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The sign of the standard cell EMF is the chemist's most economical criterion for predicting whether a redox reaction will proceed: positive E°cell signals a spontaneous forward reaction at standard conditions, negative E°cell signals that the reverse process is favoured, and zero E°cell identifies a system poised at equilibrium. This lesson turns the qualitative cell-construction picture developed in lesson 3 into a quantitative thermodynamic tool by introducing the central bridge equation ΔG° = −nFE°cell, which links electrochemistry to the Gibbs-energy framework of §3.1.8. We then assess how concentration changes shift cell potentials in line with Le Chatelier's principle, rationalise the metal-reactivity series directly from E° data, and confront the limitations of feasibility predictions — particularly the persistent confusion between thermodynamic favourability and kinetic accessibility. By the end of the lesson you should be able to write down ΔG° from any E°cell value and explain why a thermodynamically downhill reaction may still fail to occur.
Spec mapping (AQA 7405): This lesson maps to §3.1.11 (electrochemical cells, feasibility from E°cell, ΔG° = −nFE°cell). It builds on lesson 2 (standard electrode potentials), lesson 3 (cell construction and EMF arithmetic), and §3.1.8 (free-energy change, ΔG° and entropy). It also threads forwards into §3.2 inorganic chemistry, where the reactivity of Group 1 and Group 2 metals — and the trends in Group 7 oxidising power — are rationalised quantitatively from E° data. Refer to the official AQA specification document for the exact wording of each section.
Assessment objectives: Recalling ΔG° = −nFE°cell with F = 96 485 C mol⁻¹ and stating that E°cell > 0 corresponds to a thermodynamically feasible forward reaction are AO1 items. Computing ΔG° from E°cell (or vice versa), and predicting whether a given pair of half-cells will react in a stated direction, are AO2 staples on Paper 2. AO3 reasoning is tested when candidates rationalise an observed metal-reactivity sequence from E° data, predict the qualitative effect of concentration changes on EMF via Le Chatelier, or comment on why a feasible reaction has not occurred (kinetic versus thermodynamic control).
The cell EMF arithmetic established in lesson 3 — E°cell = E°(cathode) − E°(anode), or equivalently E°cell = E°(reduction half) − E°(oxidation half) using both standard electrode potentials as reduction potentials — yields a signed number whose sign carries direct thermodynamic meaning.
| E°cell | Thermodynamic interpretation |
|---|---|
| E°cell > 0 | Forward reaction is spontaneous (feasible) at standard conditions |
| E°cell = 0 | System is at equilibrium; no net reaction |
| E°cell < 0 | Reverse reaction is spontaneous; forward direction is not feasible at standard conditions |
The word feasible here has a precise meaning. A feasible reaction is one for which the thermodynamic driving force — measured by the Gibbs free-energy change — is negative. It does not mean that the reaction will occur quickly, or even on any observable timescale. A feasible reaction may be kinetically blocked (the hydrogen–oxygen reaction discussed below is the canonical example).
Key Point: "Feasibility" is a thermodynamic statement about the equilibrium position, not about the rate. Always couple a feasibility prediction with an awareness that the activation barrier may render the reaction unobservable in practice.
By convention, when two half-cells are connected, the half-cell with the more positive E° acts as the cathode (reduction occurs there) and the half-cell with the more negative E° acts as the anode (oxidation occurs there). The resulting E°cell is necessarily positive — the cell delivers electrical work to the external circuit. If you find yourself writing a negative E°cell, you have either written the reaction in the non-spontaneous direction or assigned the electrodes incorrectly.
The central equation of this lesson connects the EMF — an easily measured electrical quantity — to the Gibbs free-energy change, the universal criterion of spontaneity.
ΔG° = −nFE°cell
where:
The units balance: C mol⁻¹ × V = C mol⁻¹ × J C⁻¹ = J mol⁻¹.
Common Misconception: The "n" in ΔG° = −nFE°cell is the number of electrons transferred per mole of reaction as written, not the number of electrons per molecule. If the balanced equation specifies 2H₂ + O₂ → 2H₂O, then n = 4 (four electrons transferred in the equation as written), not 2.
The negative sign in the equation is critical: a positive E°cell gives a negative ΔG° (spontaneous forward reaction), and vice versa. The thermodynamic feasibility criterion ΔG° < 0 is exactly equivalent to the electrochemical criterion E°cell > 0.
For the Daniell cell Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s):
Overall reaction: Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)
E°cell = E°(Cu²⁺/Cu) − E°(Zn²⁺/Zn) = +0.34 − (−0.76) = +1.10 V
Each zinc atom loses two electrons; each copper(II) ion gains two; n = 2 per mole of reaction as written.
ΔG° = −nFE°cell = −2 × 96 485 × 1.10 = −212 267 J mol⁻¹ ≈ −212 kJ mol⁻¹
This highly negative ΔG° confirms the textbook expectation that zinc spontaneously reduces aqueous copper(II) ions — the basis of the classic blue-to-colourless lecture demonstration.
