Quantitative Analysis of Acids and Bases

In short: A titration finds the concentration of an acid or base by reacting it exactly with a solution of known concentration, using an indicator to show the end point. Use $n=cV$ and the mole ratio from the balanced equation to calculate the unknown.

Standard solutions

A standard solution has an accurately known concentration. It is made from a primary standard, a substance that is:

• very pure,
• stable (does not react with air or absorb water from it),
• has a high molar mass (so weighing errors are small),
• soluble in water.

Good primary standards: anhydrous sodium carbonate ($\mathrm{N}{\mathrm{a}}_2\mathrm{C}{\mathrm{O}}_3$) and oxalic acid dihydrate (${\mathrm{H}}_2{\mathrm{C}}_2{\mathrm{O}}_4\cdot 2{\mathrm{H}}_2\mathrm{O}$).

NaOH is not a primary standard: it absorbs water and carbon dioxide from the air. A NaOH solution must itself be standardised by titrating it against a primary standard.

Making a standard solution:

1. Weigh the solid accurately on an electronic balance.
2. Dissolve it in a beaker of distilled water.
3. Pour into a volumetric flask, rinsing the beaker and funnel into the flask.
4. Add distilled water until the bottom of the meniscus is on the mark.
5. Stopper and invert to mix.

Titration equipment and rinsing

Rinsing the burette or pipette with water dilutes the solution in it. Rinsing the conical flask with the solution adds extra moles. Both give wrong answers.

Titration words

• Equivalence point: the reactants have been added in exactly the mole ratio of the equation.
• End point: the point where the indicator changes colour. A good indicator makes this match the equivalence point.
• Concordant titres: titres that agree within 0.10 mL. Average only these. Leave out the rough first trial and any outliers.

Titration calculations

Follow the same steps every time:

1. Moles of the known solution: $n=cV$ (with $V$ in litres).
2. Use the mole ratio from the balanced equation.
3. Concentration of the unknown: $c=\frac{n}{V}$.
4. If the sample was diluted first, scale back up.

Titration curves and indicators

A titration curve plots pH against the volume added. The steep jump marks the equivalence point. Choose an indicator whose colour change range lies inside the steep part.

For a weak acid titration, the curve has a flat buffer region before equivalence. Halfway to equivalence, $\mathrm{pH}=\mathrm{p}{K}_a$.

Conductometric titrations

Instead of an indicator, measure the electrical conductivity as the titrant is added. The equivalence point is where the graph changes direction.

• HCl + NaOH: conductivity falls (fast-moving ${\mathrm{H}}^{+}$ is replaced by slower $\mathrm{N}{\mathrm{a}}^{+}$), reaches a minimum at equivalence, then rises as extra $\mathrm{O}{\mathrm{H}}^{-}$ and $\mathrm{N}{\mathrm{a}}^{+}$ build up.
• Weak acid + NaOH: conductivity starts low (few ions), rises slowly as salt forms, then rises faster after equivalence.

Conductometric titrations work for coloured solutions and for weak acid + weak base, where indicators fail.

Back titrations

Some samples will not dissolve, or react slowly, like chalk or antacid tablets. In a back titration:

1. Add a known excess of acid to the sample.
2. Let it react completely.
3. Titrate the leftover acid with a standard base.
4. Acid that reacted = acid added − acid left over.

Buffers

A buffer is a solution that resists changes in pH when small amounts of acid or base are added. It contains a weak acid and its conjugate base in similar amounts, such as $\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}$ / $\mathrm{C}{\mathrm{H}}_3\mathrm{CO}{\mathrm{O}}^{-}$.

$$\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons \mathrm{C}{\mathrm{H}}_3\mathrm{CO}{\mathrm{O}}^{-}+{\mathrm{H}}_3{\mathrm{O}}^{+}$$

• Add a little acid: the extra ${\mathrm{H}}_3{\mathrm{O}}^{+}$ reacts with $\mathrm{C}{\mathrm{H}}_3\mathrm{CO}{\mathrm{O}}^{-}$, so the equilibrium shifts left and the pH barely changes.
• Add a little base: the $\mathrm{O}{\mathrm{H}}^{-}$ reacts with $\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}$ (or with ${\mathrm{H}}_3{\mathrm{O}}^{+}$, which the acid then replaces), so the pH barely changes.

A buffer has a limited capacity. Add too much acid or base and it is used up. A strong acid and its salt (HCl / NaCl) is not a buffer.

The carbonic acid / hydrogen carbonate buffer (${\mathrm{H}}_2\mathrm{C}{\mathrm{O}}_3$ / $\mathrm{HC}{\mathrm{O}}_3^{-}$) keeps blood between pH 7.35 and 7.45.

Quick summary

• A primary standard is pure, stable, soluble and has a high molar mass. NaOH is not one.
• Rinse the burette and pipette with the solution they will hold; rinse the conical flask with water.
• Average concordant titres (within 0.10 mL). Use $n=cV$ and the mole ratio.
• Pick an indicator that changes colour in the steep part of the curve.
• Conductometric titrations find equivalence from where conductivity turns.
• Back titration: excess acid, then titrate what is left.
• A buffer (weak acid + conjugate base) resists pH change.

Quiz