★ Consolidation — In 2021, the NSW NESA HSC Chemistry marking centre noted that 38% of students incorrectly placed the equivalence point at pH 7 on a weak acid/strong base titration curve — and a further 21% chose phenolphthalein for a strong acid/weak base titration. Four students attempt the same curve below. Only one gets all three identifications correct. Before reading on — can you identify who, and precisely diagnose what each of the others got wrong?
Flash-drill the key distinctions that separate Band 4 from Band 6 responses.
Four printable worksheets that build from the foundations up to exam-style questions — start at whatever level suits you.
Four students are each given a copy of the same titration curve. The curve shows pH on the y-axis (0–14) and volume of NaOH added on the x-axis (0–50 mL). The curve starts at pH 3.1, rises gradually through a plateau region, has a sharp jump between pH 7.5 and 11.5 centred at 25.00 mL, and levels off above pH 12 after 30 mL. At 12.50 mL, pH = 4.74.
Each student is asked: (1) identify the equivalence point and its pH; (2) identify a suitable indicator; (3) determine the pKa of the acid.
Student A: "The equivalence point is at pH 7. I would use bromothymol blue. The pKa is 4.74."
Student B: "The EP is at 25.00 mL, pH 9.5. I would use phenolphthalein. The pKa is 4.74."
Student C: "The EP is at 25.00 mL, pH 9.5. I would use methyl orange. The pKa is 7."
Student D: "The EP is at the maximum pH — above 12. Any indicator works. The pKa is the starting pH, 3.1."
Before reading on: Which student is correct on all three? Write a precise diagnosis of each incorrect student's errors — not just "they are wrong", but exactly which misconception is operating in each answer.
📖 Know
💡 Understand
✅ Can Do
Core Content
The four students represent the four most consequential errors in titration curve interpretation
The four students represent the four most consequential errors in titration curve interpretation — and diagnosing each one with precision, rather than just identifying who is right, is the analytical rigour that Band 6 responses demonstrate.
Student B is correct on all three questions. The equivalence point is at 25.00 mL — the midpoint of the sharp jump on the volume axis — with EP pH ≈ 9.5 (midpoint of the pH range of the jump: (7.5 + 11.5)/2). Phenolphthalein (8.3–10.0) is appropriate — the EP pH of approximately 9.5 falls within its range. pKa = 4.74 — correctly read from the half-equivalence point at V_EP/2 = 12.50 mL.
Error 1 (EP): "The equivalence point is at pH 7." This is valid only for strong acid + strong base titrations. This curve shows a weak acid + strong base (buffer region before EP, EP pH above 7, starting pH ~3.1). The equivalence point is identified by volume — the midpoint of the steepest section — not by a target pH value.
Error 2 (Indicator): Bromothymol blue (6.0–7.6) does not encompass the EP pH of ~9.5. The student chose BTB because they incorrectly placed the EP at pH 7 — the two errors are causally linked. Phenolphthalein is required.
Error 3 (pKa): Student A actually identifies pKa = 4.74 correctly — this is the only answer Student A gets right.
Error 1 (Indicator): Methyl orange (3.1–4.4) transitions in the buffer region of this weak acid titration — far below the EP pH of ~9.5. Using methyl orange would give an endpoint when only ~10–20% of the acid had been neutralised, causing a catastrophic underestimate of acid concentration. The visual clarity of the colour change is irrelevant if the transition occurs at the wrong pH.
Error 2 (pKa): "pKa is 7 — the midpoint of the pH scale." pKa has nothing to do with pH 7 or the midpoint of the scale. pKa is the pH at the half-equivalence point of this specific weak acid — which is 4.74 for this curve. Student C correctly identifies the EP at 25.00 mL, pH 9.5.
Error 1 (EP): "The equivalence point is at the maximum pH on the curve — above 12." The highest pH on the curve is the post-equivalence plateau where excess NaOH dominates — this is not the equivalence point. The equivalence point is the midpoint of the steepest section at 25.00 mL, pH ~9.5.
Error 2 (Indicator): "All indicators work for all titrations." This is completely wrong — indicator selection depends on matching the transition range to the EP pH. Only phenolphthalein is appropriate here.
Error 3 (pKa): "pKa is the pH at the start of the curve — 3.1." The starting pH is determined by the initial concentration and Ka of the weak acid (pH = −log√(Ka × c)), not pKa directly. For this acid, starting pH 3.1 ≠ pKa 4.74.
| Student | EP identification | Indicator choice | pKa identification | Score |
|---|---|---|---|---|
| A | ✗ EP at pH 7 (strong/strong only) | ✗ BTB — below EP pH | ✓ pKa = 4.74 | 1/3 |
| B ✓ | ✓ 25.00 mL, pH ~9.5 | ✓ Phenolphthalein — covers EP pH | ✓ pKa = 4.74 from half-EP | 3/3 |
| C | ✓ 25.00 mL, pH 9.5 | ✗ Methyl orange — in buffer region | ✗ pKa = 7 (wrong) | 1/3 |
| D | ✗ Maximum pH point (excess base) | ✗ All indicators (wrong) | ✗ pKa = starting pH (wrong) | 0/3 |
EP = midpoint of steepest section on the volume axis — never a target pH; state BOTH volume AND pH. pKa = pH at V_EP/2 (half-equivalence volume) — never pH 7 or starting pH or EP pH. Indicator range must encompass EP pH: WA+SB → EP above 7 → phenolphthalein. Student A + C errors (EP at pH 7 + methyl orange) are causally linked and commonly paired in wrong HSC answers.
Pause — copy the highlighted definition into your book before moving on.
Which student in the Think First scenario made errors in indicator selection AND pKa identification, but correctly identified the equivalence point volume and pH?
Work through these in order — they produce every piece of information an HSC question can ask for
We just saw the four students' errors — EP at pH 7, wrong indicator, pKa misidentified. That raises a question: Is there a single systematic framework that prevents all four errors simultaneously, for any titration curve type? This card answers it → six-question sequence: acid/base types → initial conc/vol → V_EP → EP pH → pKa → indicator; answer all six before any curve sketch or calculation.
Every titration curve question — whether sketching, interpreting, or calculating — can be answered systematically by working through six questions in order. Students who memorise this framework never need to rely on pattern-matching from memory.
What are the acid and base types? Determines curve shape, starting pH, and whether a buffer region exists. Strong acid list: HCl, H₂SO₄ (1st), HNO₃, HClO₄, HBr, HI — all others are weak.
What is the initial acid concentration and volume? Determines starting pH (weak acid: ICE table; strong acid: −log(c)) and total moles of acid (sets V_EP).
What volume of titrant reaches the equivalence point? V_EP = n(acid)/c(base). Marks the end of the buffer region and the centre of the jump.
What is the EP pH? Depends on salt hydrolysis: above 7 (weak acid/strong base); at 7 (strong/strong); below 7 (strong acid/weak base); gradual (weak/weak).
What is pKa? Read from pH at V_EP/2 — only meaningful for weak acid + strong base curves.
Which indicator is appropriate? Transition range must overlap EP pH: EP > 7 → phenolphthalein; EP ≈ 7 → any; EP < 7 → methyl orange or BTB.
| Question | Answer determines | Key formula or rule |
|---|---|---|
| 1 — Acid/base types? | Curve shape, buffer presence, EP direction | Strong acid list: HCl, H₂SO₄, HNO₃, HClO₄, HBr, HI |
| 2 — Initial conc & volume? | Starting pH; V_EP | Weak acid: pH = −log√(Ka×c); strong acid: pH = −log(c) |
| 3 — V_EP? | Location of jump; stoichiometry | V_EP = c(acid)×V(acid)/c(base) |
| 4 — EP pH? | Indicator selection; curve asymmetry | Weak acid/strong base → >7; strong/strong → 7; strong acid/weak base → <7 |
| 5 — pKa? | Intrinsic acid property | pKa = pH at V_EP/2; only for weak acid curves |
| 6 — Indicator? | Practical endpoint detection | Range must include EP pH; Ph for >7; MO for <7; any for ≈7 |
Six-question sequence: (1) acid/base types; (2) initial conc/vol (sets V_EP); (3) V_EP = c(acid)×V(acid)/c(base); (4) EP pH from salt hydrolysis; (5) pKa = pH at V_EP/2; (6) indicator range vs EP pH. Buffer region is BEFORE the EP for weak acids. Three-step indicator justification: state EP pH + why; name indicator + range; confirm range covers EP pH.
Add the highlighted point to your notes before the check below.
True or False: For a strong acid + strong base titration, any of the three common indicators (methyl orange, BTB, phenolphthalein) can be used successfully.
Once this analogy is established, map-reading vocabulary transfers directly to curve reading
We just saw the six-question decision framework for any titration curve. That raises a question: Is there an analogy that makes the five curve regions intuitive — so you can navigate a curve as easily as reading familiar terrain? This card answers it → topographic map: coastal plain (start), foothills (buffer), cliff face (EP), mountain plateau (just post-EP), high plateau (excess base).
A titration curve and a topographic map share an unexpected structural parallel — and once this analogy is established, the vocabulary of map reading transfers directly to curve reading, making the abstract features of a titration curve concrete and navigable.
Imagine a topographic map showing the ascent from sea level to a mountain summit. The horizontal axis represents distance travelled (like volume of titrant). The vertical axis represents altitude (like pH). The terrain has five characteristic zones:
Zone 1 — The coastal plain (starting region): nearly flat, slight upward slope. Corresponds to the starting pH of the weak acid — slowly rising as a small fraction of the acid is neutralised.
Zone 2 — The foothills (buffer region): gradual, steady ascent. You're climbing, but the gradient is modest. Corresponds to the buffer region where both HA and A⁻ coexist — pH rises gradually and predictably via Henderson-Hasselbalch.
Zone 3 — The cliff face (near the equivalence point): sudden, near-vertical ascent. One step takes you from valley floor to mountain ledge. Corresponds to the sharp pH jump at the equivalence point — a fraction of a drop of titrant produces a dramatic pH change.