Will iron(II) ions reduce iodine to iodide under standard conditions?
Postulated reaction: 2Fe²⁺(aq) + I₂(aq) → 2Fe³⁺(aq) + 2I⁻(aq)
In this reaction iodine is the oxidising agent (it is reduced from I₂ to I⁻), so the I₂/I⁻ half-cell is the cathode and the Fe³⁺/Fe²⁺ half-cell is the anode.
E°cell = E°(I₂/I⁻) − E°(Fe³⁺/Fe²⁺) = +0.54 − (+0.77) = −0.23 V
n = 2 (two electrons transferred per mole of equation as written).
ΔG° = −2 × 96 485 × (−0.23) = +44 383 J mol⁻¹ ≈ +44 kJ mol⁻¹
Because ΔG° is positive (equivalently E°cell is negative), the postulated forward reaction is not feasible. The reverse reaction is feasible: iron(III) ions spontaneously oxidise iodide ions to iodine.
Reverse reaction: 2Fe³⁺(aq) + 2I⁻(aq) → 2Fe²⁺(aq) + I₂(aq); E°cell = +0.23 V; ΔG° = −44 kJ mol⁻¹.
This prediction is the basis of the classic qualitative test: adding iron(III) chloride to potassium iodide solution produces a brown colouration of iodine, confirmed by extraction into hexane or by reaction with starch indicator.
For a hydrogen–oxygen fuel cell operating in acidic electrolyte:
Cathode: O₂(g) + 4H⁺(aq) + 4e⁻ → 2H₂O(l); E° = +1.23 V Anode: 2H₂(g) → 4H⁺(aq) + 4e⁻; E° = 0.00 V (standard hydrogen electrode)
Overall: 2H₂(g) + O₂(g) → 2H₂O(l); E°cell = +1.23 V
n = 4 per mole of reaction as written.
ΔG° = −4 × 96 485 × 1.23 = −474 706 J mol⁻¹ ≈ −475 kJ mol⁻¹
This figure agrees within the precision of E° data with the value of ΔG°f(H₂O, l) × 2 calculated from tabulated standard formation energies — a reassuring internal consistency between the electrochemical and thermochemical thermodynamic datasets. It also rationalises the high theoretical voltage and energy density of hydrogen fuel cells (developed further in lesson 5).
The familiar reactivity series learnt at GCSE — K > Na > Ca > Mg > Al > (C) > Zn > Fe > (H) > Cu > Ag > Au — emerges naturally from standard electrode potential data. The more negative an element's M^n+/M reduction potential, the more strongly it is driven to lose electrons, the better a reducing agent it is, and the higher it sits in the reactivity series.
| Half-cell | E° / V | Position |
|---|---|---|
| K⁺/K | −2.92 | Most reactive |
| Na⁺/Na | −2.71 | Very reactive |
| Mg²⁺/Mg | −2.37 | Reactive |
| Zn²⁺/Zn | −0.76 | Moderate |
| Fe²⁺/Fe | −0.44 | Moderate |
| 2H⁺/H₂ | 0.00 | Reference |
| Cu²⁺/Cu | +0.34 | Below H |
| Ag⁺/Ag | +0.80 | Below H |
| Au³⁺/Au | +1.50 | Least reactive |
Metal X displaces metal Y from solution if X is a better reducing agent than Y — i.e. if E°(X^n+/X) is more negative than E°(Y^m+/Y).
Example: Will magnesium displace copper from copper(II) sulfate solution?
Postulated: Mg(s) + Cu²⁺(aq) → Mg²⁺(aq) + Cu(s)
E°cell = E°(Cu²⁺/Cu) − E°(Mg²⁺/Mg) = +0.34 − (−2.37) = +2.71 V
Highly positive → highly feasible. ΔG° = −2 × 96 485 × 2.71 = −523 kJ mol⁻¹. Observed: magnesium ribbon dropped into copper sulfate solution rapidly coats with red-brown copper and the blue colour fades.
The reverse — copper displacing magnesium — has E°cell = −2.71 V and ΔG° = +523 kJ mol⁻¹: not feasible. Copper does not react with magnesium sulfate solution.
A metal displaces hydrogen from dilute acid (giving M^n+ + ½n H₂) if E°(M^n+/M) is more negative than 0.00 V (the standard hydrogen electrode potential).
(Concentrated oxidising acids such as hot HNO₃ or hot concentrated H₂SO₄ can dissolve copper and silver — but the oxidising agent there is the NO₃⁻ or SO₄²⁻ ion, not the H⁺ ion, and the relevant E° is that of the NO₃⁻/NO or SO₄²⁻/SO₂ couple, not 2H⁺/H₂.)
Standard electrode potentials are defined at 1.00 mol dm⁻³ concentration of all aqueous species, 100 kPa for gases, and 298 K. When concentrations differ from standard, the half-cell potential shifts, and so does E°cell. AQA requires a qualitative treatment of these shifts in terms of Le Chatelier's principle applied to the half-cell equilibrium.
