A modular guide to electromotive force (EMF), reaction direction, and thermodynamic prediction in electrochemical systems

1. Introduction

In the previous lecture, we established the concept of standard electrode potentials (E°) and learned how to use reference cells such as the Standard Hydrogen Electrode (SHE) to define redox tendencies.
Now we move from measurement to application, using those values to predict the voltage of a cell, determine whether a reaction is spontaneous, and quantify its energy yield.

This process revolves around the electromotive force (EMF), often called the cell potential (Ecell), which represents the driving force that pushes electrons through an external circuit.
By calculating EMF from standard electrode potentials, we can predict which direction a redox reaction will proceed, how much work it can perform, and how it connects to the underlying thermodynamics of Gibbs free energy.

In this lecture, you will learn:

• How to calculate cell voltage from half-cell potentials
• How to assign anode and cathode correctly
• The relationship between EMF, Gibbs free energy (ΔG°), and equilibrium (K)
• How concentration and temperature affect spontaneity
• Practical applications in battery design, corrosion, and industrial processes

2. The Meaning of Cell Potential

The cell potential (Ecell) is the potential difference between two half-cells that make up an electrochemical cell. It is measured in volts (V), where 1 volt = 1 joule per coulomb of charge moved.

When a redox reaction occurs in a cell, electrons flow from one electrode to another through an external circuit. This flow is driven by the difference in reduction potential between the two half-cells:

• The cathode is where reduction occurs (gain of electrons).
• The anode is where oxidation occurs (loss of electrons).
• If E₍cell₎ is positive, the reaction is spontaneous under standard conditions.
• If E₍cell₎ is negative, the reaction is non-spontaneous and would require an external power source (electrolysis).

Reference: Royal Society of Chemistry – Electrochemical Cells

3. The Standard Cell Potential (E°cell)

Under standard conditions, the measured EMF is called the standard cell potential (E₍cell₎).

Where both electrode potentials are standard reduction potentials (measured versus the SHE).

Example: The Daniell Cell

A classic example pairs a zinc electrode in zinc sulphate with a copper electrode in copper sulphate:

Half-Cell Reactions (written as reductions):

Now identify:

• Cathode: copper (more positive E°) → reduction occurs.
• Anode: zinc (less positive E°) → oxidation occurs.

A positive voltage indicates that electrons flow spontaneously from zinc (anode) to copper (cathode).

Overall Reaction:

4. Assigning Anode and Cathode

A common source of confusion in electrochemistry is identifying which electrode is which.
Use this three-step rule:

1. Write both half-reactions as reductions (as they appear in data tables).
2. Compare E° values – the more positive is the cathode.
3. The half-reaction with the lower (more negative) E° is the anode (it will be oxidised).

Role	Process	Sign of E°	Electron Flow
Anode	Oxidation	Lower (more negative)	Loses electrons
Cathode	Reduction	Higher (more positive)	Gains electrons

Tip:
Remember “AnOx, RedCat”:

• Anode → Oxidation,
• Reduction → Cathode.

5. Example Calculations

(a) Magnesium and Copper Cell

Reaction:

Interpretation:
Magnesium strongly reduces copper ions; the large positive E°cell confirms this.

(b) Iron and Silver Cell

Spontaneous Reaction:

(c) Hydrogen and Copper Cell

Hydrogen gas can reduce Cu²⁺ ions under suitable conditions, forming metallic copper.

6. Relating EMF to Thermodynamics

The voltage generated by a cell is directly connected to the free energy change (ΔG°) of the reaction.
This relationship allows chemists to translate between electrical and thermodynamic work.

Where:

• ΔG° = Gibbs free energy change (J/mol)
• n = number of electrons transferred
• F = Faraday constant (96,485 C/mol)
• E°₍cell₎ = standard cell potential (V)
• If ΔG° < 0, the reaction is spontaneous.
• If ΔG° > 0, the reaction is non-spontaneous and requires external energy.

Example: The Daniell Cell Again

For the zinc–copper cell:

This means each mole of zinc oxidised releases about 212 kJ of electrical energy under standard conditions.

Reference: LibreTexts – Free Energy and EMF

7. Connecting EMF and Equilibrium Constant (K)

A spontaneous cell reaction also shifts the chemical equilibrium in favour of products.
The relationship between the standard cell potential and the equilibrium constant is:

Thus:

Where:

• R = 8.314 J mol⁻¹ K⁻¹
• T = 298 K

Example:
For the Daniell cell (E°₍cell₎ = 1.10 V, n = 2):

This immense value of K confirms that the forward reaction is overwhelmingly favoured.

