# AHL: Acid-base titration curves

> IB Chemistry HL · S3: Classification of matter
> Source: https://www.owlsprep.com/study/ib-chemistry-hl-u3-ahl-acid-base-titration-curves/

This sub-topic covers the interpretation and construction of pH titration curves for all combinations of strong/weak acids and bases. You will learn to extract key data like pKa and select the correct indicator for any titration.

**Prerequisites:** [Strong and weak acids and bases](https://www.owlsprep.com/study/ib-chemistry-hl-u3-acids-and-bases/); [Buffer solutions and Henderson-Hasselbalch equation](https://www.owlsprep.com/study/ib-chemistry-hl-u3-ahl-buffer-solutions/)

## Learning objectives

- Identify the shape of titration curves for all strong/weak acid-base combinations
- Locate equivalence and half-equivalence points on a titration curve
- Calculate pKa/pKb and Ka/Kb from titration curve data
- Select appropriate indicators based on titration curve shape

## Key Features of a Titration Curve

**Equivalence Point** — The point in a titration where the amount of titrant added is chemically equivalent to the amount of analyte present in the sample.

*Notation:* V_e

*Example:* For 25 cm³ 0.1 M monoprotic acid titrated with 0.1 M strong base, V_e = 25 cm³.

**Half-Equivalence Point** — The point where half of the analyte has been neutralized by titrant. For a weak monoprotic acid, $[HA] = [A^-]$ at this point.

*Example:* By the Henderson-Hasselbalch equation, $pH = pK_a$ here.

A titration curve plots pH of the analyte solution against the volume of titrant added. Key regions include the initial region (before much titrant is added), the buffer region (around half-equivalence, where pH changes slowly), the sharp vertical jump at equivalence, and the final region where excess titrant dominates the pH.

**Worked example:** A 0.1 M weak monoprotic acid is titrated with 0.1 M NaOH. The half-equivalence point occurs at 14.2 cm³ NaOH added, with a measured pH of 5.16. Calculate the pKa and Ka of the acid.

1. 1. Recall that for a weak monoprotic acid titrated with strong base, pH equals pKa at the half-equivalence point:
2. $$pK_a = pH = 5.16$$
3. 2. Convert pKa to Ka using the relationship $K_a = 10^{-pK_a}$:
4. $$K_a = 10^{-5.16} = 6.9 \times 10^{-6} \text{ mol dm}^{-3}$$

> **Exam tip:** Never confuse equivalence point with half-equivalence point: pH = pKa only at half-equivalence, not equivalence.

## Shapes for Different Acid-Base Combinations

The shape of a titration curve depends on whether the analyte and titrant are strong or weak electrolytes. The table below summarizes the key characteristics of all four common combinations:

| Combination | Initial pH | Equivalence pH | Jump Size at Equivalence |
| --- | --- | --- | --- |
| Strong acid + Strong base | 1-2 | 7 | Large jump (pH 4 to 10) |
| Weak acid + Strong base | 3-6 | >7 | Large jump (pH 7 to 11) |
| Strong acid + Weak base | 1-2 | <7 | Large jump (pH 3 to 7) |
| Weak acid + Weak base | 3-6 | ~7 | No large jump |

**Worked example:** Sketch the titration curve for 25 cm³ 0.1 M ammonia (weak base, $pK_b = 4.75$) titrated with 0.1 M HCl (strong acid). Label the pH at half-equivalence and equivalence.

1. 1. Initial pH: Ammonia is a weak base, so initial pH = 14 - 0.5(pKb - log c) = ~11, less than 13 for a strong base of the same concentration.
2. 2. Half-equivalence occurs at 12.5 cm³ HCl added. At this point $pOH = pK_b = 4.75$, so $pH = 14 - 4.75 = 9.25$.
3. 3. Equivalence occurs at 25 cm³ HCl added. All ammonia is converted to ammonium ions (weak acid), so equivalence pH is <7, ~5.
4. 4. The vertical jump at equivalence is between ~pH 6 and pH 3. After equivalence, pH levels off near ~1 for excess strong HCl.

## Indicator Selection

**Acid-Base Indicator** — A weak organic acid/base that changes color over a specific pH range, used to detect the end point of a titration.

For an indicator to be suitable for a titration, its entire pH color change range must overlap with the sharp vertical pH jump at the equivalence point. This ensures the end point (color change) occurs almost exactly at the equivalence point.

**Worked example:** Which of the following indicators is suitable for titration of 0.1 M propanoic acid (weak acid) with 0.1 M NaOH (strong base)? Methyl orange (3.1-4.4), Bromothymol blue (6.0-7.6), Phenolphthalein (8.2-10.0).