Consider the generic reduction half-equation:
M^n+(aq) + ne⁻ ⇌ M(s)
Increasing [M^n+] shifts the equilibrium to the right (forward), making reduction more favoured and the half-cell potential more positive. Decreasing [M^n+] does the opposite.
For a complete cell:
These shifts are typically small (tens of millivolts for order-of-magnitude concentration changes) but become significant when comparing dilute and concentrated cells, or when a borderline E°cell is close to zero.
A Daniell cell is set up with [Zn²⁺] = 1.00 mol dm⁻³ and [Cu²⁺] varied between 1.00 and 0.10 mol dm⁻³. Predict qualitatively how E°cell changes.
At standard conditions ([Cu²⁺] = 1.00): E°cell = +1.10 V.
Decreasing [Cu²⁺] to 0.10 mol dm⁻³ shifts the cathode half-cell equilibrium Cu²⁺ + 2e⁻ ⇌ Cu to the left, lowering E(cathode) and therefore reducing E°cell. The magnitude is approximately:
ΔE ≈ −(RT/nF) × ln(10) = −(8.314 × 298 / (2 × 96 485)) × 2.303 ≈ −0.030 V = −30 mV
(This is the Nernst-equation result, included here for context; the AQA syllabus asks only for the qualitative direction of the shift, not the numerical value.)
New E°cell ≈ +1.10 − 0.03 = +1.07 V — still strongly feasible. A ten-fold concentration change produces only a 3% shift in EMF: the cell is robust to moderate concentration variations, which is why the Daniell cell was historically useful as a stable voltage standard.
Could the iron(II)/iodine reaction discussed earlier (E°cell = −0.23 V) be made feasible by raising [Fe²⁺] or lowering [I⁻]?
In principle, yes — Le Chatelier's principle tells us that pushing the reactant concentrations up or product concentrations down shifts the equilibrium toward products. But the magnitude required is enormous. To compensate a −0.23 V deficit for n = 2 requires a concentration ratio shift of approximately 10^(0.23 / 0.030) ≈ 10⁷ to 10⁸. Concentrations of 10⁷ mol dm⁻³ are physically impossible — saturated solutions are typically only a few mol dm⁻³. Therefore, although the qualitative principle holds, the reaction remains practically infeasible.
The pedagogical point is general: small E°cell deficits can be overcome by reasonable concentration changes, but large deficits (more than about 0.1 V) cannot.
A feasibility prediction based on E°cell is a thermodynamic statement under three explicit assumptions. When any assumption fails, the prediction may be misleading.
1. Standard conditions assumed. E° data assume 1.00 mol dm⁻³ for all aqueous species, 100 kPa for gases, 298 K, and pure solids/liquids. Non-standard conditions require the Nernst equation:
E = E° − (RT/nF) ln Q
where Q is the reaction quotient. For dilute systems, biological pH (7.4 rather than 0), or non-aqueous solvents, the actual cell potential may differ substantially from E°cell. AQA does not require quantitative Nernst calculations but does test the qualitative direction of concentration effects.
2. Kinetics are ignored. E°cell is purely thermodynamic: it describes the equilibrium position, not the path or rate. A reaction with E°cell > 0 may have an enormous activation energy and proceed immeasurably slowly at room temperature. The canonical example is the hydrogen–oxygen reaction:
2H₂(g) + O₂(g) → 2H₂O(l); E°cell = +1.23 V; ΔG° = −475 kJ mol⁻¹
Mixed at room temperature in a sealed bulb, hydrogen and oxygen show no measurable reaction over years. A platinum catalyst, a flame, or a spark provides the activation energy needed and the reaction then proceeds explosively. The fuel cell uses platinum catalysts on its electrodes for exactly this reason — without them, the reaction is too slow to deliver useful current.
Another laboratory-scale example: many redox reactions involving iodate or persulfate ions have large positive E°cell but proceed only on heating, illustrating substantial kinetic barriers.
3. The prediction is about the equilibrium position, not the overall observable yield. E°cell tells you which direction the reaction is thermodynamically driven. It does not directly give you the equilibrium constant K — that comes from ΔG° = −RT ln K (see Going Further). A small positive E°cell means K > 1 but possibly only marginally; a large positive E°cell means K is very large and the reaction goes essentially to completion.
Exam Tip: When a question asks whether a reaction is feasible and gives non-standard concentrations, address concentration effects qualitatively via Le Chatelier. When a question gives a positive E°cell but mentions slow reaction at room temperature, address kinetic limitations. Read the stem carefully — the examiner is signalling which limitation matters.
To measure E°cell experimentally and assess feasibility from a data sheet:
Feasibility assessment from a data sheet alone follows the same logic without the experiment: identify the postulated overall reaction, decide which half-cell is being reduced (cathode) and which is being oxidised (anode), look up both E° values, compute E°cell = E°(cathode) − E°(anode), and interpret the sign.
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