Electrochemical Cells and Cell Diagrams

Lesson 2 established the standard hydrogen electrode (SHE) as the universal zero of potential and tabulated standard electrode potentials E° as intensive reduction half-potentials. This lesson turns from the tabulated thermodynamic quantity to the physical object that produces it: the galvanic (voltaic) cell, in which two half-cells coupled through an external wire and a salt bridge deliver spontaneous redox as electrical work. The cell diagram (or cell notation) is the IUPAC shorthand that captures everything an examiner needs to reconstruct the cell — the phases, the species in each compartment, their concentrations, the electrode polarities, and the orientation of the half-reactions relative to one another. We develop the convention rigorously, work through four canonical examples (Zn-Cu, Pb-Cu, hydrogen-oxygen fuel cell, Fe³⁺/Fe²⁺ vs. Cu²⁺/Cu), examine the salt bridge as more than a piece of soaked paper, distinguish the direction of conventional current from the direction of electron flow, and contrast galvanic cells with the electrolytic cells that will appear in lesson 7. Lesson 4 will then use the EMF computed here as the diagnostic for feasibility (ΔG° = −nFE°cell).

Spec mapping (AQA 7405): This lesson maps to §3.1.11 (Electrode potentials and electrochemical cells) of the AQA A-Level Chemistry specification, specifically the requirements that students can construct cell diagrams using the IUPAC convention, identify the salt bridge as the means of completing the internal circuit, and predict the direction of conventional current and electron flow from electrode potentials. Foundations were laid in lesson 2 of this course (definition of E° and the electrochemical series); lesson 4 uses cell EMF to predict feasibility (ΔG° = −nFE°cell); lesson 5 applies the same cell formalism to commercial primary, secondary, and fuel cells; lesson 7 contrasts spontaneous galvanic operation with non-spontaneous electrolysis. Refer to the AQA specification document for the exact wording of §3.1.11 and the associated assessed practical (Required Practical 8 — measurement of EMF of an electrochemical cell).

Assessment objectives: Recall of the IUPAC cell-diagram convention, the role of the SHE, and the function of the salt bridge are AO1 items. Writing the correct cell diagram from a pair of given half-cells, calculating E°cell, and identifying the polarity of each electrode are AO2 calculation skills assessed on every Paper 2. AO3 (analysis and evaluation) is tested by questions that ask students to predict the direction of electron flow, rationalise the effect of changing concentrations on the measured EMF using Le Chatelier's principle (the qualitative Nernst argument), and evaluate why certain cells require a platinum electrode while others do not.

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Galvanic (Voltaic) Cells: The Object and the Principle

A galvanic cell (sometimes called a voltaic cell, the two terms being interchangeable in A-Level usage) is a device that harnesses a spontaneous redox reaction to do electrical work on an external circuit. The defining characteristics are three:

1. The overall cell reaction is thermodynamically spontaneous: ΔG° < 0.
2. The standard cell EMF is positive: E°cell > 0.
3. The two half-reactions are physically separated into two compartments (the half-cells), so that the electrons released by oxidation are forced to travel through an external wire — and therefore to do measurable electrical work — before reaching the species being reduced.

The third point is the crucial one. If you simply drop a zinc rod into copper(II) sulfate solution, the reaction Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s) proceeds rapidly; copper plates onto the zinc and the blue colour fades. Electrons pass directly from Zn atoms to Cu²⁺ ions at the metal surface, and the released free energy is dissipated entirely as heat. No useful electrical work is extracted. The galvanic cell engineers a detour: by placing the zinc in one beaker (in ZnSO₄(aq)) and the copper in another (in CuSO₄(aq)), connected only by a salt bridge and an external wire, electrons are forced to travel through the wire to reach the Cu²⁺ ions. That wire can drive a motor, light an LED, or — in the simplest case — deflect the needle of a voltmeter. The chemistry is unchanged; the geometry converts thermal dissipation into work.

The link to lesson 2 is direct: E°cell, computed from tabulated standard electrode potentials, predicts the maximum work that this geometry can deliver per coulomb of charge transferred under standard conditions. Lesson 4 will quantify this through ΔG° = −nFE°cell.