Zone 4 — The mountain plateau (just past the EP): the sudden ascent gives way to a flatter region. Corresponds to levelling off just past the equivalence point where excess base dominates.
Zone 5 — The high plateau (post-equivalence): gently rising terrain at high altitude. Corresponds to the high-pH asymptote where excess NaOH dominates and pH changes become small again.
The equivalence point is the bottom of the cliff face — the point of maximum gradient (maximum dpH/dV). The half-equivalence point is a specific landmark in Zone 2 — the midpoint of the foothills — where the skilled hiker can read the exact altitude (pH = pKa) from the map.
Quick diagnostic: Is there a foothills region (buffer) before the cliff face (EP)? → Yes = weak acid. Is the cliff face above or below the 7-unit contour line (pH 7)? → Above = weak acid/strong base. This reading takes 10 seconds and correctly identifies the curve type before any calculation.
A weak acid + strong base curve includes a buffer region before equivalence, with the half-equivalence point giving pKa and the equivalence point sitting above pH 7.
Topographic zones: coastal plain (start) → foothills (buffer) → cliff face (EP = maximum dpH/dV) → mountain plateau (just post-EP) → high plateau (excess base). Half-EP = midpoint of foothills (pH = pKa). Quick 2-question diagnostic: buffer before EP → weak acid; cliff above pH 7 → WA+SB. Zone widths vary with concentration and Ka.
Pause — write the highlighted definition into your book before moving on.
Using the topographic map analogy, at which "zone" would you read the pKa of a weak acid from a titration curve?
The mathematical inevitability of the sharp pH jump becomes intuitive through stoichiometric depletion
We just saw the topographic map — the cliff face marks the equivalence point. That raises a question: Why is the sharp pH jump mathematically inevitable near the EP, and why is the strong acid + strong base jump larger than the weak acid version? This card answers it → parking lot analogy: buffer capacity depletes near 100% occupancy (near EP); no buffer (strong acid) = abrupt transition; buffer reserve (weak acid) = softer transition.
Imagine a parking lot with exactly 1000 spaces. Cars arrive at a steady rate. For the first 990 minutes, the lot is gradually filling and finding a space is easy — this is the buffer region, where plenty of both HA and A⁻ keep pH changes gradual. At 995 cars, only 5 spaces remain; at 999 cars, only 1 space. At 1000 cars, the lot is exactly full — this is the equivalence point.
Now: if the next car arrives (1001st car), there is absolutely no space — it must park on the street, completely changing the traffic pattern. This is the post-equivalence region — excess base dominates and pH rises sharply.
The critical insight: the transition from "nearly full" to "one car on the street" spans only a tiny volume range near the EP — because the buffering capacity (parking spaces) drops steeply near 100% occupancy. The pH jump is not abrupt because the reaction is faster near the EP — it is abrupt because of logarithm mathematics and stoichiometric depletion.
For a weak acid, the lot has a reservation system — even when main spaces are full, a small reserve (the weak acid ionisation equilibrium) provides a few extra spaces. This means the transition is slightly more gradual — a smaller pH jump. For a strong acid, there is no reservation system — the transition is abrupt and complete.
The four curve types can be distinguished by whether a buffer region appears, where the equivalence point lies, and whether a sharp enough pH jump exists for an indicator.
pH jump is sharp near EP because buffering capacity (parking spaces) depletes steeply — mathematical consequence, not kinetic. Strong acid → no buffer → largest jump. Weak acid → buffer reserve → smaller, more gradual jump. WA+WB: no sharp jump → no suitable indicator. Four curve types: SA+SB (EP~7, any indicator), WA+SB (buffer, EP>7, phenolphthalein), SA+WB (EP<7, methyl orange), WA+WB (no indicator).
Add the highlighted point to your notes before the check below.
Which of the four titration curve types lacks a sharp enough pH jump to use any common acid-base indicator reliably?
These errors reproduce themselves across HSC cohorts — diagnose each with the specific misconception at its root
We just saw the parking lot analogy for why the pH jump is sharp. That raises a question: What are ALL five of the highest-frequency titration curve errors consolidated in one reference with their root causes and fixes? This card answers it → EP at pH 7 (38%); endpoint = equivalence (21%); buffer after EP; pKa = starting pH; phenolphthalein always — all five share the same root: features identified from memory without systematic reasoning.
In 2021, NESA's HSC Chemistry marking data showed: Error 1 (EP at pH 7 for all curves) affected 38% of students; Error 2 (wrong indicator for weak acid/strong base) affected 21%; Error 3 (reading pKa at wrong volume) affected 17%. Combined, these three errors accounted for the majority of marks lost in IQ3 curve questions. Below are all five — with the precise misconception at the root of each and a specific fix.
Root cause: Students memorise "neutralisation → neutral → pH 7" without understanding that only a strong acid + strong base titration gives a neutral salt. Fix: Always apply the six-question framework; Question 4 forces salt hydrolysis reasoning before marking the EP. An EP at pH 7 for a weak acid + strong base is an automatic error.
