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Redox titrations are the quantitative cousins of the familiar acid–base titration. Instead of neutralisation, the reaction at the burette tip is an electron transfer — an oxidising agent in one container reacts stoichiometrically with a reducing agent in the other, and the end point is detected either by the disappearance or appearance of an intensely coloured species. The three workhorses of A-Level redox analysis are potassium manganate(VII) (KMnO₄), potassium dichromate(VI) (K₂Cr₂O₇), and the two-step iodine–thiosulfate (iodometric) procedure with sodium thiosulfate (Na₂S₂O₃). Permanganate and dichromate titrations are described as self-indicating — the titrant itself supplies the colour change — though dichromate is sufficiently sluggish in its colour transition that a redox indicator is normally added. Iodometry uses starch as a late-added indicator. This lesson develops the stoichiometry, worked calculations, indicator choice, and error sources for each method, and signposts Required Practical 9 (the AQA-prescribed analytical-chemistry RP, an iodine–thiosulfate analysis of copper(II) ions in a brass alloy or copper salt).
Spec mapping (AQA 7405): This lesson maps to §3.1.7 (oxidation, reduction and redox equations — quantitative applications), with the explicit specification expectation that students can carry out structured calculations on permanganate, dichromate, and iodine–thiosulfate titrations. The mechanics of combining two half-equations to obtain a balanced ionic equation are anchored in lesson 1 of this course (redox-reactions-equations); oxidation-number assignment in lesson 0. The general framework for acid–base and titration arithmetic — the n = c × V relation, pipette/burette uncertainty, indicator choice for acid–base — is developed in lesson 8 (titration calculations) of the atomic-structure course, which anchors Required Practical 1. Required Practical 9 (analysis of an organic acid by acid–base titration, and an iodine–thiosulfate analysis of a copper(II) salt) is anchored in the analytical-chemistry course (§3.3.6). Refer to the official AQA specification document for the exact wording of each section.
Assessment objectives: AO1 questions test recall of the reagents, the stoichiometric ratios (1 MnO₄⁻ : 5 Fe²⁺; 1 Cr₂O₇²⁻ : 6 Fe²⁺; 1 I₂ : 2 S₂O₃²⁻), the role of starch in iodometry, and the standard self-indicating colour changes. AO2 questions ask students to combine half-equations into balanced ionic equations, perform multi-step concentration arithmetic from titre data, and calculate percentage compositions. AO3 questions probe higher-order analysis: explaining why H₂SO₄ rather than HCl is the acidifying agent for permanganate, why dichromate requires an external indicator while permanganate does not, choosing between iodometric and direct titration on the basis of E° values, and propagating measurement uncertainty through multi-step procedures.
The manganate(VII) ion MnO₄⁻ is one of the most powerful oxidising agents in routine laboratory use. In acidic solution it is reduced to the manganese(II) ion Mn²⁺ via the half-equation
MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O E° = +1.51 V
The dramatic colour change underpins the self-indicating character of the technique: the manganate(VII) ion is an intense purple in solution (the colour arises from a ligand-to-metal charge-transfer absorption in the visible spectrum), whereas the manganese(II) ion is colourless at the concentrations encountered in a titration (Mn²⁺(aq) is a very pale pink because the d–d transitions of d⁵ high-spin Mn(II) are spin-forbidden). The titration is run by adding KMnO₄ from the burette into an acidified solution of the reducing agent in the conical flask. Each drop of purple solution is decolorised as it reacts. When the analyte is exhausted, the very next drop of KMnO₄ leaves a faint but persistent pink colour in the flask — that is the end point.
The textbook permanganate titration is the determination of Fe²⁺ in solution. The half-equations are
Multiplying the oxidation half-equation by 5 to balance the electrons and adding gives
MnO₄⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O
The stoichiometric ratio is 1 mole of MnO₄⁻ : 5 moles of Fe²⁺. Acidic conditions are provided by an excess of dilute sulfuric acid (typically 1.0 mol dm⁻³).
An iron supplement tablet (claimed mass of iron 65 mg) is crushed and dissolved in dilute sulfuric acid. The resulting solution is made up to 100.0 cm³ in a volumetric flask. A 25.00 cm³ aliquot is pipetted into a conical flask and titrated against 0.00500 mol dm⁻³ KMnO₄. The mean titre is 23.40 cm³. Calculate the mass of iron in the original tablet and comment on whether the manufacturer's claim is accurate.
