Lesson 15: Redox and Electrochemistry

Redox reactions traffic in electrons rather than protons. Oxidation is loss of electrons (OIL), reduction is gain (RIG) — the two always occur together, because electrons released must land somewhere. Bookkeeping is done with oxidation numbers: free elements 0; monatomic ions equal to their charge; oxygen −2 (except peroxides −1, and +2 in OF₂); hydrogen +1 (except metal hydrides −1); the sum over a compound is zero, over an ion its charge. An element whose oxidation number rises has been oxidised; the species that causes oxidation — and is itself reduced — is the oxidising agent (Reactivity 3.2–3.3). Half-equations keep the ledger honest: each balances atoms first, then charge with electrons, e.g. MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O, where manganese falls from +7 to +2 — a gain of five electrons, a reduction.

Voltaic cells: redox with the halves separated

Force the two half-reactions into different beakers, connect them with a wire and a salt bridge, and the electron transfer becomes a current: a voltaic (galvanic) cell. The more reactive metal (more negative electrode potential) is oxidised at the anode (negative electrode in a voltaic cell) and its electrons travel through the external circuit to the cathode, where the other species is reduced. The salt bridge (filter paper soaked in KNO₃(aq), or an agar bridge) completes the circuit and maintains charge balance as ions migrate — the cell dies without it. The activity series predicts direction: a metal reduces the ions of any metal below it, as when zinc displaces copper from CuSO₄ — the blue colour fades, copper deposits, and the mixture warms, direct evidence of a spontaneous electron transfer. Electrolysis is the reverse bargain: an external supply forces a non-spontaneous redox — molten lead(II) bromide gives lead at the cathode and bromine at the anode; aqueous solutions add the complication of preferentially discharged ions (from water itself), governed at SL level by the reactivity series and concentration.

Standard electrode potentials (HL core of the theme)

At HL the cell becomes quantitative. The standard electrode potential E⦵ of a half-cell is measured against the standard hydrogen electrode (SHE, defined as 0.00 V) under standard conditions (298 K, 100 kPa, 1.00 mol dm⁻³). Data-booklet values let you predict: E⦵cell = E⦵(positive electrode) − E⦵(negative electrode) — equivalently, right minus left as the cell is conventionally written — and a positive E⦵cell means a spontaneous reaction (ΔG = −nFE⦵cell is negative). The species with the more negative E⦵ is the stronger reducing agent and is oxidised. Predictions carry one caveat examiners prize: E⦵ is thermodynamics, not kinetics — a predicted reaction may be imperceptibly slow, or passivation (aluminium's oxide coat) may intervene.

Worked example 1: the manganate(VII)–iron(II) titration

Acidified KMnO₄ oxidises Fe²⁺ to Fe³⁺. Half-equations: MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O; Fe²⁺ → Fe³⁺ + e⁻. Multiply the iron half-equation by 5 and add: MnO₄⁻ + 8H⁺ + 5Fe²⁺ → Mn²⁺ + 4H₂O + 5Fe³⁺ — a 1 : 5 stoichiometry. In the titration, 25.00 cm³ of an Fe²⁺ solution requires 20.00 cm³ of 0.0200 mol dm⁻³ KMnO₄: n(MnO₄⁻) = 0.0200 × 0.02000 = 4.000 × 10⁻⁴ mol, so n(Fe²⁺) = 5 × 4.000 × 10⁻⁴ = 2.000 × 10⁻³ mol, and [Fe²⁺] = 2.000 × 10⁻³ ÷ 0.02500 = 0.0800 mol dm⁻³. The titration is self-indicating: the first permanent pink tinge (excess MnO₄⁻) is the endpoint — no indicator bottle required, one less source of error to cite.

Worked example 2: building and auditing a Zn/Cu cell (practical)

Assemble Zn|Zn²⁺(1.0 mol dm⁻³)||Cu²⁺(1.0 mol dm⁻³)|Cu with a KNO₃ salt bridge and a high-resistance voltmeter. Predicted E⦵cell = (+0.34) − (−0.76) = +1.10 V; a good school cell reads 1.05–1.10 V. The investigation-grade thinking begins with the shortfall: trace it to non-standard concentrations as the cell runs (the reaction shifts ion concentrations), junction potentials at the bridge, polarisation (gas films, oxide coats — clean the electrodes with sandpaper immediately before use), and the voltmeter's finite resistance drawing a small current. Let the cell run with a small motor or LED instead and the voltage visibly sags over minutes — the concentration changes become measurable, and re-measuring E against [Cu²⁺] diluted stepwise previews the Nernst behaviour HL extension questions describe qualitatively. Switch to electrolysis to close the lesson's loop: electrolyse copper(II) sulfate with copper electrodes and the cathode gains mass exactly as the anode loses it (quantitative electroplating — weigh both electrodes to ±0.01 g and the transfer is stoichiometrically accountable); with inert graphite electrodes the anode instead evolves oxygen, and the solution's blue fades as Cu²⁺ depletes. Same cell chemistry, two configurations, every observation predictable from half-equations — that is the test of understanding.

Nature of Science — and the real world

Electrode potentials are measured relative to an arbitrary zero (the SHE) — chemistry is comfortable with conventional zeros when only differences carry meaning, like altitude from sea level. Volta's pile (1800) launched electrochemistry before anyone knew what an electron was. The real-world stakes are enormous: corrosion is redox running wild (rust costs economies several percent of GDP; sacrificial zinc anodes protect ships and pipelines by being oxidised first), lithium-ion batteries are engineered voltaic cells run backwards on recharge, green hydrogen is electrolysis powered by renewables, and electroplating and aluminium smelting (Hall–Héroult electrolysis of molten alumina in cryolite) are industries built entirely on forced electron transfer.

