Acid-Base Titration Curves and Indicators
Acid-Base Titration Curves and Indicators
Titration Curves
A titration curve (pH curve) is a graph of pH (y-axis) against volume of titrant added (x-axis). The shape of the curve depends on whether the acid and base are strong or weak.
Four Types of Titration Curve
1. Strong acid + Strong base (e.g. HCl + NaOH)
- Initial pH: ~1 (strong acid, fully dissociated)
- pH rises slowly at first
- Steep vertical section around the equivalence point (pH 3.5 to 10.5)
- Equivalence point pH = 7.00 (the salt NaCl is neutral)
- pH levels off at ~13 with excess NaOH
2. Weak acid + Strong base (e.g. CH₃COOH + NaOH)
- Initial pH: ~3 (weak acid, partially dissociated — higher than a strong acid of the same concentration)
- pH rises gradually, with a buffer region in the first half (HA and A⁻ both present)
- Half-neutralisation point: When exactly half the acid has been neutralised, [HA] = [A⁻], so pH = pKa (this is how pKa is determined experimentally)
- Shorter steep section (pH ~7 to 10)
- Equivalence point pH > 7 (approximately 8.5–9) because the salt CH₃COONa is the conjugate base of a weak acid — it hydrolyses:
CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻
3. Strong acid + Weak base (e.g. HCl + NH₃)
- Initial pH: ~11 (weak base)
- pH falls gradually with a buffer region
- Shorter steep section (pH ~4 to 7)
- Equivalence point pH < 7 (approximately 5–5.5) because the salt NH₄Cl is the conjugate acid of a weak base — it hydrolyses:
NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺
- pH levels off at ~1 with excess HCl
4. Weak acid + Weak base (e.g. CH₃COOH + NH₃)
- No steep section — the pH changes gradually throughout
- Equivalence point pH depends on the relative strengths of the acid and base
- No suitable indicator can be used because there is no sharp pH transition
Reading Titration Curves
From a titration curve you can determine:
1. Equivalence point — the centre of the steep vertical section (where the moles of acid = moles of base). Read the volume from the x-axis at the midpoint of the steep rise.
2. pKa of a weak acid — at the half-equivalence volume (half the volume needed to reach the equivalence point), pH = pKa. This is because at half-neutralisation, [HA] = [A⁻], so from the Henderson-Hasselbalch equation, pH = pKa + log(1) = pKa.
3. Buffer region — the relatively flat section before the equivalence point in a weak acid/strong base titration, where the solution acts as a buffer.
Indicators
An acid-base indicator is a weak acid (HIn) whose conjugate base (In⁻) has a different colour:
HIn(aq) ⇌ H⁺(aq) + In⁻(aq)
Colour A Colour B
The indicator changes colour over a narrow pH range (approximately pKa ± 1). The colour change occurs when [HIn] ≈ [In⁻], i.e. when pH ≈ pKin (the pKa of the indicator).
Choosing the Right Indicator
The indicator must change colour within the steep section of the titration curve. This means the pKin must fall within the pH range of the steep section:
| Titration type | Equivalence pH | Steep range (approx.) | Suitable indicator |
|---|---|---|---|
| Strong acid / Strong base | 7.0 | 3.5–10.5 | Any (methyl orange, phenolphthalein, bromothymol blue) |
| Weak acid / Strong base | ~8.5 | 7–10 | Phenolphthalein (range 8.2–10.0) |
| Strong acid / Weak base | ~5.5 | 4–7 | Methyl orange (range 3.1–4.4) |
| Weak acid / Weak base | variable | No steep section | No suitable indicator |
Common Indicators
| Indicator | pH range | Colour change (acid → base) | pKin |
|---|---|---|---|
| Methyl orange | 3.1–4.4 | Red → Yellow | 3.7 |
| Bromothymol blue | 6.0–7.6 | Yellow → Blue | 7.0 |
| Phenolphthalein | 8.2–10.0 | Colourless → Pink | 9.3 |
Why the Equivalence Point pH Is Not Always 7
At the equivalence point, all the acid has reacted with all the base. The solution contains only the salt and water.
- Strong acid + Strong base: The salt (e.g. NaCl) does not hydrolyse → pH = 7
- Weak acid + Strong base: The salt (e.g. CH₃COONa) contains A⁻, which is a base that hydrolyses water → pH > 7
- Strong acid + Weak base: The salt (e.g. NH₄Cl) contains BH⁺, which is an acid that hydrolyses water → pH < 7
Polyprotic Acid Titrations
Diprotic acids (e.g. H₂SO₄, H₃PO₄ has three protons) lose protons in stages. The titration curve shows two steep sections and two equivalence points.
Example: H₃PO₄ with NaOH
- First equivalence point: H₃PO₄ → NaH₂PO₄ (one proton removed)
- Second equivalence point: NaH₂PO₄ → Na₂HPO₄ (two protons removed)
- Third equivalence may not be sharp (Ka₃ is very small)
Titration Calculations at the Equivalence Point
At the equivalence point: moles of acid = moles of base (for monoprotic acids/bases)
n(acid) = c(acid) × V(acid) = c(base) × V(base) = n(base)
Worked Example
25.0 cm³ of 0.100 mol dm⁻³ NaOH is titrated with 0.0500 mol dm⁻³ ethanoic acid. What volume of acid is needed to reach the equivalence point?
Moles NaOH = 0.100 × 25.0/1000 = 2.50 × 10⁻³ mol
Moles CH₃COOH needed = 2.50 × 10⁻³ mol (1:1 ratio)
Volume = 2.50 × 10⁻³ / 0.0500 = 0.0500 dm³ = 50.0 cm³
Back Titrations
A back titration is used when:
- The analyte is insoluble (e.g. CaCO₃)
- The reaction is slow
- The analyte would interfere with the indicator
Method: Add excess of one reagent, then titrate the unreacted excess with a standard solution. The amount of analyte is found by difference.
Exam Tips
- Sketch the correct shape for each of the four titration types — learn them as four distinct patterns
- When asked to select an indicator, explain that its pH range must lie within the steep section of the curve
- For weak acid / weak base titrations, always state that no indicator is suitable because there is no steep section
- At half-neutralisation of a weak acid, pH = pKa — this is a very commonly examined point
- Always label the equivalence point and half-equivalence point on your sketches