A modular guide to thermodynamics, spontaneity, and energy in electrochemical systems

1. Introduction

In the preceding lecture, we explored cell potentials (EMF) and how to calculate them from standard electrode potentials.
Now, we link electrochemical measurements to thermodynamics, providing a quantitative framework for predicting spontaneity, energy transfer, and equilibrium.

Every redox reaction in an electrochemical cell involves a transfer of electrons that does work on the surroundings.
The Gibbs free energy change (ΔG) is the thermodynamic quantity that tells us whether a reaction is spontaneous (ΔG < 0), at equilibrium (ΔG = 0), or non-spontaneous (ΔG > 0).

By relating ΔG to cell potential, we connect electrical measurements to chemical energy, which is essential for understanding:

• Battery efficiency and energy density
• Corrosion prevention strategies
• Industrial electrolysis and electrosynthesis
• Biological energy transduction

Reference: LibreTexts – Gibbs Free Energy and Electrochemistry

2. Gibbs Free Energy (ΔG) and Electrochemistry

Gibbs free energy quantifies the maximum reversible work a system can perform at constant temperature and pressure:

Where:

• ΔH = enthalpy change (J/mol)
• ΔS = entropy change (J/mol·K)
• T = temperature (K)

For electrochemical cells, the work done is primarily electrical work (Welec):

• n = number of electrons transferred
• F = Faraday constant (96,485 C/mol)
• E₍cell₎ = cell potential (V)

Thus, ΔG and EMF are directly related:

• If E₍cell₎ > 0, then ΔG < 0 → spontaneous reaction
• If E₍cell₎ < 0, then ΔG > 0 → non-spontaneous reaction

This equation allows chemists and engineers to predict reaction feasibility quantitatively.

3. Standard Gibbs Free Energy Change (ΔG°)

Under standard conditions (1 atm, 1 M concentration, 25 °C), the standard Gibbs free energy change is:

Where E°₍cell₎ is the standard cell potential derived from tabulated standard reduction potentials.

Example: Daniell Cell

Reaction:

From Lecture 10:

Interpretation:
The reaction is spontaneous, releasing a substantial amount of free energy per mole of zinc oxidised.

4. Connecting ΔG° to the Equilibrium Constant (K)

The standard free energy change also relates to the equilibrium constant (K):

Combining with ΔG° = −n F E°₍cell₎, we get:

• R = 8.314 J mol⁻¹ K⁻¹
• T = temperature (K)

This shows that a large positive E°cell → large K → reaction is strongly favoured at equilibrium.

Example:

Daniell cell:

Extremely large K confirms near-complete reaction under standard conditions.

Reference: Chemguide – Relating EMF to ΔG and K

5. Temperature Dependence of EMF

The temperature effect on EMF is derived from:

Implications:

• If ΔS > 0 → E₍cell₎ decreases with increasing temperature (T)
• If ΔS < 0 → E₍cell₎ increases with increasing temperature (T)

This is critical in high-temperature fuel cells, industrial electrolysis, and battery performance under varying climates.

6. Non-Standard Conditions: Nernst Equation and ΔG

Under non-standard conditions:

Where is the reaction quotient:

The corresponding cell potential:

This shows that ΔG and Ecell are both concentration-dependent, essential for sensors, batteries under load, and corrosion processes.

Example: Hydrogen/Oxygen Fuel Cell

If [H⁺] or [O₂] changes, E₍cell₎ shifts according to the Nernst equation, affecting the work the cell can perform.

Reference: RSC – Nernst Equation and Real Cell Potentials

7. Entropy, Enthalpy, and Spontaneity

While ΔG predicts spontaneity, ΔH (enthalpy) and ΔS (entropy) provide mechanistic insight:

• Exothermic reactions (ΔH < 0) tend to be spontaneous
• Endothermic reactions (ΔH > 0) may still be spontaneous if TΔS > ΔH
• Electrochemical cells often increase order locally (ions reduce to metals), but the overall entropy of the surroundings increases due to the heat released.

Example: Zinc–Copper Cell

• Oxidation of zinc releases heat → exothermic
• Reduction of copper ions decreases local disorder → ΔS negative for the system
• Overall ΔG negative → spontaneous

8. Worked Example: Iron–Copper Cell

Reaction:

Half-reactions:

9. Applications of ΔG–EMF Relationship

(a) Battery Energy Density

The maximum electrical work is limited by ΔG:

High Ecell and large n → high energy density.
This principle governs Li-ion, lead–acid, and fuel cell design.

(b) Electrolysis

Non-spontaneous reactions (Ecell < 0) require external voltage.
For electrolysis of water:

• E°cell = -1.23 V → ΔG° positive → energy input required
• Practical voltage >1.8 V due to overvoltage and kinetics

(c) Corrosion Prediction

ΔG < 0 → metal spontaneously corrodes.
Example: Iron in moist air.
Electrochemical measurements of EMF predict corrosion tendency, guiding coating, sacrificial anode, and alloy design.

Reference: NACE – Corrosion Basics

10. Summary

• Gibbs free energy (ΔG) is the key thermodynamic predictor of spontaneity in electrochemistry.
• ΔG is directly proportional to EMF: ΔG = −n F E₍cell₎.
• Standard and non-standard conditions are connected via ΔG°, ΔG, and the Nernst equation.
• Temperature, entropy, and enthalpy influence Ecell and reaction feasibility.
• Applications range from battery design, corrosion monitoring, fuel cells, to industrial electrolysis.

By mastering the ΔG–EMF relationship, chemists can quantify the energy potential of redox reactions and design electrochemical systems efficiently.

Further Reading

• LibreTexts – Gibbs Free Energy and Cell Potential
• Chemguide – Gibbs Free Energy in Redox Reactions
• Royal Society of Chemistry – Electrochemical Thermodynamics

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