Root cause: The terms are used interchangeably in casual conversation. Fix: Equivalence point = stoichiometric completion of the reaction (calculated from moles). Endpoint = observed indicator colour change (experimental detection). In ideal conditions these coincide; in practice the endpoint slightly precedes or follows the EP depending on indicator choice.
Root cause: Students know "buffer" is associated with a weak acid and guess its position. Fix: For weak acid + strong base, the buffer region is before the EP — HA and A⁻ coexist while HA is being consumed. After the EP, only excess NaOH dominates — no buffer character at all.
Root cause: Students confuse three separate pH quantities. Fix: Three distinct identities — Starting pH = −log√(Ka×c) [determined by c and Ka]; Half-EP pH = pKa [intrinsic property]; EP pH > 7 [determined by salt hydrolysis]. None of these three is the same as any other.
Root cause: Students learn "phenolphthalein for acid-base titrations" as a general rule without knowing it is only appropriate when EP pH > 7. Fix: Always use the three-step indicator rule: (1) state EP pH and explain why; (2) state indicator and its range; (3) confirm range covers EP pH. If the three-step justification cannot be completed, the selection is wrong.
| Error | Specific mistake | Root misconception | Fix |
|---|---|---|---|
| EP at pH 7 | Marking EP where curve crosses pH 7 | Neutralisation → neutral → pH 7 always | EP = midpoint of jump (volume axis); EP pH varies by type |
| Endpoint = equivalence | Using interchangeably in written response | Terms not distinguished | EP = calculated; endpoint = observed colour change |
| Buffer after EP | Drawing buffer plateau after the jump | Buffer ≈ weak acid/base type — position guessed | Buffer region is BEFORE EP for weak acid |
| pKa = starting pH or 7 | Reading pKa from wrong curve feature | Confusing three distinct pH quantities | pKa = pH at V_EP/2 only |
| Phenolphthalein always | Selecting Ph without justification | Generalised rule without EP pH reasoning | Three-step justification required; Ph only for EP > 7 |
"The equivalence point is where the curve crosses pH 7." — pH 7 is the EP only for strong acid + strong base. For any system involving a weak acid or base, the EP is above or below pH 7. The EP is identified by volume — the midpoint of the steepest section — regardless of the pH value at that point.
"pKa = 7 (the midpoint of the pH scale)." — pKa has no relationship to the midpoint of the pH scale. pKa is an intrinsic molecular property read from the half-equivalence point of the specific titration curve.
"I chose methyl orange because it gives a very clear colour change." — Visual clarity of a colour change is irrelevant to indicator selection. The only criterion is whether the indicator's transition range encompasses the EP pH.
"The endpoint and equivalence point are the same thing." — The equivalence point is the calculated stoichiometric point; the endpoint is the experimentally observed colour change.
"The buffer region appears after the equivalence point for a weak acid." — The buffer region (where HA and A⁻ coexist) appears before the EP. After the EP, only excess NaOH dominates — there is no buffering.
Five titration curve errors: (1) EP at pH 7 for all curves — EP is at midpoint of steepest section; state both volume AND pH. (2) endpoint = equivalence — endpoint = observed colour change; EP = calculated stoichiometric point. (3) buffer drawn after EP — buffer is BEFORE EP for weak acid. (4) pKa = starting pH — pKa = pH at V_EP/2 only. (5) phenolphthalein always — three-step justification required; Ph only for EP > 7.
Pause — copy the highlighted checklist into your book before the check below.
A student writes: "I titrated until I reached the equivalence point, which I identified by the colour change of phenolphthalein from colourless to pink." What is the conceptual error in this sentence?
✏️ Worked Examples
A titration curve is generated by adding 0.0500 mol/L NaOH to 40.00 mL of an unknown acid HX. The curve shows: starting pH = 1.70; a nearly vertical jump from pH 3.5 to pH 9.5 centred at 20.00 mL; no discernible buffer region before the jump; after 25 mL, pH levels above 12. (a) Identify the acid type and justify using two curve features. (b) Identify EP volume and EP pH. (c) Is phenolphthalein suitable? Justify. (d) Calculate the concentration of HX.
(a) Acid type — two features:
Feature 1: No buffer region before the equivalence point. A weak acid in the presence of partial neutralisation produces a buffer region (HA + A⁻ coexisting). The absence of any plateau is characteristic of a strong acid.
Feature 2: The jump is centred near pH 7 (midpoint of 3.5–9.5 ≈ 6.5), consistent with a neutral salt from strong acid + strong base. For a weak acid, EP pH would be above 7.
Conclusion: HX is a strong acid.
(b) EP volume and pH:
EP volume = midpoint of steepest section = 20.00 mL. EP pH = midpoint of the jump = (3.5 + 9.5)/2 = 6.5 ≈ 7.0 — consistent with strong acid + strong base.
