amazon.co.ukTitrations and Analytical Techniques
A* revision for titrations, standard solutions, redox titrations, titration curves and indicator choice, plus TLC, melting point purity testing and recrystallisation, for AQA, Edexcel, OCR, WJEC and CCEA.
🎯 Learning Objectives
- Describe the full titration procedure including rinsing rules, meniscus reading and concordant titres
- Make a standard solution and calculate concentrations, dilutions and percentage purity from titration data
- Perform redox titration calculations with MnO₄⁻/Fe²⁺ and I₂/S₂O₃²⁻, explaining the self-indicating endpoint and acid choice
- Sketch and interpret pH titration curves for all four acid-base combinations and justify indicator choice
- Use the half-equivalence point (pH = pKa) to determine Ka experimentally
- Describe recrystallisation, TLC (Rf values) and melting point purity tests, explaining how purity is checked
📋 Key Definitions and Core Concepts
Standard solution: A solution of accurately known concentration, made by dissolving an exact mass of a primary standard in a volumetric flask.
Concordant titres: Titres agreeing within 0.10 cm³, averaged to give the mean titre.
Equivalence point: The volume of titrant at which the reaction is exactly complete — the near-vertical section of a pH titration curve.
End point: The volume at which the indicator changes colour; coincides with the equivalence point when the indicator is chosen correctly.
Buffer solution: A solution that maintains approximately constant pH when small quantities of acid or base are added.
Rf value: Distance moved by a substance divided by distance moved by the solvent front in chromatography; always ≤ 1.
Recrystallisation: Purification by dissolving a solid in the minimum hot solvent, cooling to crystallise, filtering and drying — impurities remain in solution.
Self-indicating titrant: A titrant that shows its own endpoint by colour change, e.g. purple MnO₄⁻ turning colourless/pale pink.
Mixed melting point: Melting point of a mixture of prepared solid and pure standard; unchanged sharp melting point confirms identity.
Titration Technique and Required Practical
A titration determines the unknown concentration of a solution by reacting it with a standard solution of known concentration. Required practical (AQA RP1, OCR PAG1/2): make a standard solution and use it to find the concentration of an unknown acid/base. Method step by step: (1) weigh the solid by difference (mass of bottle + solid, then bottle) and dissolve in a beaker with deionised water; (2) transfer to a volumetric flask using a funnel, rinse the beaker into the flask, add water to the graduation mark (bottom of meniscus on the line), stopper and invert repeatedly to homogenise; (3) rinse the burette with the standard solution (then fill, record initial reading to 0.05 cm³); pipette 25.0 cm³ of the unknown into a conical flask with 2-3 drops of indicator; (4) run in titrant swirling continuously, adding dropwise near the endpoint until a permanent colour change remains; (5) repeat until concordant titres (within 0.10 cm³) and take the mean of concordant values only.
Accuracy rules that earn marks: rinse the burette with the solution it will hold (residual water dilutes it); rinse the pipette with the solution it transfers; rinse the conical flask with deionised water only (residual water does not change moles of acid present); remove the funnel before reading; read the bottom of the meniscus at eye level; white tile under the flask to see the colour change. Uncertainties: each burette reading ±0.05 cm³, so a titre has ±0.10 cm³; percentage uncertainty = (uncertainty/measurement) × 100 — a small titre (e.g. 10 cm³) carries a large percentage error, so use a larger titre or a more concentrated solution. Reduce uncertainty: titrate a larger volume, use a lower concentration titrant, or a smaller-graduation burette.
Indicators: phenolphthalein (colourless → pink, range 8.3-10.0) and methyl orange (red → yellow, range 3.1-4.4). Choose the indicator whose range lies entirely within the near-vertical section of the titration curve: strong acid-strong base works with either; weak acid-strong base needs phenolphthalein; strong acid-weak base needs methyl orange; weak acid-weak base has no sharp vertical section — neither indicator is suitable.
