An indicator signals the end of a titration by changing color. Picking one means matching its color change to the steep part of the titration curve.
Key idea
An indicator is a weak acid, HIn, whose acid and base forms have different colors. It changes color over roughly $\text{p}K_\text{In} \pm 1$. Choose one whose range falls on the vertical jump of the curve, which contains the equivalence point.
Why it works
$\dfrac{[\mathrm{In^-}]}{[\mathrm{HIn}]} = 10^{\text{pH} - \text{p}K_\text{In}}$. Your eye sees a mixed color only while neither form outnumbers the other by more than about 10 to 1, so the change spans about 2 pH units around $\text{p}K_\text{In}$. On the steep part of a titration curve a single drop moves the pH by several units, so an indicator anywhere on that jump changes color within a drop of the equivalence point.
| Indicator | Color change (pH) | Good for |
|---|---|---|
| methyl orange | 3.1–4.4 | strong acid with weak base (sometimes) |
| methyl red | 4.4–6.2 | weak base with strong acid (equivalence near 5) |
| bromothymol blue | 6.0–7.6 | strong acid with strong base |
| phenolphthalein | 8.2–10.0 | weak acid with strong base (equivalence near 9); also strong–strong |
Worked examples
Worked example: Weak acid, strong base
Acetic acid is titrated with NaOH; the equivalence point is at pH 8.72. Choose among methyl red, bromothymol blue and phenolphthalein.
- The jump runs from about pH 7 to 11.
- Phenolphthalein (8.2–10.0) sits on the jump. Methyl red would change color long before equivalence, while the flask is still a buffer.
Answer: Phenolphthalein.
Worked example: Weak base, strong acid
$0.100\ \text{M}$ $\mathrm{NH_3}$ is titrated with $0.100\ \text{M}$ HCl. At equivalence the flask holds $0.0500\ \text{M}$ $\mathrm{NH_4^+}$ ($K_a = 5.6 \times 10^{-10}$). Pick an indicator.
- $$[\mathrm{H_3O^+}] = \sqrt{(5.6 \times 10^{-10})(0.0500)} = 5.3 \times 10^{-6}$$ so the equivalence pH is 5.28.
- Methyl red (4.4–6.2) brackets 5.28. Phenolphthalein would change color far too early, while the solution is still basic.
Answer: Methyl red.
Worked example: Reading an indicator constant
An indicator has $K_a = 1.0 \times 10^{-9}$. Around what pH does it change color?
- It changes where $[\mathrm{HIn}] = [\mathrm{In^-}]$, at $\text{pH} = \text{p}K_a = 9.0$.
- Its useful range is about 8 to 10, so it would suit a weak acid titrated with a strong base.
Answer: Around pH 9.
Common mistake
Choosing an indicator that changes at pH 7 for every titration. Only strong acid with strong base has its equivalence point at 7. Check: find the pH at equivalence first, then pick the indicator.
Test liquids with four indicators in the Mixing Lab.