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The IUPAC Cell-Diagram Convention

The cell-diagram (or cell-notation) convention is the formal shorthand for describing a galvanic cell on paper. The IUPAC rules — adopted in AQA marking — are:

1. Write the anode (oxidation, negative electrode under standard conditions) on the left, the cathode (reduction, positive electrode) on the right.
2. Phase boundaries are shown by a single vertical line ( | ) — for example, a boundary between solid zinc and aqueous Zn²⁺ ions.
3. The salt bridge is shown by a double vertical line ( || ).
4. Within each half-cell, species are listed in the order reduced form | oxidised form moving toward the salt bridge (because we are reading "oxidation produces these ions which then move toward the bridge"); on the right of the salt bridge, the order is oxidised form | reduced form moving away.
5. Concentrations are written in brackets immediately after each aqueous species, in mol dm⁻³, where they differ from the standard 1.00 mol dm⁻³; the SHE is conventionally written with [H⁺] = 1.00 mol dm⁻³ and p(H₂) = 100 kPa understood.
6. Gas-phase species over an inert electrode are separated from the electrolyte by a single vertical line, with the gas pressure noted if non-standard.
7. Inert electrodes (typically Pt) are shown explicitly at the relevant terminus; reactive metal electrodes are themselves the terminus.
8. The standard cell EMF, written under the diagram, is computed as E°cell = E°(right) − E°(left) = E°(cathode) − E°(anode).

A simple mnemonic: read the diagram left to right in the same order as the cell reaction proceeds — electrons leave from the left (oxidation), travel through the wire (above the diagram, by convention), and arrive on the right (reduction). Cations migrate rightward through the salt bridge to follow the electrons; anions migrate leftward to balance the charge being deposited at the left electrode.

Key Point: When the right-hand E° is more positive than the left, E°cell is positive, the reaction as written (left → right) is spontaneous, and the diagram is written in the "correct" direction. If you accidentally write a diagram with the more-positive electrode on the left, you will compute a negative E°cell — which is the diagnostic that the diagram is back-to-front, not that the cell is non-spontaneous.

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Worked Example 1: The Daniell Cell (Zn-Cu)

The classical galvanic cell, devised by John Daniell in 1836, couples a zinc electrode in ZnSO₄(aq) with a copper electrode in CuSO₄(aq). Both solutions are at 1.00 mol dm⁻³ at 298 K — standard conditions.

Half-reactions (as reductions, AQA convention):

• Zn²⁺(aq) + 2e⁻ ⇌ Zn(s); E° = −0.76 V
• Cu²⁺(aq) + 2e⁻ ⇌ Cu(s); E° = +0.34 V

The Cu²⁺/Cu couple has the more positive E°; it is the cathode (reduction). The Zn²⁺/Zn couple has the less positive E°; it is the anode (oxidation). The cell diagram is:

Zn(s) | Zn²⁺(aq, 1.00 mol dm⁻³) || Cu²⁺(aq, 1.00 mol dm⁻³) | Cu(s)

E°cell = E°(cathode) − E°(anode) = (+0.34) − (−0.76) = +1.10 V

The overall cell reaction is obtained by reversing the left-hand half-reaction (because oxidation occurs there) and adding it to the right-hand half-reaction:

• Left (oxidation, reversed): Zn(s) → Zn²⁺(aq) + 2e⁻
• Right (reduction): Cu²⁺(aq) + 2e⁻ → Cu(s)
• Overall: Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s); E°cell = +1.10 V

The 2 electrons released per zinc atom equal the 2 electrons consumed per Cu²⁺ ion, so no scaling is required. (When the electron counts do not match, scale the half-reactions to match — but never scale E°, which is intensive.)

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Worked Example 2: A Pb-Cu Cell

Take a lead electrode in 1.00 mol dm⁻³ Pb(NO₃)₂(aq) (E°(Pb²⁺/Pb) = −0.13 V) coupled to a copper electrode in 1.00 mol dm⁻³ CuSO₄(aq) (E°(Cu²⁺/Cu) = +0.34 V).

Cu²⁺/Cu is more positive, so it is the cathode; Pb²⁺/Pb is the anode.