Step 1 — moles of MnO₄⁻ used:
n(MnO₄⁻) = c × V = 0.00500 × 23.40 / 1000 = 1.170 × 10⁻⁴ mol
Step 2 — moles of Fe²⁺ in the aliquot (1 : 5 ratio):
n(Fe²⁺) = 5 × 1.170 × 10⁻⁴ = 5.850 × 10⁻⁴ mol
Step 3 — moles of Fe²⁺ in the 100 cm³ stock:
n(Fe²⁺, total) = 5.850 × 10⁻⁴ × (100.0 / 25.00) = 2.340 × 10⁻³ mol
Step 4 — mass of iron:
m(Fe) = n × M = 2.340 × 10⁻³ × 55.8 = 0.1306 g = 130.6 mg
The titration result (130.6 mg) is about twice the manufacturer's stated 65 mg. In a real laboratory this would prompt a re-check of the dilution arithmetic; for the purposes of an exam answer the calculation is correct, and the candidate would comment that the tablet contains roughly 131 mg of iron — substantially more than the claimed value.
Solid KMnO₄ is not a primary standard: it decomposes slowly on standing, particularly in the presence of light or trace organic matter, and the solid frequently contains traces of MnO₂. The standard procedure is to make up an approximately 0.02 mol dm⁻³ solution and then titrate against a primary standard — almost always sodium oxalate (Na₂C₂O₄), which is available in high purity, is non-hygroscopic, and reacts cleanly with permanganate.
The half-equations are
Balancing (multiply oxidation by 5, reduction by 2) gives
2MnO₄⁻ + 5C₂O₄²⁻ + 16H⁺ → 2Mn²⁺ + 10CO₂ + 8H₂O
The ratio is 2 MnO₄⁻ : 5 C₂O₄²⁻.
A practical wrinkle: the reaction is autocatalysed by Mn²⁺. The first few drops of permanganate are decolorised slowly; once a little Mn²⁺ has formed, the rate accelerates dramatically. To avoid the temptation to over-titrate at the start, the flask is usually warmed to about 60 °C, which provides a kinetic kick-start.
The half-equations for the H₂O₂/MnO₄⁻ system are
Combining (5 × oxidation, 2 × reduction) gives
2MnO₄⁻ + 5H₂O₂ + 6H⁺ → 2Mn²⁺ + 5O₂ + 8H₂O
A pharmaceutical-grade H₂O₂ solution labelled "3% (w/v)" is diluted by a factor of 100. A 25.00 cm³ aliquot of the diluted solution is titrated against 0.0200 mol dm⁻³ KMnO₄ in dilute H₂SO₄, giving a mean titre of 22.10 cm³.
n(MnO₄⁻) = 0.0200 × 22.10 / 1000 = 4.420 × 10⁻⁴ mol
n(H₂O₂) in aliquot = (5/2) × 4.420 × 10⁻⁴ = 1.105 × 10⁻³ mol
c(H₂O₂, diluted) = 1.105 × 10⁻³ / (25.00 × 10⁻³) = 0.04420 mol dm⁻³
c(H₂O₂, original) = 0.04420 × 100 = 4.420 mol dm⁻³
Mass of H₂O₂ per dm³ = 4.420 × 34.0 = 150.3 g dm⁻³ ≈ 15.0% (w/v)
The pharmaceutical "3% (w/v)" label is the diluted-product strength; this calculation simulates the analysis of a more concentrated stock, and the candidate's task is to interpret what the number means.
Permanganate titrations are acidified with dilute sulfuric acid, never with hydrochloric acid. The reason is straightforward thermodynamics: the standard electrode potential for the Cl₂/Cl⁻ couple is E°(Cl₂|Cl⁻) = +1.36 V, which lies below E°(MnO₄⁻|Mn²⁺) = +1.51 V. Manganate(VII) is therefore capable of oxidising chloride to chlorine:
2MnO₄⁻ + 10Cl⁻ + 16H⁺ → 2Mn²⁺ + 5Cl₂ + 8H₂O
If HCl were used as the acidifying agent, some of the manganate(VII) would be consumed by this side-reaction instead of by the intended analyte, the titre would be falsely high, and Cl₂ gas would be evolved (a hazard in itself). Sulfate, by contrast, is already in its highest oxidation state and cannot be oxidised further by MnO₄⁻ under any plausible conditions; it acts purely as a spectator anion, providing H⁺ without redox interference. Nitric acid is also avoided — it is itself an oxidising agent and complicates the stoichiometry.
