24.2 Electrode and Cell Potentials and the Nernst Equation
🎯 Learning Outcomes
Candidates should be able to:
-
✓
Define the terms:
- standard electrode (reduction) potential
- standard cell potential
- ✓ Describe the standard hydrogen electrode
-
✓
Describe methods used to measure the standard electrode potentials of:
- metals or non-metals in contact with their ions in aqueous solution
- ions of the same element in different oxidation states
- ✓ Calculate a standard cell potential by combining two standard electrode potentials
-
✓
Use standard cell potentials to:
- deduce the polarity of each electrode and hence explain/deduce the direction of electron flow in the external circuit of a simple cell
- predict the feasibility of a reaction
- ✓ Deduce from E⦵ values the relative reactivity of elements, compounds and ions as oxidising agents or as reducing agents
- ✓ Construct redox equations using the relevant half-equations
- ✓ Predict qualitatively how the value of an electrode potential, E, varies with the concentrations of the aqueous ions
- ✓ Use the Nernst equation to predict quantitatively how the value of an electrode potential varies with the concentrations of the aqueous ions
- ✓ Understand and use the equation ΔG⦵ = −nE⦵cell F
1 🧭 Introduction ▶
Every battery, every rusting nail, every rechargeable phone relies on one idea: electrons moving from one substance to another release energy. Electrode potentials let chemists predict — before any reaction happens — which way electrons will flow, whether a reaction is even possible, and how much voltage a cell will produce.
🔌 Two Kinds of Electrochemical Cell
Electrochemical cells are devices for the interconversion of electrical and chemical energy. There are two main types:
| 🔋 Galvanic (Voltaic) Cell | ⚙️ Electrolytic Cell |
|---|---|
| Converts chemical energy → electrical energy | Converts electrical energy → chemical energy |
| The spontaneous chemical reaction generates electricity | Uses an external source of electricity (d.c.) |
| Reaction is spontaneous (redox reaction) | Reaction is non-spontaneous |
| Example: Daniell cell (Zn–Cu cell) | Example: electrolysis of molten NaCl |
Both galvanic and electrolytic cells involve oxidation at the anode and reduction at the cathode. The difference is whether the reaction is spontaneous or non-spontaneous.
2 🔬 Electrode Potential ▶
Dip a strip of zinc metal into a solution of zinc ions, and something interesting happens at the surface: some Zn atoms lose electrons and dissolve as Zn²⁺. In contrast, some Zn²⁺ ions gain electrons and deposit back onto the metal. An equilibrium is set up:
This metal-plus-its-ion system is called a half-cell. Because electrons build up (or are pulled away) at the metal surface, the metal develops a tiny electrical charge relative to the solution. We call this the electrode potential.
Electrode potential, E — the voltage measured for a half-cell compared with a standard hydrogen electrode, under standard conditions.
Electrode potential cannot be measured for a single half-cell alone. It is always measured relative to another electrode.
Standard Electrode Potential, E⦵
The standard electrode potential is the electrode potential of a standard electrode with an ion concentration of 1.00 mol dm⁻³ at 298 K connected to a standard hydrogen electrode (1.00 mol dm⁻³ H⁺(aq), 298 K and 100 kPa H₂(g)) using a high-resistance voltmeter and a salt bridge.
Key rule: more positive E → more easily reduced (equilibrium lies to the right).
Remember: all standard electrode potentials are written as reduction half-equations.
| Larger E⦵ | Smaller E⦵ |
|---|---|
| Better oxidising agent | Better reducing agent |
| Easily reduced | Easily oxidised |
3 🧯 Standard Hydrogen Electrode ▶
To compare half-cells fairly, chemists needed a fixed reference — like sea level for measuring a mountain’s height. That reference is the standard hydrogen electrode (SHE), arbitrarily assigned an electrode potential of exactly 0.00 V.
| Component | Standard condition |
|---|---|
| H⁺(aq) | 1.00 mol dm⁻³ |
| H₂(g) | 100 kPa, bubbled over a platinum electrode |
| Temperature | 298 K |
| Electrode surface | Platinised platinum (catalyses the equilibrium, doesn’t react itself) |
The half-equation at this electrode is:
🔩 Inert ⚡ Conducts electricity 🧫 Provides a surface for the H₂/H⁺ equilibrium 🚀 Acts as a catalyst
The SHE is the reference electrode — given 0.00 V. All E⦵ values are measured relative to it.
📏 Measuring an Electrode Potential
- Connect the unknown half-cell to the SHE.
- Use a salt bridge (to complete the circuit without the solutions mixing).
- Use a high-resistance voltmeter.
- Read the voltage — this is the half-cell’s standard electrode potential, E⦵.
4 🔗 Combining Half-Cells ▶
Join any two half-cells together, and you get a full electrochemical cell. The overall voltage it produces is the standard cell potential, E⦵cell — simply the difference between the two standard electrode potentials.
E⦵cell is always obtained by subtracting the lower reduction potential from the higher reduction potential.
Zn²⁺/Zn: E⦵ = −0.76 V Cu²⁺/Cu: E⦵ = +0.34 V
When two half-cells are joined, the half-cell with the more positive value of E⦵ accepts electrons more readily and the reaction proceeds in the forward direction. A redox reaction occurs in the direction in which the stronger oxidising agent reacts with the stronger reducing agent.
➡️ Identifying the Direction of Electron Flow
Once you know both E⦵ values, you can predict everything about how the cell behaves — no need to build it first.
| More positive E⦵ | More negative E⦵ |
|---|---|
| Easily reduced | Easily oxidised |
| Reduction | Oxidation |
| Cathode | Anode |
| Positive electrode | Negative electrode |
| Gains electrons | Loses electrons |
- The half-cell with the more positive E⦵ is the positive electrode. It attracts electrons — reduction happens here.
