8.3.2Acids and Bases
Titration Curves and Half-Equivalence Points — AP CHEMISTRY Revision Notes & Topical Questions
5 min read 5 parts Lesson 19 of 21 Unit quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Part 1 of 5Reading a Titration Curve
A titration curve plots pH against volume of titrant added, and each region tells you which species control the pH.
Starting pH
- Starting pH Before any titrant is added the pH comes only from the analyte, so a strong acid starts near 1 while a weak acid starts at a higher value.
Buffer region
- Buffer region For a weak analyte, adding titrant produces a mixture of weak acid and conjugate base,
- which resists pH change and gives a gently rising section.
Equivalence point
- Equivalence point The point where moles of titrant added exactly equal the moles of analyte originally present, found at the steepest part of the curve.
Excess region
- Excess region After equivalence the pH is controlled by leftover strong titrant, so the curve flattens and approaches the pH of the titrant.
Part 2 of 5pH at Equivalence for Different Pairings
pH at Equivalence for Different Pairings
Strong acid + strong base
- Strong acid + strong base Only a neutral salt and water form, so the pH at equivalence is exactly 7 at 25 °C.
Weak acid + strong base
- Weak acid + strong base The conjugate base of the weak acid is present at equivalence and reacts with water, so the pH is greater than 7.
Weak base + strong acid
- Weak base + strong acid The conjugate acid of the weak base is present at equivalence and donates protons to water, so the pH is less than 7.
Weak acid + weak base
- Weak acid + weak base The curve rises very gradually with no sharp vertical section,
- so the equivalence point is hard to locate and such titrations are avoided.
| Titration | Initial pH | pH at equivalence |
|---|---|---|
| Strong acid + strong base | Low (about 1) | 7 |
| Weak acid + strong base | Moderate (about 3) | Above 7 |
| Weak base + strong acid | High (about 11) | Below 7 |
Part 3 of 5The Half-Equivalence Point
1
Find the equivalence volume Vₑ on the curve, which is the volume of titrant that has completely reacted with the analyte.
2
The half-equivalence point is at exactly Vₑ/2, where half of the weak acid HA has been converted into its conjugate base A⁻.
3
At this point [HA] = [A⁻], so the ratio [A⁻]/[HA] equals 1 and the logarithm of that ratio is zero.
4
Substituting into the Henderson-Hasselbalch equation, pH = pKa + log([A⁻]/[HA]), gives pH = pKa at the half-equivalence point.
5
Reading the pH off the curve at Vₑ/2 therefore gives pKa directly, and Ka = 10⁻ᵖᴷᵃ; for a weak base the same point gives pOH = pKb.
Part 4 of 5Worked Example
Question
- 25.0 mL of 0.100 mol/L ethanoic acid (Ka = 1.8 × 10⁻⁵) is titrated with 0.100 mol/L NaOH.
- Find the volume at the half-equivalence point, the pH there, and the pH at equivalence.
- Moles of acid = 0.100 × 0.0250 = 2.50 × 10⁻³ mol, so equivalence needs 25.0 mL of NaOH and the half-equivalence point is at 12.5 mL.
- At 12.5 mL, [CH₃COOH] = [CH₃COO⁻], so pH = pKa = -log(1.8 × 10⁻⁵) = 4.74.
- At equivalence the volume is 50.0 mL and [CH₃COO⁻] = 2.50 × 10⁻³ / 0.0500 = 0.0500 mol/L.
- Kb = 1.0 × 10⁻¹⁴ / 1.8 × 10⁻⁵ = 5.6 × 10⁻¹⁰, so [OH⁻] = √(5.6 × 10⁻¹⁰ × 0.0500) = 5.3 × 10⁻⁶ mol/L.
- pOH = 5.28, so pH = 14.00 - 5.28 = 8.72.
Answer
- Half-equivalence at 12.5 mL with pH 4.74;
- pH at equivalence = 8.72.
Part 5 of 5Exam Checklist & Tips
8.3.2 – Key Points for the Exam
- Equivalence point Point at which moles of titrant added equal moles of analyte originally present.
- Half-equivalence point Point at which half the analyte has reacted, so [HA] = [A⁻] and pH = pKa.
- Buffer region Part of a weak-analyte titration curve where acid and conjugate base are both present and pH changes slowly.
- Titrant The solution of known concentration that is added from the burette.
Common Mistakes
- Assuming the equivalence point always occurs at pH 7; it only does for a strong acid with a strong base.
- Reading pKa from the equivalence volume instead of from the pH at half that volume.
- Using pH = pKa for a strong acid, which has no half-equivalence buffer behaviour because it is fully ionised.
- Confusing the endpoint (when the indicator changes colour) with the equivalence point (the stoichiometric point).
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