A small kinetic caveat: in practice, the MnO₄⁻/Cl⁻ reaction at room temperature is slow, and good titrations against Fe²⁺ in HCl can be done provided the so-called Zimmermann–Reinhardt reagent (a mixture of Mn(II), H₃PO₄ and H₂SO₄) is added to suppress chloride oxidation. This is beyond the A-Level expectation, but is worth knowing for the A* candidate who wants to demonstrate awareness of historical practice.
The dichromate(VI) ion Cr₂O₇²⁻ is a slightly milder oxidising agent than manganate(VII). In acidic solution it is reduced to the chromium(III) ion via
Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O E° = +1.33 V
The colour change is from orange (Cr₂O₇²⁻) to green (Cr³⁺(aq), a d³ ion with two spin-allowed d–d transitions in the visible). Unlike permanganate, the dichromate transition is not sharp enough to function as a self-indicator: the orange of the titrant fades only gradually through brown to green near the end point, and the eye cannot reliably distinguish an excess of one drop from a slight deficit. A redox indicator is therefore added — most commonly diphenylamine, or its more reliable derivative barium diphenylamine sulfonate. These indicators are themselves oxidised by an excess of dichromate to give an intense violet or purple colour, providing a sharp visual end point on top of the underlying green Cr(III).
The standard application is again iron(II) analysis. The balanced ionic equation is
Cr₂O₇²⁻ + 6Fe²⁺ + 14H⁺ → 2Cr³⁺ + 6Fe³⁺ + 7H₂O
Stoichiometric ratio: 1 mole of Cr₂O₇²⁻ : 6 moles of Fe²⁺.
A 1.250 g sample of an iron ore is dissolved in concentrated HCl and the iron reduced to Fe²⁺ with tin(II) chloride. The solution is diluted to 250.0 cm³. A 25.00 cm³ aliquot, acidified with dilute H₂SO₄ and H₃PO₄ and with a few drops of barium diphenylamine sulfonate indicator, is titrated against 0.01667 mol dm⁻³ K₂Cr₂O₇. The mean titre is 24.85 cm³. Calculate the percentage of iron in the ore.
n(Cr₂O₇²⁻) = 0.01667 × 24.85 / 1000 = 4.142 × 10⁻⁴ mol
n(Fe²⁺) in aliquot = 6 × 4.142 × 10⁻⁴ = 2.485 × 10⁻³ mol
n(Fe²⁺) in 250 cm³ = 2.485 × 10⁻³ × 10 = 2.485 × 10⁻² mol
m(Fe) = 2.485 × 10⁻² × 55.8 = 1.387 g
%Fe = (1.387 / 1.250) × 100 = 110.9 %
A percentage above 100% is impossible for a pure ore. This is the kind of result that, in a real exam, signals a deliberately mis-set question or a manufactured arithmetical trap; in a real laboratory it would indicate a procedural error such as failure to reduce the sample fully to Fe²⁺ before titrating, or contamination of the sample. The mark scheme would credit the correct arithmetic and an appropriate critical comment. (A more realistic ore composition — 55-65 %Fe in a high-grade haematite, for example — would emerge from a calibrated titre of, say, 14 cm³.)
Dichromate has two practical advantages over permanganate. First, K₂Cr₂O₇ is a primary standard: it can be obtained in high purity, is non-hygroscopic, and is indefinitely stable as the solid. A standardised solution can be made up directly by weighing. Second, the dichromate/chloride redox potential gap is small enough (E°(Cr₂O₇²⁻|Cr³⁺) = +1.33 V vs E°(Cl₂|Cl⁻) = +1.36 V) that dichromate does not oxidise chloride at room temperature, so HCl can be used as the acidifying agent without interference. The H₃PO₄ added in the worked example above forms a colourless complex with Fe³⁺, suppressing the otherwise pale-yellow colour of the iron(III) product and sharpening the visual end point.
The price paid for these advantages is the indicator requirement and — significantly — the toxicity and carcinogenicity of Cr(VI) salts. Modern analytical laboratories increasingly avoid dichromate where alternatives exist; for routine teaching laboratories, the technique remains a valuable demonstration of the role of redox indicators.
