HSCScience Chemistry · Y12 · M6
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Year 12 Chemistry Module 6 — Acid/Base Reactions ⏱ ~45 min Lesson 16 of 19 IQ3

Titration Curves — Interpreting & Analysing All Four Types

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.

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Today's hook — In 2003, AstraZeneca's analytical team read rosuvastatin's pKa = 4.58 directly from a titration curve's half-equivalence point — no separate calculation needed. Why does pH barely change in the buffer region, then suddenly leap at the equivalence point? And what does each feature of the curve tell you quantitatively?
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Worksheets

Practise this lesson

Four printable worksheets that build from the foundations up to exam-style questions — start at whatever level suits you.

Before You Read

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?

📐 Formulas at a Glance
At half-equivalence point (weak acid + strong base): pH = pKa
Half-EP volume = V_EP / 2  |  Read pH at that volume → that pH = pKa
Henderson-Hasselbalch (buffer region): pH = pKa + log(n(A⁻) / n(HA))
n(A⁻) = moles of conjugate base formed  |  n(HA) = moles of weak acid remaining
At EP (weak acid + strong base): Kb(A⁻) = Kw / Ka  →  [OH⁻] = √(Kb × [A⁻])
then pH = 14 − pOH  |  EP pH > 7 (conjugate base hydrolyses)
Strong + strong EP: pH = 7.00  |  Strong acid + weak base EP: pH < 7
Weak + weak: no sharp jump — no usable indicator
Learning Intentions
Know

Key facts

  • The shape and key features of all four titration curve types
  • That pKa is read from the half-equivalence point (V_EP/2)
  • Which regions correspond to which calculation method
Understand

Concepts

  • Why strong/strong has the largest pH jump (no buffer capacity)
  • Why weak/weak has no usable jump (dual buffer regions)
  • Why EP pH differs from 7 when one species is weak
Can do

Skills

  • Identify curve type from four diagnostic features
  • Read V_EP, EP pH, and pKa directly from a curve
  • Calculate pH at any of the five regions on a titration curve
Scan these before reading
Titration curve
A graph of pH vs volume of titrant added; shape reveals acid/base strength and stoichiometry.
Equivalence point on curve
The inflection point (steepest part) of a titration curve; pH at equivalence depends on the salt formed.
Strong acid + strong base
Equivalence point at pH 7; sharp steep curve; any indicator that changes in pH 4–10 is suitable.
Weak acid + strong base
Equivalence point at pH > 7 (basic salt); curve shows buffer region before equivalence point.
Strong acid + weak base
Equivalence point at pH < 7 (acidic salt); buffer region on base side of equivalence point.
Weak acid + weak base
Equivalence point near pH 7 but variable; no sharp inflection; indicator selection is difficult.
Cross-lesson links: The four curve types here build on equivalence point pH from L15 and buffer regions from L13. AstraZeneca's 2003 rosuvastatin pKa measurement (reading the half-equivalence point from a curve) is applied in L17 consolidation. The five-region calculation method in Card 5 uses all Ka/ICE table skills from L09.
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The Four Titration Curves — Shape, Features, and 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.

Strong/Strong

Start pH: Low (~1)
Buffer before EP: None
EP pH: ≈ 7.00
Jump size: Largest (~6–8 units)

Weak acid/Strong base

Start pH: Intermediate (~3)
Buffer before EP: Yes — flat plateau
EP pH: > 7 (≈ 8.7)
Jump size: Moderate (~4–6 units)

Strong acid/Weak base

Start pH: Low (~1)
Buffer before EP: None before EP
EP pH: < 7 (≈ 5.3)
Jump size: Moderate (~3–5 units)

Weak/Weak

Start pH: Intermediate (~3)
Buffer before EP: Yes — throughout
EP pH: ≈ 7 (no sharp jump)
Jump size: Very small (<2 units)
Must Do
Check these four features in order: (1) starting pH — low (strong acid) or intermediate (weak acid); (2) buffer region before EP — present (weak acid) or absent (strong acid); (3) EP pH — above, at, or below 7; (4) jump size. These four checks uniquely identify any of the four curve types.
Common Error
Students confuse the starting pH (pH of the initial solution before any titrant) with the equivalence point pH. They are different points: the starting pH is the leftmost point on the curve (zero titrant); the EP is the midpoint of the sharp jump.
Exam Tip
In acid-base calculations, always write the balanced equation first, identify the conjugate pair, and state any assumptions before substituting into the Ka expression.

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.

Pause — copy the highlighted definition into your book before moving on.

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?

