ΔG^⦵ and Standard Cell Potential HL Only

Full Notes

At first, electrochemical cells and Gibbs free energy might feel like completely separate topics. But they’re actually describing the same thing from two different perspectives.

• E^⦵cell measures how strongly a redox reaction can push electrons through a circuit and drive a current.
• ΔG^⦵ measures how thermodynamically favourable the reaction is — how much energy is released or required.

The energy available to drive an electric current (E^⦵cell) comes directly from the energy change in the chemical reaction (ΔG^⦵). These two quantities are linked by the equation:

ΔG^⦵ = –nFE^⦵cell

This allows us to connect the electrical world of electrochemical cells with the thermodynamic world of Gibbs energy — and predict spontaneity from either.

The Equation

• ΔG^⦵ = standard Gibbs free energy change (J or kJ)
• n = number of moles of electrons transferred in the balanced redox reaction
• F = Faraday constant = 96,500 C mol⁻¹
• E^⦵cell = standard cell potential (V)

How to Use the Equation

• Identify n = number of electrons transferred from half-equations
• Use E^⦵cell from the data booklet
• Use F = 96,500 C mol⁻¹
• Calculate ΔG⦵ in joules, then convert to kJ mol⁻¹

Interpreting the Result

• The sign of ΔG^⦵ shows spontaneity
• If ΔG^⦵ < 0, the reaction is spontaneous
• The more positive the E^⦵cell, the more negative the ΔG^⦵
• A negative ΔG^⦵ indicates a thermodynamically favourable reaction

Summary

• ΔG^⦵ and E^⦵cell are linked by ΔG^⦵ = –nFE^⦵cell
• A negative ΔG^⦵ means the reaction is spontaneous
• The more positive the E^⦵cell, the more negative the ΔG^⦵
• Thermodynamic data can also be used via ΔG° = ΔH° – TΔS°

Q

Reactivity 1.4 — Linked Course Question

How can thermodynamic data be used to predict the spontaneity of a reaction?

Thermodynamic data — specifically values of enthalpy change (ΔH°) and entropy change (ΔS°) — can be used to calculate the Gibbs free energy change (ΔG°) using:

ΔG° = ΔH° – TΔS°

• ΔG° = Gibbs free energy change (J mol⁻¹ or kJ mol⁻¹)
• ΔH° = standard enthalpy change
• T = temperature (K)
• ΔS° = standard entropy change (J K⁻¹ mol⁻¹)

Predicting Spontaneity:

• If ΔG° < 0, the reaction is spontaneous
• If ΔG° > 0, the reaction is non-spontaneous
• If ΔG° = 0, the system is at equilibrium

Matt’s exam tip

Make sure ΔS° is converted to kJ K⁻¹ mol⁻¹ if ΔH° is in kJ mol⁻¹. Divide by 1000 before substituting into the equation.