In simple terms
A friendly intro before the formal notes — no formulas yet.
Electrochemical Tug-of-War
Electrode potentials measure how strongly different species pull on electrons. By comparing these values, we can predict which way electrons will flow, determining the direction of a spontaneous chemical reaction.
Imagine two people of different strengths pulling on a rope. The stronger person represents the half-cell with the more positive electrode potential, and they will 'win' the rope (the electrons). The difference in their strengths is like the cell potential (E°cell), which drives the flow of electrons from the weaker person (anode) to the stronger one (cathode).
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E° measures tendency to reduce — higher E° = stronger oxidising agent.
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E°cell = E°(cathode) − E°(anode) for a spontaneous cell.
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ΔG° = −nFE°cell — link thermodynamics to electrochemistry.
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Nernst: E = E° − (RT/nF) ln Q — non-standard concentrations.
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Standard Electrode Potential (E°)
It's impossible to measure the absolute potential of a single half-cell. Instead, we measure its potential relative to a standard reference. This reference is the Standard Hydrogen Electrode (SHE), which consists of hydrogen gas at 1 atm bubbling over a platinum electrode in a 1.00 mol dm⁻³ solution of H⁺(aq) ions at 298 K. By definition, its potential is set to 0.00 V. The standard electrode potential, E°, of a half-cell is the electromotive force (e.m.f.) of a cell where the left-hand electrode is the SHE and the right-hand electrode is the half-cell in question, measured under standard conditions.
Standard Conditions: 298 K (25 °C), 1.00 mol dm⁻³ concentration of all aqueous ions, and 1 atm pressure for all gases.
Reference: The Standard Hydrogen Electrode (SHE): 2H⁺(aq) + 2e⁻ ⇌ H₂(g), E° = 0.00 V.
Interpretation: A more positive E° means the species on the left of the half-equation is a strong oxidising agent. A more negative E° means the species on the right is a strong reducing agent.
Calculating Standard Cell Potential (E°cell)
An electrochemical cell is created by connecting two different half-cells. The overall potential difference, or e.m.f., of this cell is the standard cell potential, E°cell. To get a spontaneous reaction (one that generates electricity), we must combine the half-cells correctly. The half-cell with the more positive E° value will undergo reduction (it's the cathode), and the half-cell with the more negative E° value will undergo oxidation (it's the anode). The E°cell can be calculated using the reduction potentials directly from the data booklet.
E°{cell} = E°{cathode} - E°_{anode}
A simple way to remember is E°cell = E°(more positive) - E°(more negative). This always gives a positive E°cell for a spontaneous reaction. The half-reaction with the more positive E° is the one that proceeds as a reduction (as written), and the one with the more negative E° is forced to reverse and proceed as an oxidation.
Feasibility, Spontaneity, and Gibbs Free Energy
The sign of E°cell is a direct indicator of thermodynamic spontaneity. A positive E°cell corresponds to a negative Gibbs free energy change (ΔG°), which is the condition for a spontaneous process. The magnitude of E°cell is proportional to the magnitude of ΔG°. This provides a powerful link between electrochemistry and thermodynamics.
ΔG° = -nFE°_{cell}
ΔG°: Standard Gibbs free energy change (J mol⁻¹).
n: Number of moles of electrons transferred in the balanced redox equation.
F: The Faraday constant, 96500 C mol⁻¹ (the charge of one mole of electrons).
Spontaneity: If E°cell > 0, then ΔG° < 0 (spontaneous). If E°cell < 0, then ΔG° > 0 (non-spontaneous).
The Nernst Equation: Non-Standard Conditions
Standard potentials are useful but are strictly valid only at standard conditions. In reality, concentrations change as a reaction proceeds. The Nernst equation allows us to calculate the potential of a half-cell or a full cell under any conditions of concentration and temperature. It shows how the potential deviates from the standard potential based on the ratio of products to reactants.
E: Potential under non-standard conditions.
R: Gas constant (8.314 J K⁻¹ mol⁻¹).
T: Temperature in Kelvin.
Q: Reaction quotient, [products]/[reactants]. For a half-reaction aA + ne⁻ → bB, Q = [B]ᵇ / [A]ᵃ.
Qualitative use: If the concentration of reactants increases, Q decreases, ln(Q) becomes more negative, and E becomes more positive (reaction is more favourable). If the concentration of products increases, Q increases, and E becomes less positive.
For A-Level, you are more likely to be asked to predict the effect of changing concentration on E than to perform a full Nernst calculation. For example, increasing [Cu²⁺] in the Cu²⁺/Cu half-cell makes its potential E more positive than its standard E° value.
Worked examples
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Calculate the standard cell potential for a cell constructed from zinc and copper half-cells. Predict the spontaneous direction of the reaction and write the overall cell equation.
Given: Zn²⁺(aq) + 2e⁻ ⇌ Zn(s) E° = -0.76 V Cu²⁺(aq) + 2e⁻ ⇌ Cu(s) E° = +0.34 V
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Identify cathode and anode: The Cu²⁺/Cu half-cell has a more positive E° (+0.34 V) than the Zn²⁺/Zn half-cell (-0.76 V). Therefore, the copper half-cell is the cathode (reduction) and the zinc half-cell is the anode (oxidation).
Consider the reaction between acidified permanganate(VII) ions and iron(II) ions. Calculate the standard cell potential and the standard Gibbs free energy change at 298 K.
Given: MnO₄⁻(aq) + 8H⁺(aq) + 5e⁻ ⇌ Mn²⁺(aq) + 4H₂O(l) E° = +1.51 V Fe³⁺(aq) + e⁻ ⇌ Fe²⁺(aq) E° = +0.77 V
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Identify cathode and anode: The MnO₄⁻/Mn²⁺ half-cell has the more positive E° (+1.51 V), so it is the cathode. The Fe³⁺/Fe²⁺ half-cell is the anode, and its reaction will be reversed (Fe²⁺ → Fe³⁺ + e⁻).
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What is the standard electrode potential, E°?
The potential difference of a half-cell measured against the standard hydrogen electrode (SHE) under standard conditions (298 K, 1 atm pressure for gases, 1.00 mol dm⁻³ concentration for aqueous ions).
Key takeaways
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Standard Conditions: 298 K (25 °C), 1.00 mol dm⁻³ concentration of all aqueous ions, and 1 atm pressure for all gases.
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Reference: The Standard Hydrogen Electrode (SHE): 2H⁺(aq) + 2e⁻ ⇌ H₂(g), E° = 0.00 V.
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Interpretation: A more positive E° means the species on the left of the half-equation is a strong oxidising agent. A more negative E° means the species on the right is a strong reducing agent.
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