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An indicator is a weak acid whose two forms differ in colour; it suits a titration when its colour-change range lies inside the steep part of the curve.
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By the end of this lesson you will be able to explain an indicator's colour change as a weak-acid equilibrium, state its range as about one unit either side of its $pK_{in}$, choose an indicator whose range lies inside the steep part of a titration curve, read an indicator's colour at a stated pH, and say what the wrong choice does to the end point.
You can read the steep part of a titration curve and you know it sits in different places for different pairs of acid and base. From the buffers lesson you have the equation that ties a weak acid's pH to the ratio of its two forms. An indicator is a weak acid, so that equation is all you need.
An acid–base indicator is a weak acid, written HIn, whose undissociated form and conjugate base, $\mathrm{In^-}$, have different colours. Its dissociation constant is $K_{in}$ and $pK_{in} = -\log_{10} K_{in}$. The colour-change range is the span of pH over which both colours are visibly mixed, roughly $pK_{in} \pm 1$. The end point is where the indicator changes colour; a good choice of indicator makes it coincide with the equivalence point.
Phenolphthalein is a weak acid whose molecule is colourless and whose conjugate base is pink:
$$\mathrm{HIn \rightleftharpoons H^+ + In^-} \qquad pK_{in} = 9.3$$
The buffer equation applies to it exactly as to ethanoic acid:
$$\mathrm{pH} = pK_{in} + \log_{10}\frac{[\mathrm{In^-}]}{[\mathrm{HIn}]}$$
At pH 9.3 the two forms are equal. One unit below, at 8.3, there is ten times as much colourless form, and the eye sees colourless. One unit above, at 10.3, there is ten times as much pink, and the eye sees pink. In between the solution is shades of pale pink. So an indicator does not change at a single pH; it changes across a range of about two units centred on its $pK_{in}$.
| Indicator | Acid colour | Base colour | Range |
|---|---|---|---|
| methyl orange | red | yellow | 3.1 – 4.4 |
| methyl red | red | yellow | 4.4 – 6.2 |
| bromothymol blue | yellow | blue | 6.0 – 7.6 |
| phenolphthalein | colourless | pink | 8.2 – 10.0 |
Now the rule. During a titration the pH changes by several units within a drop or two at equivalence — the steep part of the curve. An indicator whose whole range lies inside the steep part changes colour within that drop, so its end point lands on the equivalence point. An indicator whose range lies outside the steep part changes somewhere else, gradually, over several millilitres.
Another way: picture
Picture a lift shooting up several floors in one second. A light that switches on at floor 9 will switch on during the shoot, so it tells you when the shoot happened. A light that switches on at floor 4 — a floor the lift crawled past a minute earlier — tells you nothing about the shoot. The indicator is the light; the steep part of the curve is the shoot.
Another way: steps
To choose an indicator:
Put the table of ranges beside the table of curve shapes from the titration curve lesson:
| Titration | Steep part | Suitable indicator |
|---|---|---|
| strong acid + strong base | about 3 to 11 | any of the four |
| weak acid + strong base | about 7 to 11 | phenolphthalein |
| strong acid + weak base | about 3 to 7 | methyl orange or methyl red |
| weak acid + weak base | none | none: use a pH probe |
For a strong acid with a strong base the jump is so large that almost any indicator works, and the choice is about which colour change is easiest to see. For a weak acid, methyl orange is useless: its whole range is passed in the buffer region, long before equivalence. For a weak base, phenolphthalein is equally useless, for the mirror-image reason.
Litmus is rarely used for titrations. Its change is spread over pH 4.5 to 8.3, too wide to give a sharp end point even when the jump is large.
Outside its range an indicator shows one colour whatever the pH. Bromothymol blue is the same yellow at pH 5.9 and at pH 2, so a yellow result says only that the pH is at most 6.0. Universal indicator gets round this by mixing several indicators whose ranges follow one another, which is why it goes through a whole rainbow from 1 to 14.
An indicator is also added in tiny amounts — a couple of drops. Being a weak acid, it uses up a little of the titrant itself, and a few drops keep that error far below the reading error of the burette.
The end point is taken as the first permanent change. With phenolphthalein in a weak acid titration, a pink streak appears where each drop of alkali lands and vanishes when the flask is swirled, because the acid nearby absorbs the hydroxide. Near equivalence the pink lasts longer and longer; the end point is the drop after which a faint pink stays through swirling. Titrating to a deep pink overshoots, because by then several extra drops have gone in.
Choose the indicator with the brightest colour. Brightness has nothing to do with where the colour changes. The range must sit in the steep part.
An indicator changes colour at one exact pH. It changes across about two pH units, centred on its $pK_{in}$.
Every indicator changes at pH 7. Each has its own range; only bromothymol blue is centred near 7.
Any indicator changes at the equivalence point. An indicator changes at its own pH, wherever the titration happens to be. With the wrong one the end point comes early or drifts.
The indicator's colour tells you the exact pH. Only inside its range; outside it, one colour covers many pH values.
Ammonia solution is titrated with hydrochloric acid.
A weak base with a strong acid.
At equivalence the flask holds ammonium chloride, which is acidic, so the jump runs from about 7 down to 3.
The steep part is below 7.
Methyl orange, 3.1 to 4.4, lies inside it; phenolphthalein, 8.2 to 10.0, would change early, while the flask is still mostly ammonia.
Range inside the jump, not outside.
Methyl red has $pK_{in} = 5.1$; its acid form is red and its base form yellow. What does it look like at pH 4.1?
One unit below the $pK_{in}$.
$\log_{10}([\mathrm{In^-}] \div [\mathrm{HIn}]) = 4.1 - 5.1 = -1$, so there is ten times as much red form as yellow.
The buffer equation, for an indicator.
The solution looks red; at pH 5.1 it would be orange, an even mix.
The colour is a ratio made visible.
Its range is about $5.0 - 1 = 4.0$ to $5.0 + 1 = 6.0$.
Range is $pK_{in} \pm 1$.
The jump runs from 3 to 7, so the range $\ldots$
…lies entirely inside it: yes, it would give a sharp end point.
For a strong acid titrated with a weak base, the steep part of the curve runs from about pH $3$ to pH $7$. An indicator changes colour between $pK_{in} - 1$ and $pK_{in} + 1$. For which values of $pK_{in}$ does the whole colour change lie inside the steep part?
This task has no paper form; do it on a device.
benzoic acid is titrated with sodium hydroxide. The curve jumps steeply from about pH 7 to pH 11 at $20$ mL. Which indicator should be used?
Methyl orange changes from red to yellow between pH 3.1 and 4.4; bromothymol blue from yellow to blue between 6.0 and 7.6; phenolphthalein from colourless to pink between 8.2 and 10.0. Give each indicator's colour in each solution.
| at pH 2 | at pH 13 | |
|---|---|---|
| methyl orange | ||
| bromothymol blue | ||
| phenolphthalein |
Match each titration to an indicator that gives a sharp end point, or to the pH probe if none does. Methyl orange changes at 3.1 to 4.4, bromothymol blue at 6.0 to 7.6, phenolphthalein at 8.2 to 10.0.
| phenolphthalein | methyl orange | bromothymol blue | no indicator: a pH probe | |
|---|---|---|---|---|
| ethanoic acid with sodium hydroxide | ||||
| hydrochloric acid with ammonia | ||||
| hydrochloric acid with sodium hydroxide | ||||
| ethanoic acid with ammonia |
Phenolphthalein, written HIn, has $pK_{in} = 9.3$: $\mathrm{HIn \rightleftharpoons H^+ + In^-}$, where HIn is colourless and $\mathrm{In^-}$ is pink. At pH $11.3$, how many times more of the pink form than of the colourless form is there?
Answer:
Put these indicators in order of the pH at which they change colour, lowest first.
Number the steps in order (write the number in the box):
A gardener growing lettuce tests a soil extract with bromothymol blue, which is yellow at pH 6.0 and below, blue at pH 7.6 and above, and green in between. The extract turns fully yellow. Give the set of pH values the soil could have.
This task has no paper form; do it on a device.
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
The true equivalence point of an ethanoic acid titration with sodium hydroxide is at $22$ mL. A learner uses methyl orange by mistake. Where does the colour change?
You can choose an indicator by comparing two intervals and explain why. Say out loud why methyl orange gives the wrong end point for ethanoic acid. Next: a new unit, and a new thing that moves between particles — electrons, in oxidation and reduction.
10. Your turn: a new indicator has $pK_{in} = 5.0$. Could it be used for a strong acid titrated with ammonia, whose jump runs from about 3 to 7?, step 3