Standard Solutions and Titration Calculations
A standard solution is one of known concentration, made by dissolving an exact mass of a primary standard (pure, stable, not hygroscopic — e.g. anhydrous sodium carbonate, not NaOH which absorbs water) in a volumetric flask. Moles = mass/Mr; concentration = moles/volume (dm³). Concentration conversions: g dm⁻³ ÷ Mr = mol dm⁻³.
Core titration calculation: (1) moles of titrant = concentration × volume/1000; (2) moles of unknown from the equation's ratio; (3) concentration = moles × 1000/volume. Worked example: 25.0 cm³ of HCl of unknown concentration is neutralised by a mean titre of 22.30 cm³ of 0.100 mol dm⁻³ NaOH (1:1 ratio). Moles NaOH = 0.100 × 22.30/1000 = 2.23 × 10⁻³ mol. Moles HCl = 2.23 × 10⁻³. [HCl] = 2.23 × 10⁻³ × 1000/25.0 = 0.0892 mol dm⁻³.
Dilutions: C₁V₁ = C₂V₂; if the sample was diluted first, scale back by the dilution factor. Purity questions: percentage purity = (moles found × Mr / mass used) × 100. Water of crystallisation: find the anhydrous salt moles from the titre, subtract from the mass used to get the water mass, divide by 18 for moles, then divide both by the smaller to get x in Mx·xH₂O. Exam tip: always write the balanced equation first and state the ratio — most lost marks come from wrong ratios (e.g. 2:1 for H₂SO₄) or dm³/cm³ slips.
Worked purity example: 1.42 g of an impure sample of Na₂CO₃ is made up to 250.0 cm³; 25.0 cm³ aliquots need a mean titre of 24.80 cm³ of 0.100 mol dm⁻³ HCl. Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂. Moles HCl = 0.100 × 24.80/1000 = 2.48 × 10⁻³; moles Na₂CO₃ in 25.0 cm³ = 1.24 × 10⁻³; in 250 cm³ = 1.24 × 10⁻² mol; mass Na₂CO₃ = 1.24 × 10⁻² × 106 = 1.31 g; purity = 1.31/1.42 × 100 = 92.6%. Method marks: balanced equation, ratio 2:1, scaling by 10, purity formula. Back titrations reverse the logic: react the excess with a standard solution and subtract — moles of analyte = moles added − moles of excess found by titration. The same mole-math underpins water of crystallisation and percentage-yield questions, so master the four-step chain once and reuse it.
Redox Titrations
Redox titrations use a redox reaction instead of neutralisation. The classic: manganate(VII) titrations — acidified KMnO₄ in the burette oxidising Fe²⁺: MnO₄⁻ + 8H⁺ + 5Fe²⁺ → Mn²⁺ + 4H₂O + 5Fe³⁺. MnO₄⁻ is self-indicating: purple in the burette, colourless while reacting, permanent pale pink at the endpoint (first excess drop). No separate indicator needed. The acid must be dilute H₂SO₄ — HCl would be oxidised by MnO₄⁻ (giving Cl₂ and a too-large titre), and HNO₃ is itself an oxidising agent (oxidising Fe²⁺ before the titration, giving a too-small titre). This 'why not HCl/HNO₃' question is standard.
Worked example: 25.0 cm³ of Fe²⁺ solution needs 21.60 cm³ of 0.0200 mol dm⁻³ KMnO₄. Moles MnO₄⁻ = 0.0200 × 21.60/1000 = 4.32 × 10⁻⁴. Ratio 1:5 → moles Fe²⁺ = 2.16 × 10⁻³. [Fe²⁺] = 2.16 × 10⁻³ × 1000/25.0 = 0.0864 mol dm⁻³.