Pb(s) | Pb²⁺(aq, 1.00 mol dm⁻³) || Cu²⁺(aq, 1.00 mol dm⁻³) | Cu(s)

E°cell = (+0.34) − (−0.13) = +0.47 V

Overall: Pb(s) + Cu²⁺(aq) → Pb²⁺(aq) + Cu(s). Note that E°cell is smaller than for the Daniell cell — lead is a weaker reducing agent than zinc — but the reaction direction is the same: Cu²⁺ oxidises the less-noble metal.

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Worked Example 3: The Hydrogen-Oxygen Fuel Cell

The hydrogen-oxygen fuel cell (developed for, among other things, the Apollo missions and now central to the hydrogen-economy debate) is treated in detail in lesson 5; here we use it only to illustrate the cell-diagram convention for gas-phase electrodes. Under acidic conditions, the half-reactions are:

• O₂(g) + 4H⁺(aq) + 4e⁻ ⇌ 2H₂O(l); E° = +1.23 V
• 2H⁺(aq) + 2e⁻ ⇌ H₂(g); E° = 0.00 V (the SHE itself)

The oxygen couple is far more positive, so it is the cathode; the hydrogen couple is the anode. Both are gas-over-platinum half-cells. The cell diagram is:

Pt(s) | H₂(g, 100 kPa) | H⁺(aq, 1.00 mol dm⁻³) || H⁺(aq, 1.00 mol dm⁻³), O₂(g, 100 kPa) | Pt(s)

(In the acidic-electrolyte variant, both half-cells share H⁺; in practice the two compartments are not chemically separate, but the diagram is written as if they were for notational consistency.) The comma between H⁺(aq) and O₂(g) on the right indicates that they are in the same phase (the electrolyte adjacent to the platinum electrode) rather than at a phase boundary.

E°cell = (+1.23) − (0.00) = +1.23 V

Overall: 2H₂(g) + O₂(g) → 2H₂O(l); ΔG° = −nFE°cell = −4 × 96 485 × 1.23 ≈ −475 kJ mol⁻¹ (per mole of O₂ consumed). The reaction is highly spontaneous and is the basis of the fuel cell's operation.

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Worked Example 4: Fe³⁺/Fe²⁺ vs. Cu²⁺/Cu — A Two-Inert / One-Reactive Cell

A subtler cell pairs an inert-electrode redox couple (Fe³⁺/Fe²⁺, requiring Pt because both species are aqueous) with a reactive-metal couple (Cu²⁺/Cu, where copper itself serves as the electrode).

• Fe³⁺(aq) + e⁻ ⇌ Fe²⁺(aq); E° = +0.77 V
• Cu²⁺(aq) + 2e⁻ ⇌ Cu(s); E° = +0.34 V

Fe³⁺/Fe²⁺ is more positive; it is the cathode. Cu²⁺/Cu is less positive; it is the anode. The cell diagram is:

Cu(s) | Cu²⁺(aq, 1.00 mol dm⁻³) || Fe³⁺(aq, 1.00 mol dm⁻³), Fe²⁺(aq, 1.00 mol dm⁻³) | Pt(s)

E°cell = (+0.77) − (+0.34) = +0.43 V

To find the overall reaction, scale the half-reactions so the electron counts match. Cu releases 2 e⁻ per atom; Fe³⁺ accepts 1 e⁻ per ion. Multiply the iron half-reaction by 2:

• Anode (oxidation): Cu(s) → Cu²⁺(aq) + 2e⁻
• Cathode (reduction): 2Fe³⁺(aq) + 2e⁻ → 2Fe²⁺(aq)
• Overall: Cu(s) + 2Fe³⁺(aq) → Cu²⁺(aq) + 2Fe²⁺(aq); E°cell = +0.43 V

Note again that E° itself is not multiplied. Multiplying the half-reaction by 2 doubles the number of electrons transferred per "unit reaction" (which doubles ΔG° per unit reaction, because ΔG° = −nFE°cell scales with n), but E° is the work per unit charge, which is intensive and unchanged by the scaling.