Common mistakes

• Assigning oxygen −2 in peroxides (it is −1 in H₂O₂) or hydrogen +1 in metal hydrides (−1 in NaH).
• Calling the anode positive in a voltaic cell — in voltaic cells the anode (oxidation) is the negative terminal; the convention flips for electrolysis, and the safe anchor is always "anode = oxidation".
• Balancing half-equations with electrons added before the atoms and charge are counted.
• Omitting the salt bridge's function (ion flow to balance charge) and writing that electrons travel through it — electrons never pass through solutions.

IB Exam Experience

Question 1. What is the oxidation number of chromium in K₂Cr₂O₇?

• (A) +2
• (B) +3
• (C) +6
• (D) +7

Question 2. Which species is the reducing agent in Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)?

• (A) Zn
• (B) Cu²⁺
• (C) Cu
• (D) Zn²⁺

Question 3. (HL) Using E⦵ values Zn²⁺/Zn = −0.76 V and Fe²⁺/Fe = −0.44 V, what is E⦵cell for the spontaneous cell between them, and which metal is oxidised?

• (A) +0.32 V; iron is oxidised
• (B) +0.32 V; zinc is oxidised
• (C) −0.32 V; zinc is oxidised
• (D) +1.20 V; zinc is oxidised

Answer key. 1. (C) — 2(+1) + 2Cr + 7(−2) = 0 → 2Cr = +12 → Cr = +6. 2. (A) — zinc is oxidised (0 → +2), so zinc is the reducing agent; Cu²⁺ is the oxidising agent. 3. (B) — zinc has the more negative E⦵, so zinc is oxidised and iron(II) is reduced: E⦵cell = (−0.44) − (−0.76) = +0.32 V.

Structured question (Paper 2 style). A voltaic cell is constructed from a magnesium electrode in Mg²⁺(aq) and a silver electrode in Ag⁺(aq), connected by a salt bridge. E⦵(Mg²⁺/Mg) = −2.37 V; E⦵(Ag⁺/Ag) = +0.80 V. (a) Write half-equations for the reactions at each electrode, identifying the anode and cathode. [3] (b) Calculate E⦵cell. [1] (c) State the direction of electron flow in the external circuit and of ion flow in the salt bridge. [2] (d) The cell is modified by electrolysing the silver nitrate solution with inert electrodes connected to a power supply instead. State the products at each electrode. [2] Marking notes. (a) Anode (oxidation): Mg → Mg²⁺ + 2e⁻ [1]; cathode (reduction): Ag⁺ + e⁻ → Ag [1]; magnesium is the anode because it has the more negative E⦵ / is the stronger reducing agent [1]. (b) E⦵cell = (+0.80) − (−2.37) = +3.17 V [1]. (c) Electrons flow from Mg (anode) to Ag (cathode) through the wire [1]; in the bridge, cations migrate towards the cathode and anions towards the anode to maintain charge neutrality [1]. (d) At the cathode: silver (Ag⁺ + e⁻ → Ag) [1]; at the anode: oxygen (from water/hydroxide discharge, as nitrate is not discharged) [1].

IA idea: Investigate how the voltage of a voltaic cell depends on the concentration of one half-cell's electrolyte, and evaluate the trend against the predictions of electrode-potential theory.

Electrolysis products: the preferential-discharge table, and electroplating by numbers

For aqueous electrolysis with inert electrodes, the cathode discharges the least reactive available cation (below zinc in the series, metal deposits; above it, hydrogen evolves — with concentrated solutions and overpotential occasionally bending the rule, as concentrated brine gives chlorine at the anode rather than oxygen). The school canon:

The last row is purification and plating in one: impure copper anodes dissolve, pure copper deposits, and the sludge below the anode contains the noble-metal impurities — industry recovers gold from it. Quantify a plating run: a current of 0.500 A for 30.0 minutes delivers Q = It = 0.500 × 1800 = 900 C; with the Faraday constant 96 500 C mol⁻¹ (data booklet), n(e⁻) = 900 ÷ 96 500 = 9.33 × 10⁻³ mol; Cu²⁺ + 2e⁻ → Cu needs two electrons per atom, so n(Cu) = 4.66 × 10⁻³ mol and the cathode gains 4.66 × 10⁻³ × 63.55 = 0.296 g — weighable on a school balance to three figures, and a measurement of current efficiency when compared against the actual gain (bubbles and side reactions tax it). Corrosion protection closes the theme: galvanising coats steel in zinc, which corrodes preferentially — sacrificial protection — because zinc's E⦵ is the more negative; the same ledger, read defensively, protects ships' hulls with bolted-on zinc blocks and pipelines with magnesium ribbons buried alongside.

The activity series is a voltage table in disguise

Every displacement observation from earlier schooling is an electrode potential wearing plain clothes. Zinc displaces copper, copper displaces silver, magnesium displaces almost everything: order the metals by who displaces whom and you have built the E⦵ ranking (−2.37 Mg, −0.76 Zn, −0.44 Fe, +0.34 Cu, +0.80 Ag) from test tubes. The thermite reaction makes the point at industrial temperature: 2Al + Fe₂O₃ → Al₂O₃ + 2Fe, ΔH ≈ −850 kJ mol⁻¹ — aluminium's hunger for oxygen (its E⦵ of −1.66 V) drives a reaction hot enough to weld railway rails, and the same ranking explains why aluminium itself is won only by electrolysis: no chemical reducing agent sits far enough below it to be economical, so electrons are supplied by a power station instead. When an exam asks why a displacement "occurs", the full answer names the electron transfer (who is oxidised, who reduced) and — at HL — cites the sign of E⦵cell. The series, the cells and the electrolytic extractions are one table read three ways; students who see that stop memorising three topics and start using one.