁰ = 6.3 × 10⁻⁶ — correct and complete analysis.
3. A — HNO₃ is strong → Curve X: starts at pH ~1, no buffer, large jump (~6–8 units), EP at pH 7.00. HNO₂ is weak (Ka = 4.5 × 10⁻⁴, pKa = 3.35) → Curve Y: starts at higher pH, buffer region before EP, smaller jump, EP above pH 7.
4. C — At the EP of a weak acid + strong base, the salt CH₃COONa is formed. CH₃COO⁻ undergoes base hydrolysis: CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻. pH ≈ 8.72 (above 7). The error is applying pH = 7 at all equivalence points.
5. D — The student has confused pKa with the EP pH. The indicator must match the EP pH — not the pKa. Methyl orange (3.1–4.4) transitions at pH ~4.1 — which is in the buffer region, corresponding to only ~18% neutralisation. The EP pH is above 7 and requires phenolphthalein.
Q6 (4 marks): 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)
Q7 (5 marks): n(HCOOH) = 0.150 × 0.02000 = 3.00 × 10⁻³ mol. V_EP = 20.00 mL. Half-EP = 10.00 mL. (a) [H⁺] = √(1.8 × 10⁻⁴ × 0.150) = 5.20 × 10⁻³ → pH = 2.28 ✓ (b) pH = pKa = 3.74 ✓ (c) [HCOO⁻] = 3.00 × 10⁻³/0.04000 = 0.0750 mol/L. Kb = 5.56 × 10⁻¹¹. [OH⁻] = 2.04 × 10⁻⁶. pOH = 5.69. pH = 8.31 ✓
Q8 (6 marks): (a) HA is a weak acid: ① Starting pH 3.52 >> pH 1.00 (expected for strong acid at 0.1 mol/L) — partial ionisation only; ② buffer region implied (gradual rise); ③ EP pH above 7. (b) n(NaOH) = 0.1000 × 0.02000 = 2.000 × 10⁻³ mol = n(HA). c(HA) = 0.1000 mol/L. (c) Half-EP = 10.00 mL. At V = 10.00 mL, pH = 4.57 → pKa = 4.57, Ka = 2.7 × 10⁻⁵. (d) EP pH above 7 (conjugate base hydrolyses). Phenolphthalein (8.3–10.0) — EP pH falls within the sharp jump above pH 7.
Go back and check your curve identifications. Recall AstraZeneca's 2003 rosuvastatin analysis: pKa = 4.58 read from the half-equivalence point of a weak acid + strong base curve. Your curve identification criteria: 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.
A student receives a titration curve produced by adding 0.1000 mol/L NaOH to 25.00 mL of an unknown weak acid. The curve shows: starting pH = 3.28; flat plateau between 0–11 mL; at 7.50 mL, pH = 5.12; equivalence point at 15.00 mL, pH 8.20; levels above pH 12 after 20 mL. Using this curve, (a) identify the acid type and justify from three curve features; (b) calculate the acid concentration; (c) determine pKa and Ka; (d) select and justify the appropriate indicator using the three-step rule; (e) calculate the pH at the equivalence point. (10 marks)
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