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The Salt Bridge: Function, Composition, and Selection

The salt bridge is the most under-explained component of the galvanic cell at A-Level, and AO3 questions routinely probe it. Its function is fourfold:

1. Complete the electrical circuit internally. Without the salt bridge, charge cannot flow inside the cell, and electrons accumulating at the cathode and depleting from the anode would build up an electric field that immediately stops the reaction. The salt bridge provides an ionically conductive pathway.
2. Maintain electrical neutrality in each half-cell. At the anode, positive metal ions (e.g. Zn²⁺) are being released into solution, raising the positive charge density of that half-cell. At the cathode, positive ions (Cu²⁺) are being consumed and deposited as neutral metal, lowering the positive charge density. The salt bridge must remove positive charge from the anode compartment (anions migrate into it) and supply positive charge to the cathode compartment (cations migrate into it) — or, equivalently, allow cations to migrate toward the cathode and anions to migrate toward the anode.
3. Prevent bulk mixing of the two electrolytes. A salt bridge is far more viscous than free electrolyte (typically a gel or an agar-set solution), so the two electrolytes are not exchanged on the timescale of cell operation. This matters because if Cu²⁺ ions reached the zinc electrode, direct (non-galvanic) reaction would occur and the EMF would collapse.
4. Avoid introducing any species that reacts with either electrolyte. This is the constraint that determines the choice of salt.

The two standard A-Level choices are:

• Saturated KNO₃ — the default, and the answer expected on AQA mark schemes unless the question specifies otherwise. KNO₃ is chosen because K⁺ does not react with any common cathode electrolyte (it sits below all the standard cathodes on the electrochemical series), and NO₃⁻ does not react with any common anode metal under the dilute, room-temperature conditions of a teaching cell. Critically, KNO₃ is also stable in the salt bridge itself (no slow disproportionation).
• Saturated KCl — used in some industrial reference electrodes (the Ag/AgCl reference, the saturated calomel electrode) but not suitable for a cell where the cathode contains Ag⁺(aq), because Cl⁻ bleeding from the bridge would precipitate AgCl(s) and disrupt the cathode equilibrium.

A practical filter-paper-and-KNO₃-soaked-strip salt bridge is acceptable for teaching but has higher internal resistance than a properly constructed gel bridge; this is why measured EMFs from school apparatus typically read a few percent lower than the tabulated E°cell.

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Direction of Conventional Current and Electron Flow

This is a classic AO3 trap, because the two flow directions are opposite by definition.

• Conventional current is defined as the direction of flow of positive charge — a historical accident that predates the discovery of the electron. In the external wire of a galvanic cell, conventional current flows from the positive electrode (cathode) to the negative electrode (anode). Imagine an arrow on the diagram pointing from the cathode terminal of the cell, through the wire and any external device, and back to the anode terminal.
• Electron flow is opposite to conventional current. In the external wire, electrons flow from the anode (negative) to the cathode (positive) — they are released at the anode (oxidation) and consumed at the cathode (reduction).

Inside the cell, in the salt bridge, the flow direction is described in terms of ion migration:

• Cations (positive ions: K⁺, H⁺, Cu²⁺) migrate from the anode compartment toward the cathode compartment — that is, in the same direction as conventional current.
• Anions (negative ions: NO₃⁻, SO₄²⁻, Cl⁻) migrate from the cathode compartment toward the anode compartment — opposite to conventional current.

Exam Tip: "Direction of electron flow" without qualification refers to the external circuit. Marks are awarded for the unambiguous "from anode (Zn) to cathode (Cu) through the external wire." The phrase "in the salt bridge" requires you to switch to discussing ion flow, not electron flow — electrons do not travel through electrolyte solutions in a working galvanic cell.

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Practical Construction: Electrode Choice and the Inert-Electrode Rule

For a metal/metal-ion couple (Zn²⁺/Zn, Cu²⁺/Cu, Pb²⁺/Pb, Fe²⁺/Fe), the metal itself serves as the electrode. The metal is a solid conductor, it is in direct contact with its own ions in solution, and the half-reaction occurs at the metal-solution interface. The standard concentration is 1.00 mol dm⁻³ of the metal ion.

For a couple in which neither species is a metal in its standard state, an inert electrode is required — almost always platinum. Examples:

• Fe³⁺(aq)/Fe²⁺(aq) — both species are aqueous; Pt electrode required.
• MnO₄⁻/Mn²⁺ in acidic solution — both species aqueous; Pt required (acidic medium is supplied by additional H⁺(aq), typically dilute sulfuric acid).
• Cl₂(g)/Cl⁻(aq) — gas over Pt with chloride electrolyte.
• 2H⁺(aq)/H₂(g) — the SHE itself; Pt electrode coated with platinum black (high surface area) and bathed by H₂ gas at 100 kPa, with [H⁺] = 1.00 mol dm⁻³.