1. 1. Weak acid-strong base titration has a vertical pH jump between ~7 and ~11, with equivalence pH >7.
2. 2. Methyl orange changes color between 3.1 and 4.4, which is far below the jump, so it will change color long before equivalence, it is unsuitable.
3. 3. Bromothymol blue changes up to 7.6, which only partially overlaps the start of the jump, leading to an inaccurate end point.
4. 4. Phenolphthalein's entire range (8.2-10.0) lies within the vertical jump, so it is the suitable indicator.

> **Exam tip:** Always justify indicator selection by referencing overlap with the vertical equivalence jump, not just the equivalence pH.

## Calculations from Titration Curves

Titration curves can be used to extract multiple key values: the concentration of the analyte from the equivalence volume, the pKa/pKb of weak acids/bases from the half-equivalence point, and the Ka/Kb from pKa/pKb.

**Worked example:** A 25.0 cm³ sample of a diprotic weak acid is titrated with 0.100 mol dm⁻³ NaOH. Two equivalence points are observed at 12.4 cm³ and 24.8 cm³ NaOH. What is the concentration of the original acid solution?

1. 1. A diprotic acid has two replaceable protons, so 2 moles of NaOH react with 1 mole of diprotic acid.
2. 2. Moles of NaOH at the second equivalence point = concentration × volume = $0.100 × 0.0248 = 0.00248$ mol.
3. 3. Moles of diprotic acid = moles NaOH / 2 = $0.00248 / 2 = 0.00124$ mol.
4. 4. Concentration of acid = moles / volume (dm³) = $0.00124 / 0.0250 = 0.0496$ mol dm⁻³.

**Check your understanding**

Test your understanding:

1. What is the pH at the equivalence point of a titration of hydrochloric acid (strong acid) with methylamine (weak base)?

   - A. pH = 7
   - B. pH < 7
   - C. pH > 7
   - D. pH = 14

   *Why:* Correct! The product of the reaction is methylammonium ions, which are acidic, so pH < 7 at equivalence.

## Common pitfalls

- **Wrong:** Stating pH = pKa at the equivalence point of a weak acid titration
  - Why it fails: pH equals pKa only at the half-equivalence point, when half the acid is neutralized
  - Correct: Locate the half-equivalence point at half the equivalence volume, then read pH to get pKa
- **Wrong:** Selecting phenolphthalein for a strong acid-weak base titration
  - Why it fails: Phenolphthalein changes color above pH 8.2, which is after the vertical jump that ends near pH 6 for this titration
  - Correct: Use an indicator with an acidic range, like methyl orange, that overlaps the vertical jump
- **Wrong:** Assuming all titration curves have a sharp equivalence jump
  - Why it fails: Weak acid-weak base titrations produce only a gradual pH change with no large jump
  - Correct: Recognize that no indicator is suitable for weak acid-weak base titrations; a pH meter is required to find equivalence
- **Wrong:** Forgetting that polyprotic acids have multiple equivalence points
  - Why it fails: Each proton on a polyprotic acid reacts sequentially, producing a separate equivalence point for each proton
  - Correct: Count the number of equivalence points to find the number of ionizable protons on a polyprotic acid
- **Wrong:** Starting a 0.1 M strong acid titration at pH 7
  - Why it fails: Strong acids fully dissociate, so 0.1 M strong acid has a pH of 1, not neutral
  - Correct: Calculate initial pH from the concentration of the starting analyte before any titrant is added

## Cheatsheet

| Acid-Base Combination | Equivalence pH | Best Indicator | Key Data |
| --- | --- | --- | --- |
| Strong acid + Strong base | 7 | Any (4-10 range) | Equivalence at V jump |
| Weak acid + Strong base | >7 | Phenolphthalein | pKa = pH at ½ equivalence |
| Strong acid + Weak base | <7 | Methyl orange | pKb = 14 - pH at ½ equivalence |
| Weak acid + Weak base | ~7 | None | pH meter required |
| Polyprotic acid + Strong base | Variable | Depends on jump | One pKa per equivalence point |

## What's next

Mastering acid-base titration curves is a core requirement for IB Chemistry HL, and this topic regularly appears in both Paper 1 multiple choice and Paper 2 extended response questions. You will apply the skills learned here to buffer solution calculations, practical titration assessments, and more advanced topics like amino acid titration and pH-dependent organic reactions. This topic also builds on your understanding of weak acid equilibria, which is a major component of the acids and bases unit.

- [R1: What drives chemical reactions?](https://www.owlsprep.com/study/ib-chemistry-hl-u4-overview/)
- [Enthalpy change and calorimetry](https://www.owlsprep.com/study/ib-chemistry-hl-u4-enthalpy-change-and-calorimetry/)
- [Hess's Law](https://www.owlsprep.com/study/ib-chemistry-hl-u4-hess-s-law/)

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