pH Titration Curves

Spec Mapping — OCR H432 Module 5.1.3 — Acids, bases and buffers, sub-topic on pH titration curves for all four combinations of strong / weak acid with strong / weak base: shape of each curve, location of the equivalence point and its dependence on acid-base strength, identification of the half-equivalence point where pH = $\text{p}K_a$pKa​ for a weak-acid titration, recognition of the buffer region, indicator selection criteria from curve geometry, and experimental determination of $\text{p}K_a$pKa​ from a curve (refer to the official OCR H432 specification document for exact wording). This lesson unites lessons 1–8 into a single visual framework — strong-acid pH (lesson 3), weak-acid pH ($\sqrt{K_a c}$Ka​c​, lesson 5), buffer pH (Henderson-Hasselbalch, lessons 7–8), and strong-base pH (lesson 6) all appear on different segments of the same titration curve.

The pH titration curve is OCR's preferred summative visual for the whole module — it lets a single diagram test recall of strong-vs-weak distinctions, $K_a$Ka​/$K_w$Kw​ calculations, buffer behaviour, and indicator choice simultaneously. Mastery of the four curve shapes (strong/strong, weak/strong, strong/weak, weak/weak) is non-negotiable. You must be able to (i) sketch each shape from memory; (ii) place the equivalence point at the correct pH; (iii) mark the half-equivalence point on weak-acid curves; (iv) identify the buffer region; (v) match an appropriate indicator using the indicator's pH range against the vertical jump of the curve.

Key Identities for Weak-Acid Titration (lesson 9 + lesson 10): $\text{At half-equivalence: } [\text{HA}] = [\text{A}^-] \Rightarrow \text{pH} = \text{p}K_a$At half-equivalence: [HA]=[A−]⇒pH=pKa​ $\text{At equivalence: pH determined by the salt formed (} \text{A}^- \text{ hydrolysis if weak acid + strong base)}$At equivalence: pH determined by the salt formed (A− hydrolysis if weak acid + strong base) $\text{Indicator } \text{p}K_{In} \text{ must fall within the vertical jump}$Indicator pKIn​ must fall within the vertical jump

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What is a pH titration curve?

A pH titration curve is a graph of pH (y-axis) against the volume of titrant added (x-axis), recorded continuously as the titrant is delivered from a burette into the analyte in a conical flask. In a typical experiment a pH probe is immersed in the flask and the pH is logged digitally; alternatively the pH can be measured manually after each addition. The shape of the curve depends on whether the acid and the base are strong or weak.

OCR requires you to know and interpret four shapes:

1. Strong acid + strong base (e.g. HCl titrated with NaOH) — sharp vertical jump from pH ~3 to pH ~11, equivalence at exactly pH 7.
2. Weak acid + strong base (e.g. CH₃COOH titrated with NaOH) — shallower initial rise, distinct buffer region with pH = $\text{p}K_a$pKa​ at half-equivalence, vertical jump from ~pH 7 to ~pH 11, equivalence above pH 7.
3. Strong acid + weak base (e.g. HCl titrated with NH₃) — sharp jump from ~pH 3 to ~pH 7, equivalence below pH 7, then post-equivalence buffer region around $\text{p}K_a$pKa​(NH₄⁺) = 9.25.
4. Weak acid + weak base — no sharp jump anywhere; smooth S-curve; no indicator works, must use a pH meter.

flowchart TD
  A["Acid-base titration"] --> B{"Is the acid strong?"}
  B -- "Yes" --> C{"Is the base strong?"}
  B -- "No" --> D{"Is the base strong?"}
  C -- "Yes" --> E["SA/SB: jump pH 3-11, equivalence at pH 7"]
  C -- "No" --> F["SA/WB: jump pH 3-7, equivalence below 7"]
  D -- "Yes" --> G["WA/SB: jump pH 7-11, equivalence above 7"]
  D -- "No" --> H["WA/WB: no sharp jump"]
  E --> I["Either indicator works"]
  F --> J["Methyl orange"]
  G --> K["Phenolphthalein"]
  H --> L["No indicator works - use pH meter"]

The decision tree above is the master template for all four curves. The remaining sections walk through each in detail.

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The four titration curves — a unified visual

Memorise this four-panel layout — examiners use the same template.

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The equivalence point — definition and dependence on acid-base strength

The equivalence point (or stoichiometric point) is the point at which the moles of acid and base added are equal, according to the balanced equation. It is not always at pH 7 — the pH at equivalence depends on the conjugate acid-base behaviour of the salt formed.

Combination	Equivalence pH	Reason
Strong acid + strong base	= 7.00	Salt is from strong-strong pair — neither Na⁺ nor Cl⁻ hydrolyses
Strong acid + weak base	< 7	Salt (e.g. NH₄Cl) — NH₄⁺ is a weak acid, hydrolyses to give H⁺
Weak acid + strong base	> 7	Salt (e.g. CH₃COONa) — CH₃COO⁻ is a weak base, hydrolyses to give OH⁻
Weak acid + weak base	≈ 7 (depends on relative pKa, pKb)	Both ions hydrolyse partially; near-cancellation

The equivalence point is identified on the graph as the centre of the steepest section of the curve. It is not the buffer-region midpoint (that is the half-equivalence point), nor the pH 7 point (unless strong-strong).

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Curve 1 — strong acid + strong base (HCl + NaOH)

Titrating 25.0 cm³ of 0.100 mol dm⁻³ HCl in the flask with 0.100 mol dm⁻³ NaOH from the burette.