Other redox titrations: iodine/thiosulfate (I₂ + 2S₂O₃²⁻ → 2I⁻ + S₄O₆²⁻) used to find oxidising agents by adding excess KI and titrating the liberated I₂ (starch indicator, blue-black → colourless near the endpoint); dichromate(VI) titrations of Fe²⁺ (Cr₂O₇²⁻ + 14H⁺ + 6Fe²⁺ → 2Cr³⁺ + 7H₂O + 6Fe³⁺, ratio 1:6, diphenylamine indicator). Determining formulae: the Fe²⁺ percentage in an iron tablet, or x in FeSO₄·xH₂O, follows from the titre plus mass data. Percentage uncertainty handling is identical to acid-base titrations; the MnO₄⁻ titre reading can be against the meniscus top (dark colour obscures the bottom) as long as you are consistent.
Titration Curves, Indicators and Buffers in Context
A pH titration curve plots pH against volume of titrant. The equivalence point is the near-vertical section — the volume at which the reaction is exactly complete. Curve shapes: strong acid-strong base starts at pH ~1 and ends ~13 with a huge vertical section; weak acid-strong base starts higher (partial dissociation) and the vertical section sits above 7 (equivalence pH > 7 because the salt hydrolyses — CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻); strong acid-weak base has its vertical section below 7; weak-weak curves are shallow with no vertical section. Half-equivalence: at half the equivalence volume [HA] = [A⁻], so pH = pKa — used to find Ka experimentally.
Indicator choice (from the equivalence-point rule): the indicator's colour-change range must lie entirely within the vertical section. Phenolphthalein (8.3-10.0) for weak acid-strong base; methyl orange (3.1-4.4) for strong acid-weak base; either for strong-strong. Buffer regions of the curve: before the equivalence point the weak acid/conjugate base pair formed in the flask acts as a buffer, so pH changes slowly — the flat section around half-equivalence.
Buffers in analysis: a buffer solution maintains approximately constant pH when small quantities of acid or base are added — made from a weak acid plus its conjugate base (or weak base plus conjugate acid). Buffer action: added H⁺ reacts with A⁻ (A⁻ + H⁺ → HA, equilibrium shifts left); added OH⁻ reacts with HA (HA + OH⁻ → A⁻ + H₂O, shifts right). Buffer pH: [H⁺] = Ka × ([HA]/[A⁻]), or pH = pKa + log([A⁻]/[HA]). Blood buffering (H₂CO₃/HCO₃⁻) is the standard application question. Half-equivalence gives pKa directly, so a titration curve is an experimental route to Ka — a common 6-marker combining curves, indicators and Ka.
Purity and Separation: Recrystallisation, TLC and Melting Point
Recrystallisation (required practical: purifying an organic solid): (1) dissolve the crude solid in the minimum volume of hot solvent (hot so it dissolves; minimum so it crystallises on cooling); (2) filter hot to remove insoluble impurities; (3) cool slowly to crystallise the product (pure crystals form first — impurities stay in solution); (4) filter under reduced pressure (Buchner funnel) and wash with cold solvent; (5) dry. The solvent choice: product dissolves hot, not cold; impurities dissolve cold. Yields: percentage yield = actual/theoretical × 100; losses occur at every transfer and filtration step.
Thin layer chromatography (TLC): a spot of sample on a silica (polar stationary phase) plate is placed in solvent (mobile phase); components separate as they travel different distances — less polar substances travel further (weaker adsorption to the stationary phase). Rf = distance moved by substance / distance moved by solvent front (always ≤ 1). Compare Rf values with known data or run pure standards alongside; a single spot indicates purity. UV light or iodine vapour locates colourless spots. Two spots = impurity or two components.
Melting point purity test: pure substances melt sharply at a characteristic temperature; impurities lower and broaden the melting point range. A mixed melting point — mixing the prepared solid with a pure standard — confirms identity: unchanged sharp melting point means identical; depressed/broadened means different. Gas chromatography (GC) separates volatile mixtures; retention time identifies components and peak area gives relative amounts — used with MS (GC-MS) for definitive identification. Distillation separates liquids by boiling point (simple/fractional); washing and drying with anhydrous agents (CaCl₂) removes residual water from organic liquids. These techniques together answer the standard 'how would you check the purity of your product' question: melting point sharpness + TLC single spot + comparison of Rf/melting data with pure samples.
