AHL: Acid-base titration curves

IB Chemistry HL· Topic 3 (Classification of Matter) AHL Acid-base Titrations· 15 min read

1. Key Features of a Titration Curve★★☆☆☆HL only⏱ 4 min

📘 Definition

Equivalence Point

V_e

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

Example:

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

📘 Definition

Half-Equivalence Point

The point where half of the analyte has been neutralized by titrant. For a weak monoprotic acid, $[H A] = [A^{-}]$ at this point.

Example:

By the Henderson-Hasselbalch equation, $p H = p K_{a}$ 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
1. Convert pKa to Ka using the relationship $K_{a} = 1 0^{- p K_{a}}$ :
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.

2. Shapes for Different Acid-Base Combinations★★★☆☆HL only⏱ 5 min

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, $p K_{b} = 4.75$ ) 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
1. Half-equivalence occurs at 12.5 cm³ HCl added. At this point $pO H = p K_{b} = 4.75$ , so $p H = 14 - 4.75 = 9.25$ .
3
1. Equivalence occurs at 25 cm³ HCl added. All ammonia is converted to ammonium ions (weak acid), so equivalence pH is <7, ~5.
4
1. The vertical jump at equivalence is between ~pH 6 and pH 3. After equivalence, pH levels off near ~1 for excess strong HCl.

3. Indicator Selection★★★☆☆HL only⏱ 4 min

📘 Definition

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
1. 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
1. Bromothymol blue changes up to 7.6, which only partially overlaps the start of the jump, leading to an inaccurate end point.
4
1. 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.

4. Calculations from Titration Curves★★★★☆HL only⏱ 5 min

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
1. Moles of NaOH at the second equivalence point = concentration × volume = $0.100 \times 0.0248 = 0.00248$ mol.
3
1. Moles of diprotic acid = moles NaOH / 2 = $0.00248/2 = 0.00124$ mol.
4
1. Concentration of acid = moles / volume (dm³) = $0.00124/0.0250 = 0.0496$ mol dm⁻³.

✓ Quick check

Test your understanding:

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
Reveal answer
B —
Correct! The product of the reaction is methylammonium ions, which are acidic, so pH < 7 at equivalence.

5. Common Pitfalls

Wrong move:

Stating pH = pKa at the equivalence point of a weak acid titration

Why:

pH equals pKa only at the half-equivalence point, when half the acid is neutralized

Correct move:

Locate the half-equivalence point at half the equivalence volume, then read pH to get pKa

Wrong move:

Selecting phenolphthalein for a strong acid-weak base titration

Why:

Phenolphthalein changes color above pH 8.2, which is after the vertical jump that ends near pH 6 for this titration

Correct move:

Use an indicator with an acidic range, like methyl orange, that overlaps the vertical jump

Wrong move:

Assuming all titration curves have a sharp equivalence jump

Why:

Weak acid-weak base titrations produce only a gradual pH change with no large jump

Correct move:

Recognize that no indicator is suitable for weak acid-weak base titrations; a pH meter is required to find equivalence

Wrong move:

Forgetting that polyprotic acids have multiple equivalence points

Why:

Each proton on a polyprotic acid reacts sequentially, producing a separate equivalence point for each proton

Correct move:

Count the number of equivalence points to find the number of ionizable protons on a polyprotic acid

Wrong move:

Starting a 0.1 M strong acid titration at pH 7

Why:

Strong acids fully dissociate, so 0.1 M strong acid has a pH of 1, not neutral

Correct move:

Calculate initial pH from the concentration of the starting analyte before any titrant is added

6. Quick Reference 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

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2022 · 2
Titration curve shape and indicator selection
2021 · 1
pKa calculation from half-equivalence data
2019 · 2
Sketch titration curve for weak diprotic acid

Going deeper

Official ResourceIB Chemistry Data BookletContains indicator pH ranges for reference

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.