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The Weak Acid + Strong Base Curve — Five Regions in Detail

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 1 — Before any titrant: pH from weak acid ICE table. [H⁺] = √(Ka × c).
  • Region 2 — Buffer region (before half-EP): both HA and A⁻ present; Henderson-Hasselbalch applies; pH rises gradually.
  • Region 3 — Half-equivalence point: n(A⁻) = n(HA) exactly; pH = pKa. Locate at V_EP/2 on the x-axis.
  • Region 4 — Equivalence point: all HA → A⁻; pH determined by Kb of A⁻; pH > 7.
  • Region 5 — After equivalence: excess NaOH dominates; [OH⁻] = n(excess)/V(total); pH levels off at high values.
RegionWhat's in solutionCalculationKey feature
Before titrantOnly HA[H⁺] = √(Ka × c)Starting pH < 7
Buffer regionHA + A⁻Henderson-HasselbalchGradual rise; flat plateau
Half-EP (V_EP/2)HA = A⁻ (equal moles)pH = pKaRead pKa from graph here
Equivalence pointOnly A⁻Kb = Kw/Ka; [OH⁻] = √(Kb × [A⁻])Sharp jump ends; pH > 7
After equivalenceExcess NaOH + A⁻[OH⁻] = n(excess)/VtotalLevels off at high pH
Must Do
The half-equivalence point (pH = pKa) is a standalone HSC exam skill named in the Module 6 syllabus. To locate it: (1) find V_EP (midpoint of the sharp jump); (2) calculate V_EP/2; (3) read pH at V_EP/2. Many students miss this completely — it is one of the most reliable Band 6 discriminators in titration curve questions.
Common Error
Students identify the half-equivalence point as pH 7 — confusing it with the "midpoint of the pH scale." The half-EP is at V_EP/2 on the x-axis, at pH = pKa on the y-axis. For acetic acid (pKa = 4.74), the half-EP is at pH 4.74 — nothing to do with pH 7.

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?

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Why the Strong/Strong Jump Is Largest

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.

Jump size

Strong/Strong: ~6–8 units
Weak acid/Strong base: ~4–6 units
Reason: Buffer region moderates pH change near EP

EP centred at

Strong/Strong: pH 7.00
Weak acid/Strong base: pH > 7
Reason: Conjugate base hydrolyses; produces OH⁻

Buffer region

Strong/Strong: None
Weak acid/Strong base: Before EP
Reason: Weak acid partially ionised → HA and A⁻ coexist
Must Do
When asked to explain why strong/strong has a larger jump, your answer must include: (1) no buffer capacity — only H⁺ and spectator ions, nothing resists pH change near the EP; (2) the weak acid system has buffer capacity (HA + A⁻ coexisting) that moderates the pH change even very close to the EP.
Common Error
"The strong acid + strong base jump is larger because strong acids are more reactive." Incorrect — the jump size is entirely explained by the presence or absence of buffer capacity near the equivalence point. A weak acid titration goes to the same extent of completion — it is the buffer region, not reactivity, that reduces the jump.

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.

Pause — write the highlighted definition into your book before moving on.

The strong acid + strong base titration has the largest pH jump because strong acids are more reactive than weak acids.

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Reading and Interpreting Features from a Titration Curve

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.

Method
Midpoint of steepest section (x-axis)
y-axis reading at V_EP
pH at V_EP/2
Flat plateau before EP
Result
Volume for concentration calculation
> 7 (weak acid/SB), 7 (strong/strong), < 7 (SA/weak base)
pKa of the weak acid
Henderson-Hasselbalch applies here
Must Do
In HSC questions asking you to "identify the equivalence point," never select the highest or lowest point on the curve — always select the midpoint of the steepest section (point of inflection). For weak acid + strong base, the EP is above pH 7 — a common error is marking pH 7 as the EP.
Common Error
Students mark the half-equivalence point at pH 7 on a weak acid + strong base curve. The half-EP is at pH = pKa — which is almost never 7. For any common organic weak acid (pKa 4–5), the half-EP is well below 7.

