Relation between Gibbs energy change and EMF of a cell
The thermodynamic relationship (ΔG = -nFEcell) connecting spontaneity and cell potential.
What is Relation between Gibbs energy change and EMF of a cell?
The maximum amount of non-expansion work that can be extracted from a closed system at constant temperature and pressure; it determines the spontaneity of a process.
Key formula / rule: Relation between Gibbs Energy Change and EMF
Key points
- To understand the thermodynamic basis of cell potential.
- To derive and apply the equation relating ΔG and Ecell.
- To predict the spontaneity of a cell reaction using its EMF.
- To calculate Ecell from ΔG or vice versa.
Common exam trap
Forgetting the negative sign in the equation ