Titrations

A titration measures exactly what volume of one solution reacts with a known volume of another.

Method (acid–alkali)

1. Use a pipette to measure 25.0 cm^3 of alkali into a conical flask. 2. Add a few drops of indicator, such as phenolphthalein (pink in alkali, colourless in acid) or methyl orange (yellow in alkali, red in acid). 3. Fill a burette with acid and record the starting volume. 4. Add acid while swirling the flask, slowly and drop by drop near the end, until the indicator just changes colour: the end point. 5. Record the final volume. The difference is the titre. 6. Repeat until titres are concordant (within 0.10 cm^3) and average them.

Universal indicator is not used because its gradual colour change gives no sharp end point.

Calculation

25.0 cm^3 of sodium hydroxide is neutralised by 20.0 cm^3 of 0.100 mol dm^{-3} hydrochloric acid.

• Moles of HCl = 0.100 \times 20.0/1000 = 0.00200 mol.
• \mathrm{NaOH + HCl \rightarrow NaCl + H_2O} is a 1:1 ratio, so 0.00200 mol NaOH.
• Concentration = 0.00200 \div (25.0/1000) = 0.0800 mol dm^{-3}.

Remember to divide volumes in cm^3 by 1000 to convert them to dm^3.

Standard solutions

A standard solution has an accurately known concentration. To make one, weigh the solid accurately (by difference), dissolve it in a beaker of distilled water, transfer with washings to a volumetric flask, make up to the mark so the bottom of the meniscus sits on the line, and invert to mix. Primary standards such as sodium carbonate or potassium hydrogen phthalate are pure, stable and not hygroscopic.

Acid–base titrations

Choose an indicator whose colour change lies within the vertical section of the titration curve: phenolphthalein for weak acid–strong base, methyl orange for strong acid–weak base, either for strong–strong.

Redox titrations

• Manganate(VII): \mathrm{MnO_4^- + 8H^+ + 5Fe^{2+} \rightarrow Mn^{2+} + 4H_2O + 5Fe^{3+}}. It is self-indicating: the end point is the first permanent pale pink. Acidify with dilute sulfuric acid, not hydrochloric acid, which would be oxidised to chlorine.
• Iodine–thiosulfate: an oxidant liberates I_2 from excess iodide, then \mathrm{I_2 + 2S_2O_3^{2-} \rightarrow 2I^- + S_4O_6^{2-}}. Add starch near the end (when the solution is pale yellow); the blue-black colour disappears at the end point.

Worked example

An iron tablet is dissolved in acid and titrated with 0.0200 mol dm^{-3} KMnO_4; the mean titre is 18.50 cm^3. n(\mathrm{MnO_4^-}) = 0.0200 \times 0.01850 = 3.70\times10^{-4} mol, so n(\mathrm{Fe^{2+}}) = 5 \times 3.70\times10^{-4} = 1.85\times10^{-3} mol, which is 1.85\times10^{-3} \times 55.8 = 0.103 g of iron.

Back titrations

When a sample is insoluble or reacts slowly (calcium carbonate in limestone, say), add a known excess of reagent, then titrate the leftover. Reagent used by the sample = amount added − amount left.

Uncertainty

A burette reading is ±0.05 cm^3, and a titre involves two readings, so ±0.10 cm^3. Percentage uncertainty = 0.10/\text{titre} \times 100; larger titres reduce it.