Gibbs Energy Change and EMF of a Cell 

Electrochemistry is a key part of physical chemistry and forms an important segment in competitive exams like JEE Main & Advanced. One of the most fundamental concepts is the relationship between Gibbs free energy change (ΔG) and the electromotive force (EMF) of an electrochemical cell.

This guide covers definitions, equations, derivations, and examples to help students build a strong conceptual foundation.

1.0Introduction 

In chemistry, particularly in thermodynamics and electrochemistry, two important terms are often linked together – Gibbs free energy (ΔG) and the electromotive force (EMF, Ecell) of a cell.

• Gibbs Free Energy (ΔG):
• • It is the maximum usable work a system can perform at constant temperature and pressure.
  • A negative ΔG indicates that the reaction is spontaneous (favorable), while a positive ΔG means the reaction is non-spontaneous.
• Electromotive Force (EMF):
• • EMF of a cell is the potential difference between the two electrodes when no current is flowing.
  • It represents the driving force of an electrochemical reaction.
  • A positive EMF indicates that the cell reaction is spontaneous, while a negative EMF suggests it cannot proceed without external energy.

The relation connects the two:

$\Delta G=-nF{E}_{\text{cell}}$

where n = number of electrons transferred, and F = Faraday’s constant.

This means:

• Positive EMF → Negative ΔG → Reaction is spontaneous.
• Negative EMF → Positive ΔG → Reaction is non-spontaneous.

2.0What is Gibbs Free Energy?

Gibbs free energy (G) is the thermodynamic potential that measures the maximum reversible work obtainable from a chemical process at constant temperature and pressure.

• Expression:

$\Delta G=\Delta H-T\Delta S$

where:

• ΔH = enthalpy change
• ΔS = entropy change
• T = absolute temperature

Significance of ΔG:

• If ΔG < 0 → reaction is spontaneous
• If ΔG > 0 → reaction is non-spontaneous
• If ΔG = 0 → system is at equilibrium

3.0EMF of a Cell

Electromotive force (EMF), or cell potential (E_cell), is the potential difference between the two electrodes of an electrochemical cell that drives the flow of electrons from the anode to the cathode. It is measured in Volts (V).

• Spontaneity and E_cell ​:
• • If E_cell>0, the cell reaction is spontaneous in the forward direction.
  • If E_cell<0, the cell reaction is non-spontaneous.
  • If E_cell=0, the cell is at equilibrium.

4.0Relationship between Gibbs Energy Change and EMF of a Cell

The electrical work done by an electrochemical cell is equal to the product of the charge flowing and the cell potential. The maximum electrical work obtainable from a cell reaction is equal to the decrease in its Gibbs free energy. This leads to the fundamental relationship:

$\Delta G=-nF{E}_{\text{cell}}$

Where:

• ΔG is the Gibbs free energy change in Joules (J).
• n is the number of moles of electrons transferred in the balanced cell reaction.
• F is the Faraday constant, which is the charge on one mole of electrons. Its value is approximately 96485
• E_cell​ is the EMF of the cell in Volts (V).

Why the negative sign? 

A spontaneous reaction has a negative ΔG and a positive E_cell. The negative sign ensures that a spontaneous process has a negative Gibbs energy change.

5.0Derivation of ΔG = –nFE_cell

1. Maximum non-expansion work in an electrochemical reaction is given by:

$\Delta G=W_{\text{max}}$

1. For a redox reaction involving the transfer of n moles of electrons, the total charge (Q) transferred is:
   Q=nF
2. Electrical work done is:
   w=Q×E=nFE
3. Hence, maximum electrical work:

$\Delta G=-nF{E}_{\text{cell}}$

This equation links thermodynamics (ΔG) with electrochemistry (Ecell).

6.0Conditions for Spontaneity

From the relation ΔG = –nFE_cell :

• If E_cell > 0, then ΔG < 0 → reaction is spontaneous.
• If E_cell < 0, then ΔG > 0 → reaction is non-spontaneous.
• If E_cell = 0, then ΔG = 0 → reaction is at equilibrium.

7.0Differences between Gibbs Free Energy and EMF