# pH titration curves and indicators

> CIE A-Level Chemistry · 9701 Further chemical equilibria
> Source: https://www.owlsprep.com/study/cie-9701-u18-ph-titration-curves-and-indicators/

This sub-topic explains how pH changes during acid-base titrations, how to interpret different titration curve shapes, and how to select the correct indicator for accurate titration results, a frequent exam and practical topic.

**Prerequisites:** [Bronsted-Lowry acids and bases](https://www.owlsprep.com/study/cie-9701-u17-bronsted-lowry-acids-bases/); [pH and pKa calculations](https://www.owlsprep.com/study/cie-9701-u18-ph-and-pka-calculations/)

## Learning objectives

- Sketch and interpret pH titration curves for all combinations of strong/weak acids and bases
- Explain the difference between equivalence point and end point
- Relate indicator pKa to the pH range of its colour change
- Select a suitable indicator for a given acid-base titration

## Shapes of titration curves for different acid-base combinations

The shape of a pH titration curve depends only on the strengths of the acid and base used. All titrations of strong/weak monoprotic acids with strong/weak bases have a characteristic sigmoid shape, with a large vertical change in pH at the equivalence point.

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

*Example:* For 25 cm³ 0.1 mol dm⁻³ HCl titrated with 0.1 mol dm⁻³ NaOH, equivalence point occurs at 25 cm³ NaOH added

| Acid strength | Base strength | Equivalence pH | Vertical pH range |
| --- | --- | --- | --- |
| Strong | Strong | 7 | 3 → 11 |
| Strong | Weak | <7 | 3 → 8 |
| Weak | Strong | >7 | 6 → 11 |
| Weak | Weak | ~7 | None (very small change) |

**Worked example:** Sketch the pH titration curve when 0.1 mol dm⁻³ ethanoic acid (weak acid) in a conical flask is titrated with 0.1 mol dm⁻³ sodium hydroxide (strong base). Label the equivalence point pH.

1. 1. Initial pH: Ethanoic acid is a weak acid, so initial pH is ~3, between 1 and 7.
2. 2. As NaOH is added, pH increases slowly, forming a buffer region where pH changes very little.
3. 3. Equivalence point occurs when moles of NaOH equal moles of ethanoic acid. All ethanoic acid is converted to ethanoate ions, so pH is basic (~8.5).
4. 4. The vertical region of the curve spans approximately pH 6 to 11, matching the table above.
5. 5. After equivalence, pH levels off around 13 as excess strong NaOH is added.

> **Exam tip:** Always check which species is in the conical flask to get the correct initial pH for the curve.

## Key features: the half-equivalence point

Titration curves have other useful features beyond the equivalence point. The half-equivalence point gives a direct way to calculate the pKa of a weak acid or pKb of a weak base.

**Half-equivalence point** — The point where half the volume of titrant needed to reach equivalence has been added. At this point, the concentration of the weak acid equals the concentration of its conjugate base.

*Example:* For the titration above with equivalence at 25 cm³ NaOH, half-equivalence is at 12.5 cm³ NaOH added.

$$pH = pK_a + \log\frac{[A^-]}{[HA]} = pK_a + \log 1 = pK_a$$

**Worked example:** A 25 cm³ sample of unknown weak monoprotic acid is titrated with 0.10 mol dm⁻³ NaOH. Equivalence is reached at 18.5 cm³ NaOH. At 9.25 cm³ NaOH added, pH is 3.72. What is the pKa of the acid?

1. 1. 9.25 cm³ is exactly half of 18.5 cm³, so this is the half-equivalence point.
2. 2. At half-equivalence, pH equals pKa for a weak acid analyte.
3. 3. Therefore pKa = 3.72.

## Indicators as weak acids

Acid-base indicators are weak acids (or rarely weak bases) where the undissociated acid (HIn) and conjugate base (In⁻) have distinct different colours. The dissociation equilibrium is:

$$HIn(aq) \rightleftharpoons H^+(aq) + In^-(aq)$$

The human eye can only see the dominant colour when one form is at least 10 times more concentrated than the other. This means the indicator changes colour over the pH range $pK_a \pm 1$.

**End point** — The point in a titration where the indicator changes colour, which is the experimental signal to stop adding titrant. A good indicator has an end point that matches the equivalence point pH.

**Worked example:** Phenolphthalein has a pKa of 9.4. What pH range does it change colour over?

1. 1. The colour change range is always $pK_a \pm 1$.
2. 2. Range = $9.4 - 1$ to $9.4 + 1$ = 8.4 to 10.4.

## Selecting a suitable indicator

An indicator is suitable for a titration if its entire pH range of colour change falls within the vertical region of the titration curve. This ensures the end point occurs at the same volume as the equivalence point.

> **warning**
>
> Weak acid-weak base titrations have no vertical pH change at equivalence, so no indicator will give a sharp end point. These titrations are not used for quantitative analysis.

**Worked example:** Which indicator is suitable for titration of hydrochloric acid (strong acid) with ammonia (weak base): methyl orange (3.1-4.4) or phenolphthalein (8.2-10.0)?

1. 1. For strong acid + weak base, the vertical region of the titration curve is pH 3 to 8.
2. 2. Methyl orange's range 3.1-4.4 falls entirely within this vertical region.
3. 3. Phenolphthalein's range 8.2-10.0 is above the vertical region, so it will change colour after equivalence, giving an inaccurate result.
4. 4. Therefore methyl orange is the suitable indicator.

## Common pitfalls

- **Wrong:** Confusing equivalence point and end point
  - Why it fails: Equivalence point is the theoretical point where moles are equal; end point is the experimental point where the indicator changes colour. They are not identical.
  - Correct: Remember that a good indicator is chosen so that end point is as close as possible to equivalence point.
- **Wrong:** Starting the curve at pH 7 when the conical flask contains a strong acid
  - Why it fails: Failing to account for excess analyte before any titrant is added, leading to an incorrect initial pH.
  - Correct: Always check which species is in the conical flask to get the correct starting pH for the curve.
- **Wrong:** Claiming pH = pKb at half-equivalence for a weak base titrated with strong acid
  - Why it fails: For a weak base analyte, it is pOH that equals pKb at half-equivalence, not pH.
  - Correct: For weak base analytes, $pOH = pK_b$ so $pH = 14 - pK_b$ at half-equivalence.
- **Wrong:** Choosing an indicator with pKa = 7 for any titration
  - Why it fails: Equivalence point is only pH 7 for strong acid + strong base titrations.
  - Correct: Always match the indicator's $pK_a \pm 1$ range to the vertical region of the specific titration.
- **Wrong:** Using an indicator for weak acid-weak base titrations
  - Why it fails: There is no sharp vertical pH change at equivalence, so the indicator changes colour gradually instead of suddenly.
  - Correct: Weak acid-weak base titrations are not used for quantitative analysis with indicators.

## Cheatsheet

| Titration Type | Equivalence pH | Vertical Range | Suitable Indicator |
| --- | --- | --- | --- |
| Strong acid + Strong base | 7 | 3 – 11 | Phenolphthalein / Methyl orange |
| Strong acid + Weak base | <7 | 3 – 8 | Methyl orange (pKa ~3.7) |
| Weak acid + Strong base | >7 | 6 – 11 | Phenolphthalein (pKa ~9.4) |
| Weak acid + Weak base | ~7 | None | No suitable indicator |

## What's next

Understanding titration curves is the foundation for learning about acid-base buffers, as the buffer region of a titration curve corresponds to the range where a solution resists pH changes. This topic is also heavily linked to pKa determination, a common extended response question that tests your understanding of half-equivalence points. For practical exams, you will need to apply this knowledge to select indicators for unknown titrations and interpret given titration curves to extract data. Mastery of this sub-topic is essential for all further acid-base equilibrium topics in CIE A-Level Chemistry.

- [Further electrochemistry](https://www.owlsprep.com/study/cie-9701-u19-overview/)
- [Standard electrode potentials](https://www.owlsprep.com/study/cie-9701-u19-standard-electrode-potentials/)
- [Electrochemical cells](https://www.owlsprep.com/study/cie-9701-u19-electrochemical-cells/)

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