Reference: Chemguide – Using E° to Find K

8. Non-Standard Conditions and the Nernst Equation

Real systems rarely operate under standard conditions.
When concentrations, pressures, or temperatures differ, the actual cell potential (E) is given by the Nernst equation:

Where is the reaction quotient:

At 25 °C (298 K), this simplifies to:

Example: Daniell Cell Under Non-Standard Conditions

If [Zn²⁺] = 0.10 M and [Cu²⁺] = 1.00 M:

The cell potential increases slightly because the forward reaction is favoured.

Reference: Royal Society of Chemistry – The Nernst Equation

9. Practical Applications

(a) Battery Design

All battery voltages are derived from the difference in standard potentials between the two electrode materials.
By selecting metals or ions with large E° differences, chemists can design high-voltage cells.

Cell Type	Reaction Summary	E°cell (V)
Zn–Cu (Daniell)	Zn → Zn²⁺ + 2e⁻; Cu²⁺ + 2e⁻ → Cu	1.10
Zn–MnO₂ (Alkaline battery)	Zn → ZnO; MnO₂ + H₂O + e⁻ → MnOOH + OH⁻	1.50
Li–CoO₂ (Lithium-ion)	LiC₆ ↔ Li⁺ + e⁻; CoO₂ + Li⁺ + e⁻ ↔ LiCoO₂	3.70

(b) Corrosion Prediction

The electrochemical series can be used to predict which metals will corrode when in contact.

Example:
If iron (E° = −0.44 V) is in contact with copper (E° = +0.34 V), electrons flow from Fe → Cu.
Thus, iron acts as the anode and corrodes.

This is why galvanised steel uses a zinc coating (E° = −0.76 V), zinc oxidises first, protecting the underlying iron.

Reference: Corrosion Science – Electrochemical Mechanisms

(c) Electroplating

By applying a controlled voltage slightly greater than the standard potential difference, ions can be reduced onto a metal surface.
This principle governs the deposition of silver, nickel, or chromium coatings.

10. Cell Diagrams Revisited

Chemists use cell notation to represent electrochemical cells concisely.

Symbol Meaning

Symbol	Meaning
Single vertical line ∣	Phase boundary within a half-cell
Double vertical line ∥	Salt bridge or boundary between two half-cells
Left-hand side (LHS)	Anode (site of oxidation)
Right-hand side (RHS)	Cathode (site of reduction)

Example: Fe–Ag Cell

Interpretation:

• Anode (Fe):

• Cathode (Ag):

• Electrons flow from Fe to Ag through the external circuit.
• The salt bridge (∥) maintains charge neutrality by allowing ion migration.

11. Limitations and Real-World Factors

In practice, measured voltages may differ slightly from calculated E° values due to:

• Overpotential (overvoltage): Extra energy required to overcome reaction barriers.
• Activity coefficients: Non-ideal behaviour at high ion concentrations.
• Temperature variations: Affect reaction kinetics and equilibrium.
• Electrode surface condition: Oxide films, impurities, and roughness can alter potentials.

These effects are explored in detail in Lecture 16: Electrode Kinetics and Activation Energy.

12. Worked Example with Free Energy and Equilibrium

Reaction:

Half-cells:

Hence, the reaction is strongly spontaneous with a very large equilibrium constant.

13. Visualising Energy Flow

Electrochemical potential can be imagined as a hill between two energy levels:

• Electrons “fall” from higher energy (anode) to lower energy (cathode).
• The greater the height difference (potential), the more work can be done.

This analogy connects voltage to chemical driving force, a useful mental model for students and engineers alike.

14. Summary and Learning Outcomes

By completing this lecture, you should be able to:

Calculate standard cell potentials using tabulated E° values.
Identify which electrode is the anode and which is the cathode.
Predict the spontaneity of redox reactions from E°cell.
Relate EMF to Gibbs free energy and equilibrium constants.
Apply the Nernst equation for non-standard conditions.
Recognise the practical applications in batteries, corrosion, and plating.

Further Reading

• Royal Society of Chemistry – Electrochemical Cells
• LibreTexts – Cell Potentials and Free Energy
• Chemguide – Standard Potentials and Predicting Reactions

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