- The half-cell with the more negative E⦵ is the negative electrode. It releases electrons — oxidation happens here.
- Electrons flow through the external circuit from the more negative electrode to the more positive electrode.
In the Daniell cell above: zinc (−0.76 V) is the negative electrode and loses electrons; copper (+0.34 V) is the positive electrode and gains them. Electrons flow from zinc to copper through the wire.
⚡ Electrons always flow from Anode → Cathode.
🚦 Predicting Feasibility
A reaction between two half-cells will only proceed as written if the overall cell potential is positive.
| E⦵cell value | What it means |
|---|---|
| E⦵cell > 0 🟢 | Reaction is feasible (thermodynamically favourable / spontaneous) |
| E⦵cell < 0 🔴 | The reverse reaction is feasible, instead |
“Feasible” only tells you a reaction can happen based on energetics — it says nothing about the rate. A reaction can be feasible and still too slow to observe, due to high activation energy.
🧩 Constructing Redox Equations from Half-Equations
Because a redox reaction is just two half-reactions happening simultaneously, you can build the full ionic equation systematically:
- Write both reduction half-equations.
- The higher E⦵ stays unchanged (reduction, forward).
- Reverse the lower E⦵ (it now shows oxidation).
- Balance electrons.
- Add the equations.
- Cancel the electrons.
Combine Fe³⁺(aq) + e⁻ ⇌ Fe²⁺(aq), E⦵ = +0.77 V with I₂(aq) + 2e⁻ ⇌ 2I⁻(aq), E⦵ = +0.54 V
Fe³⁺/Fe²⁺ is more positive, so it stays as reduction; I₂/I⁻ is reversed (oxidation) and both are scaled ×2 for the Fe half-equation:
5 🧮 The Nernst Equation ▶
🧪 Variation with Concentration
🤔 Does the voltage of a cell always stay the same?
When we calculated E⦵cell = +1.10 V, we assumed [Zn²⁺] = [Cu²⁺] = 1.0 mol dm⁻³. But what if the concentrations change? Will the cell still produce 1.10 V? No. The cell potential changes whenever ion concentrations change — and the equation used to calculate the new potential is called the Nernst equation.
- Equilibrium shifts left
- Electrons accumulate
- Electrode becomes more negative
- Electrode potential decreases
- Equilibrium shifts right
- Electrons removed
- Electrode becomes less negative
- Electrode potential increases
🧮 The Nernst Equation
Take the zinc–copper cell again. If we reduce the concentration of zinc ions in the zinc half-cell, the equilibrium Zn²⁺(aq) + 2e⁻ ⇌ Zn(s) is displaced to the left, and the negative charge on the zinc rod becomes bigger. Qualitatively, this can be predicted from Le Chatelier’s Principle — it always happens when the concentration of the oxidised form is reduced below the standard value of 1.0 mol dm⁻³.
This change in E from non-standard conditions is calculated using the Nernst equation. For a half-cell against a standard hydrogen electrode at room temperature:
where z is the number of electrons added to the oxidised species to form the reduced species.
A ten-fold change in concentration only shifts E by 0.059 V for a single electron transfer, and 0.030 V for the transfer of two electrons. These are very small changes — which is why E⦵ values remain such a good guide to the feasibility of a reaction, even under non-standard conditions.
✅ Before Using the Nernst Equation
- Write the reduction half-equation.
- Count the electrons transferred (z).
- Ignore solids — only aqueous species go in the ratio.
- Write the oxidised species on top.
E⦵ = +0.34 V. If [Cu²⁺] is reduced from 1.00 mol dm⁻³ to 0.010 mol dm⁻³ (z = 2, and Cu(s) doesn’t appear in the log term):
🧫 Changes in pH
A typical pH meter consists of a glass electrode (which allows the passage of H⁺ ions) attached to a reference electrode by a salt bridge. The H⁺ concentration frequently varies between 1.0 mol dm⁻³ (e.g. 1.0 mol dm⁻³ HCl) and 10⁻¹⁴ mol dm⁻³ (e.g. 1.0 mol dm⁻³ NaOH). This has a profound effect on Ecell values, and forms the basis for accurate pH measurement.
Because pH = −log₁₀[H⁺], we can write the Nernst equation in the form:
6 🔥 Gibbs Free Energy and Cell Potential ▶
Voltage tells us whether electrons want to flow. The Gibbs free energy equation links this electrical energy to chemical spontaneity.
| Symbol | Meaning | Value |
|---|---|---|
| n | Electrons transferred in the overall equation | no unit |
| F | Faraday constant | 96 500 C mol⁻¹ |
| E⦵cell | Cell potential | Volts (V) |
| ΔG⦵ | Standard Gibbs free energy change | J mol⁻¹ |
For the Daniell cell, E⦵cell = +1.10 V and n = 2 (two electrons transferred). Calculate ΔG⦵.
Large and negative → strongly spontaneous, matching the healthy positive E⦵cell.
Don’t forget n is the number of electrons in the balanced overall equation, not in a single half-equation — always check you’ve scaled correctly before substituting into ΔG⦵ = −nE⦵cell F.
More positive E⦵cell ⇒ more negative ΔG⦵ ⇒ more thermodynamically favourable reaction. Concentration and pH shift E via the Nernst equation — and, through ΔG⦵ = −nE⦵cell F, they quietly shift the free-energy change too.