Electrode Potentials and Electrochemical Cells

Electrode Potentials and Electrochemical Cells

Standard Electrode Potential (E°)

The standard electrode potential of a half-cell is the EMF (electromotive force) measured when that half-cell is connected to a standard hydrogen electrode (SHE) under standard conditions.

Standard conditions:

• Temperature: 298 K (25 °C)
• Pressure: 100 kPa (1 bar)
• Concentration: 1.00 mol dm⁻³ for all aqueous species

The Standard Hydrogen Electrode

The SHE is assigned a potential of exactly 0.00 V. It consists of:

• Platinum electrode coated in platinum black (to increase surface area)
• Immersed in 1.00 mol dm⁻³ H⁺(aq)
• H₂(g) bubbled over the electrode at 100 kPa

Half-equation: 2H⁺(aq) + 2e⁻ ⇌ H₂(g) E° = 0.00 V

Measuring Standard Electrode Potentials

1. Set up the half-cell of interest (e.g. Zn²⁺/Zn — a zinc rod in 1.00 mol dm⁻³ ZnSO₄)

2. Connect it to the SHE via a salt bridge (e.g. filter paper soaked in KNO₃, or a glass tube filled with KNO₃ solution) — this completes the circuit by allowing ion flow while preventing mixing

3. Connect the electrodes to a high-resistance voltmeter (draws negligible current, so the reading reflects the true EMF)

4. The voltmeter reading is the standard electrode potential

Convention: Half-equations are always written as reductions (electrons on the left):

Zn²⁺(aq) + 2e⁻ ⇌ Zn(s) E° = −0.76 V

Cu²⁺(aq) + 2e⁻ ⇌ Cu(s) E° = +0.34 V

A more positive E° means the species is a stronger oxidising agent (more tendency to be reduced).

A more negative E° means the species is a stronger reducing agent (more tendency to be oxidised).

Electrochemical Cells

When two half-cells are connected, the half-cell with the more negative E° is oxidised (loses electrons), and the half-cell with the more positive E° is reduced (gains electrons). Electrons flow from the more negative electrode to the more positive electrode through the external circuit.

Cell EMF:

E°(cell) = E°(right/cathode) − E°(left/anode)

Or equivalently:

E°(cell) = E°(reduction half-cell) − E°(oxidation half-cell)

A positive E°(cell) means the reaction is thermodynamically feasible under standard conditions.

Worked Example: Daniell Cell

Zn²⁺/Zn: E° = −0.76 V

Cu²⁺/Cu: E° = +0.34 V

Zinc is more negative, so it is oxidised: Zn(s) → Zn²⁺(aq) + 2e⁻

Copper is more positive, so it is reduced: Cu²⁺(aq) + 2e⁻ → Cu(s)

Overall: Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

E°(cell) = +0.34 − (−0.76) = +1.10 V

Predicting Feasibility

A reaction is thermodynamically feasible if E°(cell) > 0.

However, a positive E°(cell) does not guarantee the reaction will occur:

• The reaction may be kinetically slow (high activation energy)
• Conditions may not be standard (concentrations, temperature, pressure differ)
• E° values are thermodynamic — they tell you about equilibrium position, not rate

Concentration Effects (The Nernst Equation)

The actual electrode potential changes with concentration. Qualitatively:

• Increasing the concentration of the oxidised form (the species being reduced) makes the potential more positive (favours reduction)
• Increasing the concentration of the reduced form makes the potential more negative

The quantitative relationship is given by the Nernst equation (not always required at A-Level):

E = E° + (RT / nF) × ln([oxidised] / [reduced])

At 298 K: E = E° + (0.0592 / n) × log₁₀([oxidised] / [reduced])

Non-Standard Half-Cells

Not all half-cells involve a metal dipping into a solution of its ions:

Gas electrode: A platinum electrode in contact with a gas and a solution of its ions (e.g. the SHE, or Cl₂/Cl⁻ half-cell)

Ion-ion electrode: Both the oxidised and reduced forms are in solution (e.g. Fe³⁺/Fe²⁺) — a platinum electrode provides a surface for electron transfer

Metal-insoluble salt electrode: E.g. Ag/AgCl electrode — the metal is coated with its insoluble salt, in contact with a solution of the anion

Linking E° to ΔG and K

E°(cell) and Gibbs free energy:

ΔG° = −nFE°(cell)

Where n = moles of electrons transferred, F = Faraday constant (96,485 C mol⁻¹).

A positive E°(cell) gives a negative ΔG° → feasible.

E°(cell) and equilibrium constant:

E°(cell) = (RT / nF) × ln K

A large positive E°(cell) means a large K → products strongly favoured at equilibrium.

Storage Cells and Fuel Cells

Rechargeable cells (e.g. lithium-ion batteries) use reversible electrode reactions. During discharge, the spontaneous cell reaction occurs; during charging, an external voltage forces the reverse reaction.

Hydrogen fuel cells combine H₂ and O₂ to produce electricity and water:

• Anode: H₂(g) → 2H⁺(aq) + 2e⁻
• Cathode: O₂(g) + 4H⁺(aq) + 4e⁻ → 2H₂O(l)
• Overall: 2H₂(g) + O₂(g) → 2H₂O(l)
• Advantages: no CO₂ emissions, high efficiency, water is the only product
• Disadvantages: hydrogen storage (flammable, low density), platinum catalyst cost, infrastructure needed

Exam Tips

• Always write half-equations as reductions when using E° values
• The more negative half-cell is the anode (oxidation), the more positive is the cathode (reduction)
• State both thermodynamic feasibility AND kinetic limitations when discussing whether a reaction will actually occur
• When the question gives non-standard concentrations, discuss the qualitative effect on E using Le Chatelier reasoning