Indicators and Titration Curves (Senior 6 Chemistry): free lessons | Ganzaa

Indicators and Titration Curves

Lessons

Senior 6 · Chemistry

Indicators and Titration Curves

3 lessons

Lesson 1 of 3

Acid–Base Indicators and How They Work

25 min

Why does cabbage juice change colour?

Chop a few leaves of red cabbage, pour hot water over them and leave them to stand: the water turns a deep purple. Add a few drops of lemon juice and the purple liquid turns red. Add a pinch of baking soda (sodium hydrogencarbonate) instead, and it turns blue-green. The liquid has not been "dyed" by the lemon or the soda. It contains coloured molecules, anthocyanins, whose colour depends on how many protons they carry, and so on the pH around them.

That is exactly what a chemist needs in a titration. In Senior 3 you titrated acids against alkalis, and in Unit 8 you calculated the pH of acids, bases, salts and buffers. But when a colourless acid is neutralised by a colourless alkali, nothing in the flask shows you the moment it happens. An indicator makes that moment visible. This lesson explains why each indicator changes colour where it does.

Red (purple) cabbage leaves soaking in hot water in a beaker on a wire gauze. The dark purple liquid that forms is a home-made acid–base indicator. Photo: Millars, CC BY 4.0, via Wikimedia Commons

Definition

Acid–base indicator: a weak acid (or weak base), written HIn, whose undissociated form and conjugate base $\mathrm{In^{-}}$ have different colours. Example: methyl orange is red as HIn and yellow as $\mathrm{In^{-}}$ .

Indicator constant, $K_{\mathrm{In}}$ : the acid dissociation constant of the indicator, $K_{\mathrm{In}} = \frac{[\mathrm{H_3O^{+}}][\mathrm{In^{-}}]}{[\mathrm{HIn}]}$ , with $\mathrm{p}K_{\mathrm{In}} = -\log_{10}K_{\mathrm{In}}$ . Example: methyl red has $\mathrm{p}K_{\mathrm{In}} \approx 5.1$ .

Colour-change range (transition range): the pH interval over which a mixture of the two colours is seen, roughly $\mathrm{p}K_{\mathrm{In}} \pm 1$ . Example: phenolphthalein changes between pH 8.3 and 10.0.

End point: the point in a titration at which the indicator changes colour. It should coincide with the equivalence point, where the acid and base have reacted in exactly the mole ratio of the equation.

Universal indicator: a mixture of several indicators chosen so that the colour changes gradually across the whole pH scale. It estimates pH but is useless for titrations, because it has no single sharp change.

An indicator is a weak acid in equilibrium

In water an indicator sets up the equilibrium

$\underset{\text{colour A}}{\mathrm{HIn(aq)}} + \mathrm{H_2O(l)} \rightleftharpoons \mathrm{H_3O^{+}(aq)} + \underset{\text{colour B}}{\mathrm{In^{-}(aq)}}$

Add acid, and the extra $\mathrm{H_3O^{+}}$ pushes the equilibrium to the left (Le Chatelier's principle): HIn dominates and you see colour A. Add alkali, and $\mathrm{OH^{-}}$ removes $\mathrm{H_3O^{+}}$ , so the equilibrium shifts to the right: $\mathrm{In^{-}}$ dominates and you see colour B.

Where exactly does the colour change?

Take logarithms of the expression for $K_{\mathrm{In}}$ , exactly as you did for buffers in Unit 8:

$\mathrm{pH} = \mathrm{p}K_{\mathrm{In}} + \log_{10}\frac{[\mathrm{In^{-}}]}{[\mathrm{HIn}]}$

When $\mathrm{pH} = \mathrm{p}K_{\mathrm{In}}$ , the ratio is 1: the two forms are equal and you see the in-between colour.
The eye sees only colour A once $[\mathrm{HIn}]$ is about ten times $[\mathrm{In^{-}}]$ , that is, at $\mathrm{pH} \le \mathrm{p}K_{\mathrm{In}} - 1$ .
It sees only colour B once $[\mathrm{In^{-}}]$ is about ten times $[\mathrm{HIn}]$ , at $\mathrm{pH} \ge \mathrm{p}K_{\mathrm{In}} + 1$ .

So the colour changes over about two pH units, centred on $\mathrm{p}K_{\mathrm{In}}$ . Figure 1.1 shows this for methyl red.

Figure 1.1: The fraction of methyl red in its yellow form rises from about 9% to 91% between pH 4.1 and pH 6.1.

Common laboratory indicators

Indicator	Colour in acid (HIn)	Colour-change range (pH)	Colour in alkali ( $\mathrm{In^{-}}$ )
Thymol blue (first change)	red	1.2–2.8	yellow
Methyl orange	red	3.1–4.4	yellow
Methyl red	red	4.4–6.2	yellow
Litmus	red	4.5–8.3	blue
Bromothymol blue	yellow	6.0–7.6	blue
Phenolphthalein	colourless	8.3–10.0	pink
Thymolphthalein	colourless	9.3–10.5	blue

The real ranges are not always exactly $\mathrm{p}K_{\mathrm{In}} \pm 1$ . The eye notices some colours more easily than others: a little pink in a colourless solution is obvious, so phenolphthalein appears to "change" as soon as about a tenth of it is in the pink form. Litmus has a very wide range, which is why it is never used in titrations. Figure 1.2 compares the ranges on one pH scale.

Figure 1.2: Each indicator changes colour over its own narrow band of pH. Outside that band its colour no longer changes, however much more acid or alkali is added.

Worked example

Problem. Methyl red has $\mathrm{p}K_{\mathrm{In}} = 5.1$ . It is red as HIn and yellow as $\mathrm{In^{-}}$ . Calculate the ratio $\frac{[\mathrm{In^{-}}]}{[\mathrm{HIn}]}$ at pH 4.1 and at pH 6.1, and state the colour seen at each pH and at pH 5.1.

Solution. Rearranging $\mathrm{pH} = \mathrm{p}K_{\mathrm{In}} + \log_{10}\frac{[\mathrm{In^{-}}]}{[\mathrm{HIn}]}$ :

$\frac{[\mathrm{In^{-}}]}{[\mathrm{HIn}]} = 10^{\,\mathrm{pH} - \mathrm{p}K_{\mathrm{In}}}$

pH 4.1: $10^{4.1-5.1} = 10^{-1} = 0.10$ . HIn is ten times $\mathrm{In^{-}}$ : red.
pH 6.1: $10^{6.1-5.1} = 10^{1} = 10$ . $\mathrm{In^{-}}$ is ten times HIn: yellow.
pH 5.1: $10^{0} = 1$ . Equal amounts: orange, the mixed colour.

Answer: 0.10 (red) at pH 4.1 and 10 (yellow) at pH 6.1; orange at pH 5.1. The two pH values bracket the observed range, 4.4–6.2.

Worked example

Problem. An indicator is red as HIn and blue as $\mathrm{In^{-}}$ . In a buffer of pH 5.40, measurement with a colorimeter shows $\frac{[\mathrm{In^{-}}]}{[\mathrm{HIn}]} = 0.25$ . Calculate $\mathrm{p}K_{\mathrm{In}}$ and $K_{\mathrm{In}}$ , and predict the indicator's approximate colour-change range.

Solution.

$\mathrm{p}K_{\mathrm{In}} = \mathrm{pH} - \log_{10}\frac{[\mathrm{In^{-}}]}{[\mathrm{HIn}]} = 5.40 - \log_{10}0.25 = 5.40 + 0.60 = 6.00$

$K_{\mathrm{In}} = 10^{-6.00} = 1.0 \times 10^{-6}\,\mathrm{mol\,dm^{-3}}$

The range is about $\mathrm{p}K_{\mathrm{In}} \pm 1$ , i.e. pH 5.0 to 7.0.

Answer: $\mathrm{p}K_{\mathrm{In}} = 6.00$ , $K_{\mathrm{In}} = 1.0 \times 10^{-6}\,\mathrm{mol\,dm^{-3}}$ ; it changes from red to blue over roughly pH 5 to 7, passing through purple.

Worked example

Problem. Phenolphthalein's first colour change can be treated as $\mathrm{HIn} \rightleftharpoons \mathrm{H^{+}} + \mathrm{In^{-}}$ with $\mathrm{p}K_{\mathrm{In}} \approx 9.3$ . What fraction of the indicator is in the pink form at pH 8.3, where a faint pink is first seen?

Solution. $\frac{[\mathrm{In^{-}}]}{[\mathrm{HIn}]} = 10^{8.3-9.3} = 0.10$ . The fraction in the pink form is

$\frac{[\mathrm{In^{-}}]}{[\mathrm{HIn}] + [\mathrm{In^{-}}]} = \frac{0.10}{1 + 0.10} = 0.091$

Answer: about 9%, roughly one molecule in eleven. That small amount is enough to see, because pink stands out against colourless.

Warning

Common mistakes with indicators

Thinking every indicator changes at pH 7. Methyl orange is already yellow at pH 4.4, and phenolphthalein is still colourless at pH 8.
Adding a lot of indicator "to see it better". An indicator is itself a weak acid, so it reacts with the titrant. Use two or three drops only.
Writing the ratio upside down. A higher pH means MORE $\mathrm{In^{-}}$ , so $\frac{[\mathrm{In^{-}}]}{[\mathrm{HIn}]}$ grows as pH rises.
Using universal indicator or litmus for a titration. Their changes are spread over many pH units, so no sharp end point is seen.

Tip

Remember "pKIn ± 1". An indicator's colour change is centred on its $\mathrm{p}K_{\mathrm{In}}$ and is about two pH units wide. If you are given $K_{\mathrm{In}}$ , take $-\log_{10}$ first; then the range is one unit either side.

Khan Academy: Acid–base indicators. Watch how the HIn ⇌ H⁺ + In⁻ equilibrium shifts as acid or base is added, and how the ratio of the two forms sets the colour you see.

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Practice

Write the equilibrium for an indicator HIn in water and explain, using Le Chatelier's principle, why it shows its acid colour when acid is added.
Bromothymol blue has $\mathrm{p}K_{\mathrm{In}} = 7.0$ . Predict its approximate colour-change range, and its colour at pH 4 and at pH 10.
An indicator has $K_{\mathrm{In}} = 6.3 \times 10^{-5}\,\mathrm{mol\,dm^{-3}}$ . Calculate $\mathrm{p}K_{\mathrm{In}}$ and its approximate range.
For the indicator in question 3, calculate the percentage present as $\mathrm{In^{-}}$ at pH 3.0.
Use the table to name an indicator that would be yellow in a solution of pH 5.0 and one that would be colourless in the same solution.
A solution turns methyl orange yellow and phenolphthalein colourless. What can you conclude about its pH? Explain why this is not enough to call it neutral.
Explain why the observed range of phenolphthalein (8.3–10.0) is not centred exactly on its $\mathrm{p}K_{\mathrm{In}}$ of about 9.3.

Show answersHide answers

$\mathrm{HIn + H_2O \rightleftharpoons H_3O^{+} + In^{-}}$ . Added $\mathrm{H_3O^{+}}$ increases a product concentration, so the position of equilibrium moves left; HIn becomes the main form and its colour is seen.
About pH 6 to 8. Yellow at pH 4 (well below the range); blue at pH 10 (well above it).
$\mathrm{p}K_{\mathrm{In}} = -\log_{10}(6.3 \times 10^{-5}) = 4.20$ ; range about 3.2 to 5.2.
$\frac{[\mathrm{In^{-}}]}{[\mathrm{HIn}]} = 10^{3.0-4.2} = 0.063$ ; fraction $= \frac{0.063}{1.063} = 0.059$ , about 5.9%.
Methyl orange is yellow above pH 4.4, so it is yellow at pH 5.0. Phenolphthalein is colourless below pH 8.3, so it is colourless at pH 5.0.
The pH lies between about 4.4 and 8.3. That covers weakly acidic, neutral and weakly alkaline solutions, so a pH meter or a narrow-range indicator is needed to decide.
The eye detects a small amount of pink in a colourless solution far more easily than a small amount of "colourless" in pink. So the change is noticed when only about 9% is pink (pH 8.3), while full pink needs most of the indicator ionised (pH 10.0).

Sources and credits

Indicator colour-change ranges: pH indicator; $\mathrm{p}K_{\mathrm{In}}$ of methyl red and bromothymol blue: Methyl red and Bromothymol blue; Wikipedia contributors, Wikipedia, licensed under CC BY-SA 4.0, adapted by Ganzaa.
Image: Purple cabbage used as pH indicator 02.jpg by Millars, via Wikimedia Commons, licensed under CC BY 4.0.
Video: Acid–base indicators, Khan Academy, embedded from YouTube.
The text, figures, table layout, worked examples and Practice items were written and drawn by Ganzaa.
This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1Why does cabbage juice change colour?

2An indicator is a weak acid in equilibrium

3Where exactly does the colour change?

4Common laboratory indicators

Why does cabbage juice change colour?

An indicator is a weak acid in equilibrium

Where exactly does the colour change?

Common laboratory indicators