The iodine–thiosulfate titration is a two-step indirect method. It is the analytical workhorse for oxidising agents that are too coloured, too dilute, or too sluggish to be titrated directly with a manganate(VII) or dichromate(VI) burette. The strategy is to liberate iodine from an excess of iodide and then to titrate that iodine with a standardised thiosulfate solution. The technique therefore involves two distinct redox reactions, and the stoichiometry must be carefully tracked through both.
The analyte (an oxidising agent X) is added to a known excess of potassium iodide in dilute acid. The oxidising agent oxidises some of the iodide to iodine, and is itself reduced. The amount of iodine liberated is stoichiometrically equivalent to the analyte. Worked examples of step-1 reactions follow.
For copper(II) (the AQA Required Practical 9 anchor):
2Cu²⁺ + 4I⁻ → 2CuI(s) + I₂
Note that the copper(II) is reduced to copper(I) — but the product is insoluble copper(I) iodide CuI, a cream-coloured solid that drops out of solution as the reaction proceeds. The ratio is 2 Cu²⁺ : 1 I₂.
For hydrogen peroxide:
H₂O₂ + 2I⁻ + 2H⁺ → I₂ + 2H₂O ratio 1 H₂O₂ : 1 I₂
For manganate(VII) in acidic solution:
2MnO₄⁻ + 10I⁻ + 16H⁺ → 2Mn²⁺ + 5I₂ + 8H₂O ratio 2 MnO₄⁻ : 5 I₂
For dichromate(VI):
Cr₂O₇²⁻ + 6I⁻ + 14H⁺ → 2Cr³⁺ + 3I₂ + 7H₂O ratio 1 Cr₂O₇²⁻ : 3 I₂
For chlorate(I) (hypochlorite, in household bleach):
ClO⁻ + 2I⁻ + 2H⁺ → I₂ + Cl⁻ + H₂O ratio 1 ClO⁻ : 1 I₂
The iodine generated in step 1 is then titrated against a standardised solution of sodium thiosulfate, Na₂S₂O₃. The half-equations are
giving the overall equation
I₂ + 2S₂O₃²⁻ → 2I⁻ + S₄O₆²⁻
The stoichiometry is 1 mole of I₂ : 2 moles of S₂O₃²⁻. The tetrathionate ion S₄O₆²⁻ is the oxidation product; its formation is what makes thiosulfate such a clean iodine reagent — the product is a single, well-defined species and there is no over-oxidation to sulfate at neutral or slightly alkaline pH. (At low pH, thiosulfate disproportionates to sulfur and sulfur dioxide, which is why iodometric titrations must be performed in neutral or weakly acidic conditions and never in strong acid. Solutions stored at slightly alkaline pH are most stable.)
The iodine solution at the start of step 2 is deep red-brown. As thiosulfate is added, the colour fades — first to a paler brown, then to a straw-yellow. Starch is added only at this late stage — typically when the colour has faded to the pale-yellow region just before the end point. Starch forms a deep blue-black complex with iodine (specifically, iodide and tri-iodide threaded through the helical amylose chain), which is many times more sensitive to small concentrations of I₂ than the naked eye is to the residual yellow-brown. As the next few drops of thiosulfate are added, the blue colour disappears sharply — that is the end point.
Two practical points justify the late addition. First, if starch is added at the very beginning, when iodine concentrations are high, the iodine becomes adsorbed deep into the amylose helix and is slowly released; the end point is then approached sluggishly and over-titration is likely. Second, the colour change from intense blue to colourless near the end point is one of the most visually striking end points in analytical chemistry — far easier to call to the nearest drop than the gradual fade from yellow.
A 0.500 g sample of brass (a copper–zinc alloy) is dissolved in concentrated nitric acid. The resulting solution is carefully neutralised with sodium carbonate and re-acidified with dilute acetic acid (to avoid liberating nitrous oxide species that would interfere with iodide). An excess of potassium iodide is added, and the liberated iodine is titrated against 0.100 mol dm⁻³ Na₂S₂O₃, requiring a mean titre of 14.80 cm³ to discharge the blue starch–iodine colour at the end point. Calculate the percentage copper in the brass.