💡 Worked Example
Exam-style: 25.0 cm³ of a solution of ethanoic acid of unknown concentration required a mean titre of 22.30 cm³ of 0.100 mol dm⁻³ NaOH for neutralisation (1:1 ratio). Calculate the concentration of the ethanoic acid and state the indicator that should be used, justifying your choice.
Mark-scheme logic: Moles NaOH = 0.100 × 22.30/1000 = 2.23 × 10⁻³ mol. Ratio 1:1, so moles CH₃COOH in 25.0 cm³ = 2.23 × 10⁻³ mol. [CH₃COOH] = 2.23 × 10⁻³ × 1000/25.0 = 0.0892 mol dm⁻³. Indicator: phenolphthalein — weak acid-strong base titration, so the vertical section of the curve lies above 7 (equivalence pH > 7 from hydrolysis of the ethanoate salt); phenolphthalein's range 8.3-10.0 falls within it, whereas methyl orange (3.1-4.4) changes colour well before the equivalence point. Mark points: moles of titrant; correct ratio; concentration with units; indicator named; justification via curve shape.
❓ Practice Questions & Mark Schemes
Describe the rinsing rules for the burette, pipette and conical flask in a titration, and explain why the conical flask is rinsed differently.
Answer: Burette and pipette: rinse with the solution they will hold/transfer — residual deionised water would dilute the solution and change the moles delivered. Conical flask: rinse with deionised water only — any water remaining does not change the moles of acid present, so the titre is unaffected. Full marks require the reasoning, not just the rule.
25.0 cm³ of Fe²⁺(aq) required 21.60 cm³ of 0.0200 mol dm⁻³ KMnO₄ (acidified with H₂SO₄). Calculate [Fe²⁺].
Answer: MnO₄⁻ + 8H⁺ + 5Fe²⁺ → Mn²⁺ + 4H₂O + 5Fe³⁺. Moles MnO₄⁻ = 0.0200 × 21.60/1000 = 4.32 × 10⁻⁴. Ratio 1:5 → moles Fe²⁺ = 2.16 × 10⁻³. [Fe²⁺] = 2.16 × 10⁻³ × 1000/25.0 = 0.0864 mol dm⁻³.
Why is dilute sulfuric acid used rather than hydrochloric acid in manganate(VII) titrations?
Answer: HCl would be oxidised by MnO₄⁻ (Cl⁻ → Cl₂), consuming extra MnO₄⁻ and giving a titre too large. HNO₃ is itself an oxidising agent and would oxidise Fe²⁺ before titration, giving a titre too small. H₂SO₄ (dilute) is neither oxidised nor an oxidant under these conditions.
Sketch the pH curve for a weak acid titrated with a strong base and state which indicator to use, with justification.
Answer: Starts at pH ~3-4 (partial dissociation), rises slowly, sharp vertical section above 7 (equivalence pH > 7: the salt hydrolyses, CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻), finishing at pH ~13. Indicator: phenolphthalein (8.3-10.0) — its range lies entirely within the vertical section; methyl orange would change colour before equivalence.
In recrystallisation, why must the solid be dissolved in the minimum volume of hot solvent?
Answer: Hot minimum solvent ensures the product dissolves when hot but crystallises out on cooling; too much solvent reduces yield (more product stays dissolved) and an impure/insoluble residue indicates the wrong solvent. Impurities remain dissolved in the cold mother liquor.
A TLC plate shows the solvent front at 6.0 cm and a spot at 4.2 cm. Calculate Rf and state what a single spot indicates.
Answer: Rf = 4.2/6.0 = 0.70. A single spot indicates the sample is pure (one component); two spots would indicate an impurity or a mixture. Compare Rf with known data or pure standards for identification.