(c) Phenolphthalein suitability:
EP pH ≈ 7.0. The sharp jump spans approximately pH 3.5–9.5. Phenolphthalein's range (8.3–10.0) falls within this jump — phenolphthalein is suitable. So are methyl orange and BTB — all three indicator ranges fall within the large jump of a strong/strong titration.
(d) Concentration of HX:
At EP: n(NaOH) = n(HX)
n(NaOH) = c × V = 0.0500 × 0.02000 = 1.00 × 10⁻³ mol
c(HX) = n/V = 1.00 × 10⁻³ / 0.04000 = 0.0250 mol/L
A titration curve is produced by adding 0.100 mol/L NaOH to 25.00 mL of propanoic acid (CH₃CH₂COOH, Ka = 1.3 × 10⁻⁵). Selected data: V = 0.00 mL → pH 3.03; V = 6.25 mL → pH 4.44; V = 12.50 mL → pH 4.89; V = 18.75 mL → pH 5.34; V = 25.00 mL → pH 8.57; V = 31.25 mL → pH 12.10. (a) Identify EP volume and EP pH. (b) Verify pKa from the half-EP. (c) Calculate starting pH theoretically. (d) A student uses methyl orange and records endpoint at 6.25 mL — calculate the percentage error in reported acid concentration. (e) Identify the appropriate indicator with full three-step justification.
(a) EP identification: The large pH jump occurs centred near V = 25.00 mL. EP volume = 25.00 mL. EP pH ≈ 8.57 — above 7, consistent with weak acid + strong base.
(b) pKa verification:
Half-EP volume = V_EP/2 = 25.00/2 = 12.50 mL
At V = 12.50 mL, pH = 4.89 → pKa(experimental) = 4.89
pKa(theoretical) = −log(1.3 × 10⁻⁵) = 5 − log(1.3) = 4.89 ✓
(c) Theoretical starting pH:
c(acid) = (0.100 × 0.02500)/0.02500 = 0.100 mol/L. Check: Ka/c = 1.3 × 10⁻⁴ < 0.0025 ✓ (assumption valid).
x = √(Ka × c) = √(1.3 × 10⁻⁵ × 0.100) = 1.140 × 10⁻³ mol/L
Theoretical starting pH = −log(1.140 × 10⁻³) = 2.94
Observed: 3.03. Difference = 0.09 pH units — within ±0.1 pH units graphical precision ✓.
(d) Methyl orange error calculation:
n(NaOH) at endpoint = 0.100 × 0.00625 = 6.25 × 10⁻⁴ mol
Reported c(acid) = 6.25 × 10⁻⁴ / 0.02500 = 0.02500 mol/L
Percentage error = |0.02500 − 0.1000| / 0.1000 × 100% = 75.0% underestimation
The student stopped when only 6.25/25.00 = 25% of the propanoic acid had been neutralised.
(e) Three-step indicator justification:
Step 1 (EP pH and why): The EP pH is approximately 8.6 — above 7 because the salt formed at equivalence is sodium propanoate. The propanoate ion (CH₃CH₂COO⁻) is the conjugate base of a weak acid and undergoes base hydrolysis: CH₃CH₂COO⁻ + H₂O ⇌ CH₃CH₂COOH + OH⁻, producing OH⁻ and raising pH above 7.
Step 2 (indicator and range): Phenolphthalein — transition range pH 8.3–10.0.
Step 3 (confirmation): The EP pH of 8.6 falls within phenolphthalein's range (8.3–10.0). The sharp pH jump at equivalence passes through 8.3–10.0 — phenolphthalein changes from colourless to faint pink, giving a clear, reproducible endpoint coinciding with the equivalence point.
(8 marks) Two acid solutions of the same concentration (0.100 mol/L) and volume (20.00 mL): Solution P is HCl; Solution Q is HF (Ka = 6.8 × 10⁻⁴). Both are titrated with 0.100 mol/L NaOH. (a) For each: (i) starting pH; (ii) half-EP pH; (iii) EP volume and EP pH. (b) Describe five key differences between the two curves. (c) Evaluate the claim: "Since HCl and HF are both monoprotic hydrogen halides, their titration curves should be identical." (d) Identify the appropriate indicator for each titration and justify both choices.
(a)(i) Starting pH:
HCl (strong acid): pH = −log(0.100) = 1.00
HF (weak acid — Ka/c = 6.8 × 10⁻³, quadratic required):
x² + 6.8 × 10⁻⁴x − 6.8 × 10⁻⁵ = 0 → x = 7.91 × 10⁻³ mol/L
Starting pH(HF) = −log(7.91 × 10⁻³) = 2.10
(a)(ii) Half-EP:
HCl: No half-EP — the concept of a half-equivalence point (pH = pKa) applies only to weak acid curves. HCl has no buffer region and no Ka in the weak acid sense.
HF: Half-EP at V = 10.00 mL; pKa(HF) = −log(6.8 × 10⁻⁴) = 3.17.
(a)(iii) EP volume and pH:
Both: V_EP = (0.100 × 0.02000)/0.100 = 20.00 mL.
HCl → NaCl (neutral salt): EP pH = 7.00.
HF → NaF; F⁻ + H₂O ⇌ HF + OH⁻:
Kb(F⁻) = Kw/Ka = 1.0 × 10⁻¹⁴ / 6.8 × 10⁻⁴ = 1.47 × 10⁻¹¹
[F⁻] at EP = 0.0500 mol/L → [OH⁻] = √(1.47 × 10⁻¹¹ × 0.0500) = 8.57 × 10⁻⁷
pOH = 6.07 → EP pH(HF) = 7.93
(b) Five key differences:
1. Starting pH: HCl = 1.00; HF = 2.10. HCl fully ionised; HF only ~7.9% ionised → fewer H⁺ → higher starting pH.
2. Buffer region: HCl has none; HF has a significant buffer region before EP.
3. Jump size: HCl gives ~7 pH units; HF gives ~4–5 units (buffer moderates approach to EP).
4. EP pH: HCl → 7.00 (neutral salt); HF → 7.93 (F⁻ hydrolyses).
5. Half-EP: HCl has no meaningful half-EP; HF half-EP at 10.00 mL gives pH = pKa = 3.17.
(c) Evaluating the claim: Incorrect. While both are monoprotic hydrogen halides, HCl is a strong acid (Ka → ∞, complete ionisation); HF is a weak acid (Ka = 6.8 × 10⁻⁴, ~7.9% ionised). Their curves differ in starting pH (1.00 vs 2.10), buffer region, jump size, and EP pH (7.00 vs 7.93). Ka determines curve shape — not halide identity. The H–F bond (570 kJ/mol) is significantly stronger than H–Cl (432 kJ/mol), making proton donation from HF far less favourable.
(d) Indicator selection:
HCl + NaOH (strong/strong, EP pH = 7.00): Sharp jump spans ~pH 4–10. All three indicators suitable; phenolphthalein gives clearest visual change.
HF + NaOH (weak acid + strong base, EP pH = 7.93): Step 1: EP pH = 7.93 — above 7 because F⁻ (conjugate base of weak acid) hydrolyses. Step 2: Phenolphthalein — range 8.3–10.0. Step 3: EP pH 7.93 is just below 8.3, but the sharp jump extends from ~pH 6.5 to 11.5 — phenolphthalein transitions within the upper part of this jump.
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Activities
For each student statement below, identify the specific error (what is wrong), the root misconception (why the student made the error), and the correct answer. Do not just write "incorrect" — diagnose with precision.
1. A student examining a titration curve for CH₃COOH + NaOH marks the equivalence point where the curve crosses pH 7. Diagnose this error.
2. A student reads the pKa of a weak acid from a titration curve as pH 9.4 — the pH at the equivalence point. Diagnose this error.
3. A student selects methyl orange for a titration of formic acid (HCOOH, Ka = 1.8 × 10⁻⁴) with NaOH because "it gives a vivid, easy-to-see colour change." Diagnose this error and calculate the percentage error in acid concentration if the methyl orange endpoint occurs at 20% of the true titre volume.
4. A student writes in their practical report: "I titrated until I reached the equivalence point, which I identified by the colour change of phenolphthalein from colourless to pink." Identify the conceptual error in this sentence and rewrite it correctly.
The following data is obtained by adding 0.200 mol/L NaOH to 15.00 mL of an unknown weak acid HA. Apply the six-question framework to determine all key features.
| V (NaOH) mL | pH | V (NaOH) mL | pH |
|---|---|---|---|
| 0.00 | 3.28 | 15.00 | 8.20 |
| 3.75 | 4.52 | 18.75 | 12.05 |
| 7.50 | 5.12 | 22.50 | 12.35 |
| 11.25 | 5.72 | 26.25 | 12.55 |
❓ Multiple Choice
1. A student examines a titration curve: starting pH = 4.2; buffer plateau before EP; EP at V = 30.00 mL, pH = 9.8; at V = 15.00 mL, pH = 6.4. Which correctly extracts all key information?
2. Two students titrate 25.00 mL of 0.100 mol/L CH₃COOH with 0.100 mol/L NaOH. Student X uses phenolphthalein and records endpoint at 25.10 mL. Student Y uses methyl orange and records endpoint at 5.40 mL. Which student gives the more accurate acid concentration, and why?
3. A student examines a curve: sharp jump from pH 6.5 to 11.5; midpoint at V = 15.00 mL; pH at V = 7.50 mL reads 5.12. The student claims: "pKa = 5.12; Ka = 7.6 × 10⁻⁶; and since the EP is at 15.00 mL using 0.200 mol/L NaOH with 15.00 mL of acid, acid concentration = 0.200 mol/L." Evaluate this claim.