Step 1 — moles of thiosulfate:
n(S₂O₃²⁻) = 0.100 × 14.80 / 1000 = 1.480 × 10⁻³ mol
Step 2 — moles of I₂ (1 : 2 ratio):
n(I₂) = ½ × 1.480 × 10⁻³ = 7.400 × 10⁻⁴ mol
Step 3 — moles of Cu²⁺ (2 : 1 ratio from the step-1 reaction 2Cu²⁺ + 4I⁻ → 2CuI + I₂):
n(Cu²⁺) = 2 × 7.400 × 10⁻⁴ = 1.480 × 10⁻³ mol
Step 4 — mass and percentage:
m(Cu) = 1.480 × 10⁻³ × 63.5 = 0.0940 g
%Cu = (0.0940 / 0.500) × 100 = 18.8 %
This is a slightly atypical brass — most commercial brasses are 60-70% copper — and again the candidate would be expected to comment that the result is consistent with a low-copper / high-zinc alloy, or to suggest re-checking the sample identity. In a real AQA-style RP9 question the titre and starting mass would typically be set so as to give a chemically plausible answer near 60-70%.
A 10.00 cm³ sample of a commercial household bleach is diluted to 250.0 cm³ in a volumetric flask. A 25.00 cm³ aliquot is taken, acidified with dilute acetic acid, and treated with excess KI. The liberated iodine is titrated against 0.100 mol dm⁻³ Na₂S₂O₃, with a mean titre of 21.50 cm³. Calculate the concentration of NaClO in the original bleach (in mol dm⁻³ and as "% available chlorine", a w/v figure conventionally expressed as g Cl₂ per 100 cm³).
n(S₂O₃²⁻) = 0.100 × 21.50 / 1000 = 2.150 × 10⁻³ mol
n(I₂) = ½ × 2.150 × 10⁻³ = 1.075 × 10⁻³ mol
For ClO⁻ + 2I⁻ + 2H⁺ → I₂ + Cl⁻ + H₂O, the ratio is 1 ClO⁻ : 1 I₂, so
n(ClO⁻) in aliquot = 1.075 × 10⁻³ mol
n(ClO⁻) in 250 cm³ stock = 1.075 × 10⁻³ × 10 = 1.075 × 10⁻² mol
This came from 10.00 cm³ of bleach, so
c(NaClO, bleach) = 1.075 × 10⁻² / (10.00 × 10⁻³) = 1.075 mol dm⁻³
The "available chlorine" convention expresses the bleaching power as the equivalent mass of Cl₂. Since 1 mole of ClO⁻ delivers the same oxidising power as 1 mole of Cl₂ (both supply 2 electrons of oxidising capacity per formula unit in the relevant reactions), the equivalent mass of Cl₂ per dm³ is 1.075 × 71.0 = 76.3 g dm⁻³, or 7.63 g per 100 cm³. Commercial domestic bleach is typically labelled "around 5% available chlorine"; the slightly higher value here is consistent with a "thick bleach" formulation.
Practical Skills — RP9 essentials.
- KMnO₄ in a brown glass burette. Concentrated KMnO₄ solutions decompose slowly in light to give brown MnO₂ deposits, which both reduce the effective concentration and obscure the meniscus. Use a brown burette and standardise the solution against sodium oxalate on the day of use.
- Thiosulfate stability. Aqueous Na₂S₂O₃ is stable at near-neutral or slightly alkaline pH (typically buffered around pH 9-10 with a trace of Na₂CO₃) for several weeks. It decomposes in acid (giving S and SO₂) and is also sensitive to atmospheric CO₂ (lowering the pH) and to dissolved oxygen in the presence of trace transition-metal catalysts. Re-standardise frequently against a primary standard such as potassium iodate KIO₃ via the reaction IO₃⁻ + 5I⁻ + 6H⁺ → 3I₂ + 3H₂O followed by titration of the liberated iodine.
- Starch indicator timing. Add starch only when the iodine colour has faded from red-brown to pale straw-yellow. Adding it too early gives over-titration; adding it too late risks missing the end point.
- Air-oxidation of Fe²⁺ and I⁻. Iron(II) solutions slowly oxidise to Fe³⁺ on standing in air; iodide solutions slowly oxidise to iodine. Both sources of error inflate or deflate the titre. Prepare solutions fresh and titrate promptly.
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