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:

5
Calculating pH at Specific Points — The Five-Region Method

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):

  • Start (Vb = 0): [H⁺] = √(Ka × c₀)
  • Buffer (0 < Vb < V_EP): n(HA)_remaining = n(HA)_initial − n(OH⁻); n(A⁻) = n(OH⁻); pH = pKa + log(n(A⁻)/n(HA)_remaining)
  • Half-EP (Vb = V_EP/2): pH = pKa
  • EP (Vb = V_EP): [A⁻] = n(A⁻)/Vtotal; Kb = Kw/Ka; [OH⁻] = √(Kb × [A⁻]); pH = 14 − pOH
  • After EP (Vb > V_EP): n(OH⁻)_excess = n(OH⁻) − n(HA)_initial; [OH⁻] = n(excess)/Vtotal; pH = 14 − pOH
Must Do
Before applying any formula, always identify the region explicitly by comparing n(OH⁻) added to n(HA) initial. Write: "n(OH⁻) = X mol; n(HA) = Y mol; since X < Y, we are in the buffer region." This prevents applying the wrong formula — the most common error in multi-part titration curve questions.
Common Error
At the EP of a weak acid + strong base, students write pH = 7.00. This is wrong — the EP pH is above 7. The correct calculation uses Kb for the conjugate base: [OH⁻] = √(Kb × [A⁻]) → pOH → pH = 14 − pOH. pH = 7 at EP is only valid for strong/strong.

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.

Pause — copy the highlighted definition into your book before moving on.

At the equivalence point of a weak acid + strong base titration, which method correctly calculates the EP pH?

!
Misconceptions to Fix
✗ "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.
Worked Example 1 — Reading a Titration Curve

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.

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(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).

2

(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).

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(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⁻.

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(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.

Worked Example 2 — pH at Five Points on a Weak Acid Curve

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.

1

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.

2

(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

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(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

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(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

5

(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 ✓)

6

(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.

Worked Example 3 — Extended Response: Identifying an Unknown Acid from Curve Data (8 marks)

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?

1

(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).

2

(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

3

(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.

4

(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).

5

(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.

Copy Into Your Books

Four Curve Types

  • Strong/Strong: start low, no buffer, EP=7, largest jump
  • Weak acid/SB: start intermediate, buffer before EP, EP>7, moderate jump
  • SA/Weak base: start low, no buffer before EP, EP<7, moderate jump
  • Weak/Weak: start intermediate, buffer throughout, no jump

pKa Rule

  • Read pH at V_EP/2 → that pH = pKa (weak acid + strong base only)
  • Half-EP: n(A⁻) = n(HA); H-H gives pH = pKa + log(1) = pKa

EP Identification

  • Midpoint of steepest section (NOT highest pH; NOT pH 7)
  • State both volume AND pH in any HSC answer

EP pH Calculation

  • Strong/strong: pH = 7.00
  • Weak acid/SB: Kb = Kw/Ka; [OH⁻] = √(Kb×[A⁻]); pH = 14−pOH
  • SA/weak base: Ka(BH⁺) = Kw/Kb; [H⁺] = √(Ka×[BH⁺])
Interactive Tool — Acid-Base Titration Open fullscreen ↗
True or false?
In a titration (shown in the tool), the equivalence point is where moles of acid exactly equal moles of base reacted.
🔬 Predict — Then Reveal +8 XP
Before looking at titration curves: predict the equivalence point pH for (a) strong acid + strong base, (b) weak acid + strong base, and (c) strong acid + weak base. Explain your reasoning for each.
Your predictionExpert answerCompare

Complete the Learn phase to unlock Practice.

A
Curve Identification Practice

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.

B
pKa Extraction and Indicator Selection

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.

ApplyBand 4

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?

UnderstandBand 3

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?

AnalyseBand 4

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?

ApplyBand 4

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?

EvaluateBand 5

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.

SHORT ANSWER QUESTIONS
UnderstandBand 4(4 marks)

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.

ApplyBand 5(5 marks)

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.

EvaluateBand 6(6 marks)

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.

Show All Answers

MC Answers

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.

Short Answer Model Answers

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.

Check Your Initial Identifications

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.

Extended Response — Titration Curves

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)

What is the EP pH for a strong acid + strong base titration?
pH = 7.00 — the salt (e.g. NaCl) is neutral; neither Na⁺ nor Cl⁻ hydrolyses.
How do you read pKa from a titration curve?
Find V_EP (midpoint of steepest section), calculate V_EP/2, read the pH at that volume — that pH = pKa.
Why does weak acid + strong base have a smaller pH jump than strong + strong?
The buffer region (HA + A⁻ coexisting before EP) moderates pH change even close to the EP — buffer capacity reduces the jump size.
For weak acid + strong base, which calculation applies at the EP?
Kb = Kw/Ka; [OH⁻] = √(Kb × [A⁻]); pH = 14 − pOH. EP pH is above 7 because A⁻ (conjugate base) hydrolyses.
Why is there no suitable indicator for a weak acid + weak base titration?
The dual overlapping buffer regions produce no sharp pH jump — the pH changes gradually throughout. No indicator has a transition range narrow enough to detect this.
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