✍️ Short Answer
4. A titration curve is produced by adding 0.100 mol/L NaOH to 20.00 mL of a weak acid HA (Ka = 4.0 × 10⁻⁶). The equivalence point is at 20.00 mL of NaOH, with EP pH = 9.1. (a) State the concentration of HA. (b) Identify the appropriate indicator and write a complete three-step justification. (c) Identify the pH at the half-equivalence point and explain what this quantity represents. 5 MARKS
5. A student titrates 0.100 mol/L ammonia solution (NH₃, Kb = 1.8 × 10⁻⁵) with 0.100 mol/L HCl. (a) Identify the titration type and predict whether the EP pH is above, at, or below 7 — justify with a relevant equation. (b) Identify the appropriate indicator from methyl orange, BTB, or phenolphthalein — apply the three-step justification. (c) Explain why phenolphthalein would be unsuitable for this titration, with reference to the curve shape. 5 MARKS
6. Band 6 Extended Response (7 marks). A research laboratory has two 0.0500 mol/L acid solutions: Solution X is hydrochloric acid (HCl); Solution Y is lactic acid (CH₃CH(OH)COOH, Ka = 1.4 × 10⁻⁴). Both are titrated with 0.100 mol/L NaOH. (a) Calculate the starting pH of each solution. (b) Calculate the EP volume for each (assume 25.00 mL of each acid). (c) Describe four differences between the titration curves of X and Y, explaining why each difference arises with reference to acid strength. (d) Identify the appropriate indicator for each titration, applying the three-step justification for Solution Y. (e) A student claims the two curves should have identical shapes because they have the same concentration and are both titrated with the same NaOH concentration. Evaluate this claim quantitatively — use the half-equivalence point of Solution Y to support your argument. 7 MARKS
1. Error: Student marks EP at the pH 7 crossing point rather than the midpoint of the steepest section on the volume axis. Root misconception: "neutralisation → neutral → pH 7 always." Correct: for CH₃COOH + NaOH (weak acid + strong base), the EP pH is above 7 (~8.7) because acetate ion undergoes base hydrolysis: CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻. EP must be identified by volume at the point of inflection.
2. Error: pKa read from the EP pH (9.4) rather than the half-EP pH. Root misconception: confusing the three distinct pH quantities. Correct method: half-EP volume = V_EP/2; read pH at that volume — that pH equals pKa.
3. Error: Indicator selected based on visual clarity, not EP pH. Why MO fails: EP pH for HCOOH + NaOH ≈ 8.7 (weak acid + strong base → EP above 7). Methyl orange (3.1–4.4) transitions in the early buffer region of the formic acid titration (pKa = 3.74), far below the EP. Percentage error: endpoint at 20% of true titre → reported c = 20% of true c → 80% underestimation.
4. Error: "I reached the equivalence point at the colour change" implies the colour change is the equivalence point. Corrected: "The endpoint (colour change of phenolphthalein from colourless to faint pink) was used to detect the equivalence point — the theoretical stoichiometric point at which all acetic acid had reacted with NaOH. In ideal conditions, the endpoint and equivalence point coincide."
Q1 — Acid type: Weak acid — starting pH 3.28 is above what a strong acid would show; buffer plateau visible in gradual rise from 3.28 to 5.72 between V = 0 and V = 11.25 mL.
Q2 — EP: Large pH jump at V = 15.00 mL (pH 8.20). EP volume = 15.00 mL; EP pH ≈ 8.20 — above 7, consistent with weak acid + strong base.
Q3 — pKa: Half-EP at V_EP/2 = 7.50 mL; pH at 7.50 mL = 5.12 → pKa = 5.12.
Q4 — Ka: Ka = 10⁻⁵·¹² = 7.6 × 10⁻⁶.
Q5 — c(HA): n(NaOH) at EP = 0.200 × 0.01500 = 3.00 × 10⁻³ mol = n(HA). c(HA) = 3.00 × 10⁻³/0.01500 = 0.200 mol/L.
Q6 — Indicator: Step 1: EP pH = 8.20 — above 7 because A⁻ (conjugate base of weak acid HA) hydrolyses: A⁻ + H₂O ⇌ HA + OH⁻. Step 2: Phenolphthalein — range 8.3–10.0. Step 3: EP pH 8.20 is just below phenolphthalein's lower limit (8.3), but the sharp jump extends from ~6 to 12 — phenolphthalein transitions within this jump. Methyl orange is completely unsuitable.
Q7 — Equation: A⁻(aq) + H₂O(l) ⇌ HA(aq) + OH⁻(aq) — base hydrolysis of conjugate base produces OH⁻ → solution is basic at equivalence → EP pH above 7.
1. B — Starting pH 4.2, buffer plateau, EP pH 9.8 all confirm weak acid + strong base. Half-EP = 30.00/2 = 15.00 mL; pH at 15.00 mL = 6.4 → pKa = 6.4. Ka = 10⁻⁶·⁴ = 4.0 × 10⁻⁷. Phenolphthalein (8.3–10.0) covers EP pH 9.8. Option A: identifies as strong/strong — wrong. Option C: reads pKa from EP pH — wrong. Option D: reads pKa from starting pH — wrong.
2. B — For CH₃COOH + NaOH, EP pH ≈ 8.7. Phenolphthalein (8.3–10.0) covers this EP → Student X accurate. Methyl orange transitions in buffer region — Student Y stops at 5.40/25.00 = 21.6% of EP volume → 78.4% underestimation. Options A and C prioritise visual clarity over EP pH criterion incorrectly.