Volume NaOH / cm³	pH (approx)
0	1.00
10	1.37
20	1.95
24	2.69
24.9	3.70
25.0 (equivalence)	7.00
25.1	10.30
26	11.29
30	12.05
50	12.52

Shape: starts at pH 1 (strong acid, lesson 3); rises slowly through the early region as excess H⁺ is consumed (excess-species calculation, lesson 6); has a vertical jump of about 6 units (pH 3.7 → 10.3) centred on the equivalence at 25.0 cm³; post-equivalence pH rises slowly as the now-strong-base excess is diluted.

Equivalence pH = 7.00: the salt NaCl is from a strong-strong pair and does not hydrolyse. The only ionisation contributing to pH is water self-ionisation.

Indicator choice: either methyl orange (3.1–4.4) or phenolphthalein (8.3–10.0) — both fall within the vertical jump 3.7–10.3. Phenolphthalein is preferred for visual clarity (colourless → bright pink).

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Curve 2 — weak acid + strong base (CH₃COOH + NaOH)

Titrating 25.0 cm³ of 0.100 mol dm⁻³ ethanoic acid ($\text{p}K_a = 4.76$pKa​=4.76) with 0.100 mol dm⁻³ NaOH.

Volume NaOH / cm³	pH	Notes
0	2.88	Pure weak acid, $\sqrt{K_a c}$Ka​c​ from lesson 5
5	4.14	Buffer region begins
12.5 (half-equivalence)	4.76	pH = $\text{p}K_a$pKa​
20	5.38	Buffer region
24	6.14	Buffer breaking
24.9	7.14	Vertical jump beginning
25.0 (equivalence)	8.72	Salt (CH₃COONa) is basic
25.1	10.30	Vertical jump complete
30	11.96	Excess strong base, lesson 6
50	12.52	Heavily excess NaOH

Shape: starts at pH 2.88 (weak acid, much higher than the strong-acid start of 1); rises moderately fast through the first cm³ or so as A⁻ forms; then enters a buffer region from about 5 cm³ to 22 cm³ where CH₃COOH and CH₃COO⁻ coexist and pH changes only slowly; vertical jump from pH ~7 to ~11 over the equivalence point; post-equivalence approaches the strong-base curve.

Half-equivalence point at 12.5 cm³ (half the equivalence volume): here exactly half the HA has been converted to A⁻, so $[\text{HA}] = [\text{A}^-]$[HA]=[A−] and pH = $\text{p}K_a$pKa​ = 4.76 by Henderson-Hasselbalch. This is the experimental route to measuring $\text{p}K_a$pKa​. Drop a pH probe into the flask and add NaOH until exactly half the calculated equivalence volume has been delivered; the recorded pH equals $\text{p}K_a$pKa​.

Equivalence pH = 8.72 (not 7). At equivalence the only solute is CH₃COONa(aq) and the pH comes from the hydrolysis of CH₃COO⁻:

$\text{CH}_3\text{COO}^- + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COOH} + \text{OH}^-$CH3​COO−+H2​O⇌CH3​COOH+OH−

This produces a small but measurable $[\text{OH}^-]$[OH−], hence pH > 7.

Indicator choice: must be within the vertical jump pH 7 → 11. Phenolphthalein (8.3–10.0) is the standard choice. Methyl orange (3.1–4.4) is wrong — it would change colour in the buffer region, far before the equivalence point.

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Curve 3 — strong acid + weak base (HCl + NH₃)

Titrating 25.0 cm³ of 0.100 mol dm⁻³ HCl with 0.100 mol dm⁻³ NH₃. $\text{p}K_a(\text{NH}_4^+) = 9.25$pKa​(NH4+​)=9.25.

Shape: starts low (strong acid); sharp jump of about 3.5 units (pH ~3 → ~7) around equivalence; equivalence pH below 7 because NH₄Cl is acidic. Post-equivalence the curve enters a buffer region centred on $\text{p}K_a$pKa​(NH₄⁺) = 9.25, because excess NH₃ creates the NH₃ / NH₄⁺ pair.

Equivalence pH = 5.28 (below 7), from $\sqrt{K_a c}$Ka​c​ applied to the 0.0500 mol dm⁻³ NH₄⁺ solution ($K_a = 5.6 \times 10^{-10}$Ka​=5.6×10−10): $[\text{H}^+] = 5.3 \times 10^{-6}$[H+]=5.3×10−6, pH = 5.28.

Indicator choice: methyl orange (3.1–4.4) falls inside the pH 3–7 vertical jump. Phenolphthalein (8.3–10.0) is wrong — it would change long after equivalence, in the post-equivalence buffer region.

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Curve 4 — weak acid + weak base (CH₃COOH + NH₃)

Shape: no sharp vertical jump anywhere on the curve. The pH rises smoothly from about 2.9 (weak acid start) through about 7 (near equivalence) to about 9 (post-equivalence weak base) — a smooth S-curve with no inflection sharp enough to host an indicator colour change.

The reason: at every stage of the titration both the weak acid and the weak base are partially hydrolysed, so neither species cleanly disappears. The pH changes continuously rather than jumping.

Equivalence pH is approximately 7 in the symmetric case ($\text{p}K_a$pKa​(HA) = $\text{p}K_b$pKb​(B)) but can be slightly above or below depending on relative strengths.

Indicator choice: no suitable indicator exists. No indicator's colour-change range falls inside a vertical jump because there is no vertical jump. For practical analytical work on weak-weak systems, chemists use: