Indicator Choice and Titration Error

Introduction

The equivalence point of a titration is a stoichiometric idea: it is reached when the moles of titrant exactly match the analyte. The end point is what you actually observe, usually a colour change. A good titration makes these two coincide as closely as possible. That depends on matching the pH range over which an indicator changes colour to the steep, near-vertical part of the titration curve, and on understanding how large an error results when the match is poor.

Core explanation

Indicators are weak acids. An indicator HIn establishes HIn ⇌ H⁺ + In⁻, with KIn = [H⁺][In⁻]/[HIn]. Rearranging gives pH = pKIn + log([In⁻]/[HIn]). The two forms have different colours.

Transition range. The eye sees mostly the acid colour when [HIn] is about ten times [In⁻], and mostly the base colour when the ratio is reversed. The visible change therefore spans roughly pKIn − 1 to pKIn + 1, about two pH units. The exact range varies because some colours are more intense than others.

Indicator Approximate range Colour change (acid to base) --- --- --- Methyl orange 3.1 – 4.4 red to yellow Methyl red 4.4 – 6.2 red to yellow Bromothymol blue 6.0 – 7.6 yellow to blue Phenolphthalein 8.3 – 10.0 colourless to pink

The matching rule. Near equivalence, a single drop of titrant changes the pH by several units. If the whole transition range of the indicator lies within that steep section, the colour changes within one drop of equivalence. If the range lies on a flat part, the colour change is gradual and occurs at the wrong volume.

- Strong acid with strong base: the steep region spans about pH 3 to 11, so any of the four indicators works. - Weak acid with strong base: steep region about pH 7 to 11, centred near 8.7; phenolphthalein is right. - Weak base with strong acid: steep region about pH 3 to 7, centred near 5.3; methyl red or methyl orange suits. - Weak acid with weak base: there is no sharp steep region, so no indicator gives a reliable end point; a pH meter or conductivity method is used instead.

Estimating titration error. Suppose ethanoic acid (pKa 4.74) is titrated with NaOH but the titration stops at pH 7.0 using bromothymol blue. At that pH the ratio [HA]/[A⁻] = 10^(pKa − pH) = 10^(−2.26) = 5.5 × 10⁻³. About 0.55% of the acid is still unreacted, so the titre is about 0.55% too small. With phenolphthalein stopping at pH 9.0, [HA]/[A⁻] = 10^(−4.26), which is negligible, and the excess OH⁻ is only about 1 × 10⁻⁵ mol dm⁻³. In 50 cm³ that is 5 × 10⁻⁷ mol, roughly 0.02% of 2.5 × 10⁻³ mol, a far smaller error.

Step-by-step reasoning

1. Identify the acid and base as strong or weak. 2. Calculate or sketch the pH at equivalence and the extent of the steep region. 3. Choose an indicator whose transition range lies inside the steep region, ideally bracketing the equivalence pH. 4. If asked for the error, calculate the fraction of analyte unreacted, or titrant in excess, at the end point pH.

Visual explanation

Overlay coloured horizontal bands for each indicator range on a sketched titration curve. For the ethanoic acid curve, the phenolphthalein band crosses the vertical section, while the methyl orange band crosses the flat buffer plateau, where many cubic centimetres of titrant are needed to pass through it.

Real-world analogy

Choosing an indicator is like placing a finish-line sensor on a racetrack. If the sensor sits where the runners are sprinting, it records the finishing moment precisely. If it sits on a long slow bend, runners drift past it gradually and the recorded time is unreliable.

Real-world example

Pharmaceutical laboratories assay aspirin, a weak acid, by titration with standard sodium hydroxide. Phenolphthalein is the specified indicator because its range lies in the basic steep region. Using methyl orange would give a gradual, early colour change and a seriously low assay result.

Why?

Why does the indicator itself not disturb the titration? It is added in tiny amounts, typically a few drops of a dilute solution, so the moles of HIn are negligible compared with the analyte. That is also why adding too much indicator is poor practice: it consumes measurable titrant.

Common misconception

"The indicator changes colour exactly at its pKIn, so choose an indicator with pKIn equal to 7." The colour changes across a range, and the aim is to match the equivalence pH of the specific titration, which is 7 only for strong acid with strong base.

Worked example

Question: Methyl red (changing near pH 5.0) is mistakenly used in titrating ethanoic acid (pKa 4.74) with NaOH. Estimate the percentage of acid unreacted at the colour change.

Reasoning: [HA]/[A⁻] = 10^(4.74 − 5.0) = 10^(−0.26) = 0.55. Fraction unreacted = 0.55 ÷ (1 + 0.55) = 0.35.

Answer: About 35% of the acid is still unreacted, so the titre would be about 35% too low.

Quick check

1. Why is phenolphthalein unsuitable for titrating aqueous ammonia with hydrochloric acid? Answer: Its range of 8.3 to 10.0 lies in the buffer region, well above the acidic steep section near pH 5.

Exam focus

State both the equivalence pH and the indicator range when justifying a choice. For weak acid with weak base, say that no indicator is suitable and explain why. Quantitative error questions use pH = pKa + log ratio at the end point pH.

Advanced insight

Visual end points depend on the observer and on lighting. Mixed indicators, such as bromocresol green with methyl red, combine colours so that the change becomes sharp and grey at a single pH, narrowing the effective range. Where accuracy matters most, potentiometric end points located from the maximum of the first derivative dpH/dV remove indicator error altogether.

Summary

An indicator is a weak acid whose colour changes over about pKIn ± 1. The end point matches equivalence only if this range lies within the steep part of the titration curve. Phenolphthalein suits weak acid with strong base, methyl red or methyl orange suits weak base with strong acid, and any common indicator suits strong with strong. Titration error can be estimated from the acid-to-base ratio at the end point pH.

Practice questions

1. Choose an indicator for titrating methanoic acid with sodium hydroxide and justify your choice. Answer: Phenolphthalein, because the equivalence point is basic and its range of 8.3 to 10.0 lies in the steep region. 2. An indicator has pKIn = 5.0. Over what pH range does it change colour? Answer: Approximately pH 4.0 to 6.0. 3. Explain why no indicator is suitable for ethanoic acid titrated with aqueous ammonia. Answer: The curve has no sharp vertical section, so any colour change would be spread over a large volume of titrant. 4. At what ratio of [In⁻] to [HIn] is an indicator at the midpoint of its colour change, and what is the pH then? Answer: The ratio is 1, and the pH equals pKIn.