3. B — pKa = 5.12 (from half-EP) ✓; Ka = 10⁻⁵·¹² = 7.6 × 10⁻⁶ ✓. Concentration claim is numerically correct for these specific values (V(acid) = V_EP = 15.00 mL → equal volumes → equal concentrations at 0.200 mol/L) but the reasoning "equal concentrations" only holds when V(acid) = V_EP — the reasoning is incomplete, not wrong in this case.
Q4 (5 marks): (a) At EP: n(NaOH) = n(HA) → n(HA) = 0.100 × 0.02000 = 2.00 × 10⁻³ mol; c(HA) = 2.00 × 10⁻³/0.02000 = 0.100 mol/L. [1 mark.] (b) Step 1: EP pH = 9.1 — above 7 because A⁻ (conjugate base) undergoes base hydrolysis: A⁻ + H₂O ⇌ HA + OH⁻. [1 mark.] Step 2: Phenolphthalein — transition range pH 8.3–10.0. [1 mark.] Step 3: EP pH 9.1 falls within phenolphthalein's range (8.3–10.0) — transitions within sharp jump at equivalence. [1 mark.] (c) pH at half-EP = pKa = −log(4.0 × 10⁻⁶) = 5.40. Half-EP at V_EP/2 = 10.00 mL. pKa is the intrinsic ionisation constant — the pH at which half the acid has been neutralised, [HA] = [A⁻], and the Henderson-Hasselbalch log term = 0. [1 mark.]
Q5 (5 marks): (a) Strong acid (HCl) + weak base (NH₃). EP pH below 7 because the salt formed is NH₄Cl; NH₄⁺ (conjugate acid of NH₃) undergoes acid hydrolysis: NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺, producing H₃O⁺ and lowering pH below 7. [2 marks.] (b) Step 1: EP pH below 7 — NH₄⁺ hydrolyses to give H₃O⁺. Step 2: Methyl orange — range 3.1–4.4, or BTB — range 6.0–7.6. Step 3: The sharp jump for strong acid + weak base is centred below pH 7 — methyl orange or BTB both transition within this jump. [2 marks.] (c) Phenolphthalein (8.3–10.0) is unsuitable — its transition range is above the EP pH. The curve for strong acid + weak base levels off at low pH above 7 in the post-EP region — phenolphthalein would not change colour during the titration, as the solution never reaches pH 8.3. [1 mark.]
Q6 — Band 6 (7 marks): (a) X (HCl): pH = −log(0.0500) = 1.30. Y (lactic acid): Ka/c = 2.8 × 10⁻³ > 0.0025 — quadratic required → x ≈ 2.61 × 10⁻³ mol/L → pH(Y) ≈ 2.58. [1 mark.] (b) Both: n(acid) = 0.0500 × 0.02500 = 1.25 × 10⁻³ mol; V_EP = 1.25 × 10⁻³/0.100 = 12.50 mL for both. [1 mark.] (c) Four differences: (i) Starting pH: X = 1.30; Y = 2.58 — X lower because HCl fully ionised, lactic acid only partially ionised. (ii) Buffer region: X has none; Y has a buffer plateau before EP. (iii) Jump size: X larger (~7 units); Y smaller (~3–4 units). (iv) EP pH: X = 7.00 (NaCl neutral); Y above 7 (lactate ion hydrolyses). [2 marks.] (d) X: any indicator; recommend phenolphthalein. Y — 3-step: Step 1: EP pH above 7 because lactate ion (conjugate base) undergoes base hydrolysis. Step 2: Phenolphthalein — range 8.3–10.0. Step 3: EP pH for Y is above 7 within phenolphthalein's range; methyl orange completely unsuitable. [2 marks.] (e) Claim incorrect. Both have same concentration and V_EP but fundamentally different curve shapes because Ka governs shape. Quantitative: half-EP of Y at V = 6.25 mL; pH = pKa(lactic acid) = −log(1.4 × 10⁻⁴) = 3.85. No equivalent feature exists on X's curve — HCl has no meaningful half-EP. The two curves produce different pH values at every volume between 0 and V_EP. Ka is the decisive variable, not concentration. [1 mark.] Total: 7 marks.
Go back to your Think First response at the top of this lesson. Recall the 2021 NESA data: 38% of students placed EP at pH 7 for all curves; 21% chose wrong indicator. Now that you've worked through all five errors, both analogies, and three worked examples:
Without referencing the lesson, write a complete response explaining why a student who correctly identifies the equivalence point pH as 9.5 for a weak acid + strong base titration but then selects bromothymol blue (BTB, range 6.0–7.6) as the indicator is making a fundamentally different error from a student who selects phenolphthalein for the same titration. Include: the three-step indicator justification for the correct choice, and a calculation showing the magnitude of error if BTB were used and the endpoint fell at pH 7.0 when the true EP volume was 25.00 mL and the acid was 25.00 mL of 0.100 mol/L HA.
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