Platinum is chosen because it is chemically inert under cell conditions (does not oxidise, does not react with halide or sulfate or nitrate), it is a good electronic conductor, and it catalyses many electrode reactions (notably the hydrogen electrode and oxygen electrode) so that the measured potential approaches the thermodynamic E° quickly.

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Cell-EMF Calculation, Revisited

The single equation that students must master is:

E°cell = E°(cathode) − E°(anode) = E°(right electrode in cell diagram) − E°(left electrode in cell diagram)

Both potentials are looked up as reduction potentials (the AQA convention). The cathode is whichever has the more positive E°. There is no need — and no justification — for multiplying E° by stoichiometric coefficients. If the electron counts in the two half-reactions do not match, scale the half-reactions to balance them, then add them; E° remains untouched.

Common Misconception: "I multiplied the iron half-reaction by 2, so I should multiply E°(Fe³⁺/Fe²⁺) by 2." No. E° is an intensive property (work per unit charge); it does not scale with stoichiometry. The quantity that does scale — ΔG° = −nFE°cell — scales through the factor n (the number of electrons transferred in the balanced overall reaction), not through E°. This distinction is the most common error at the C/B boundary.

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Concentration Effects on EMF (Qualitative)

Under non-standard concentrations, the measured cell EMF (now denoted E_cell, no degree symbol) differs from E°cell. The quantitative description is the Nernst equation — strictly beyond A-Level and treated in the Going Further section below — but the qualitative argument from Le Chatelier's principle is fully within scope and routinely examined.

Consider the Daniell cell with the cathode half-reaction Cu²⁺(aq) + 2e⁻ ⇌ Cu(s).

• Increasing [Cu²⁺] pushes this equilibrium to the right (more reduction). The cathode potential becomes more positive, so E_cell > E°cell — the cell delivers a higher voltage.
• Decreasing [Cu²⁺] pushes the equilibrium to the left. The cathode potential becomes less positive, E_cell < E°cell.

Analogously, at the anode (where the half-reaction is written Zn²⁺(aq) + 2e⁻ ⇌ Zn(s), still as a reduction in the tabulated convention, but operating as oxidation in the working cell):

• Decreasing [Zn²⁺] pulls the equilibrium to the right as a reduction — that is, it makes the anode more "reluctant" to be oxidised, so the anode potential becomes more positive (less negative), which reduces the E°cell difference. E_cell falls.
• Increasing [Zn²⁺] pushes the equilibrium to the left as a reduction — the anode potential becomes more negative, the difference E°(cathode) − E°(anode) widens, and E_cell rises.

The two rules of thumb that AQA mark schemes accept:

1. Increasing the concentration of the species on the same side as the electrons in either half-equation (i.e. the oxidised form: Cu²⁺ at the cathode, Zn²⁺ at the anode if read as a reduction) increases E_cell.
2. Decreasing the concentration of the species on the opposite side from the electrons (the reduced form) also increases E_cell.

The quantitative version of this argument is the Nernst equation, E = E° − (RT/nF) ln Q, which collapses to E = E° at standard conditions (Q = 1). It is included in the Going Further section.

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Galvanic vs. Electrolytic Cells

This is the contrast that previews lesson 7 (electrolysis).

Feature	Galvanic (voltaic) cell	Electrolytic cell
Spontaneity	Spontaneous overall reaction	Non-spontaneous overall reaction
ΔG°	< 0 (negative)	> 0 (positive)
E°cell	> 0 (positive)	< 0 (negative)
Energy direction	Chemical → electrical	Electrical → chemical
Power source	None — the cell is the source	External DC source required
Cathode polarity	+ (positive terminal)	− (negative terminal — driven by external source)
Anode polarity	− (negative terminal)	+ (positive terminal — driven by external source)
Typical application	Batteries, fuel cells	Aluminium extraction (Hall-Héroult), electroplating, chlor-alkali
Example	Daniell cell, Zn-Cu	Electrolysis of molten Al₂O₃; copper refining

The polarity reversal is the source of much A-Level confusion. In both cell types:

• Reduction occurs at the cathode.
• Oxidation occurs at the anode.