Volumetric Analysis: Standards, Titrations and Indicators

4.1Equivalent weight, normal and molar solutions

Volumetric (titrimetric) analysis finds the amount of a substance from the volume of a standard solution that reacts with it exactly. The point of exact reaction is the equivalence point; the point where the indicator changes is the end point, and a good method keeps them close.

Equivalent weight and n-factor

• Acids: n = replaceable H⁺ used in the reaction (HCl 1, H₂SO₄ 2, oxalic acid 2, H₃PO₃ 2, H₃BO₃ 1). Bases: OH⁻ given or H⁺ taken (NaOH 1, Ca(OH)₂ 2, Na₂CO₃ 2 when titrated to CO₂, 1 to HCO₃⁻).
• Oxidants and reductants: n = electrons gained or lost per formula unit. KMnO₄ 5 in acid (→ Mn²⁺), 3 in neutral or faintly alkaline (→ MnO₂), 1 in strong alkali (→ MnO₄²⁻); K₂Cr₂O₇ 6 (→ 2Cr³⁺); Mohr’s salt 1 (Fe²⁺ → Fe³⁺); oxalate 2 (C₂O₄²⁻ → 2CO₂); Na₂S₂O₃ 1 (2S₂O₃²⁻ → S₄O₆²⁻); I₂ 2.
• The same substance can have different equivalent weights in different reactions. In the iodometric estimation of copper (2Cu²⁺ + 4I⁻ → 2CuI + I₂), Cu²⁺ → Cu⁺ is a 1-electron change, so the equivalent weight of CuSO₄·5H₂O equals its molar mass.

Concentration terms

• Molarity and normality change slightly with temperature (volume expands); molality and % (w/w) do not.
• Law of equivalence: at the equivalence point equivalents are equal, N₁V₁ = N₂V₂. With molarities, include the stoichiometry: H₂SO₄ + 2NaOH needs 2M_acidV_acid = M_baseV_base. Forgetting the factor 2 is the commonest slip.
• Dilution: M₁V₁ = M₂V₂ (moles unchanged).

4.2Primary and secondary standards

A primary standard is a substance pure enough to be weighed and dissolved to give a solution of exactly known concentration. A secondary standard is a solution whose concentration has to be found by titrating it against a primary standard.

Requirements of a primary standard

• Available in very high purity (impurities about 0.01–0.02 % or less), of known, definite composition.
• Stable in air and on storage: not hygroscopic, not efflorescent, not oxidised by air, not attacked by CO₂.
• High equivalent weight, so that weighing errors are small.
• Readily soluble, and reacting quickly, completely and stoichiometrically with a sharp end point.

• Mohr’s salt is a primary standard: in the solid state it resists aerial oxidation far better than FeSO₄·7H₂O, so it contains very little Fe³⁺. Its solutions are made in dilute H₂SO₄ to stop hydrolysis and oxidation.
• Sodium thiosulphate is not a primary standard, though it can be bought pure: the crystals are efflorescent, and its solution is decomposed by dissolved CO₂ (S₂O₃²⁻ + H⁺ → HSO₃⁻ + S), by sulphur bacteria, and faster in light. It is standardised against K₂Cr₂O₇ or KIO₃ through liberated iodine.
• A pair such as NaNO₃/KNO₂ belongs to no precipitation titration: they give no precipitate with any common titrant.

4.3Acid–base titrations and indicators

An acid–base indicator is itself a weak acid HIn whose acid form and base form have different colours: HIn ⇌ H⁺ + In⁻.

• The eye sees one colour only when that form is about 10 times the other. The basic colour appears when [In⁻]/[HIn] ≥ 10, i.e. pH ≥ pK_In + 1; the acid colour when [HIn]/[In⁻] ≥ 10, i.e. pH ≤ pK_In − 1. So the transition range is about 2 pH units.
• Choose an indicator whose range lies inside the steep part of the titration curve.

• Strong acid–strong base: equivalence at pH 7; the jump runs from about 3 to 11, so any of the common indicators works.
• Weak acid–strong base: the salt hydrolyses, so equivalence is at pH about 8.7; only phenolphthalein changes inside the jump.
• Strong acid–weak base: equivalence below 7 (NH₄⁺ hydrolyses); use methyl orange or methyl red.
• Weak acid–weak base: no sharp jump; no indicator gives a good end point (a conductometric titration works).
• Na₂CO₃ with HCl: two end points. Phenolphthalein marks CO₃²⁻ → HCO₃⁻ (pH about 8.3); methyl orange marks HCO₃⁻ → CO₂ (pH about 4). Mixtures of NaOH/Na₂CO₃ or NaHCO₃/Na₂CO₃ are analysed this way (double-indicator method).
• Boric acid (pK_a 9.2, a weak Lewis acid, B(OH)₃ + H₂O ⇌ B(OH)₄⁻ + H⁺) gives no sharp end point. Adding a cis-diol (glycerol, mannitol, sorbitol) forms a stable borate–diol complex and releases H⁺ fully; the acid then behaves as a fairly strong monobasic acid and is titrated with NaOH using phenolphthalein.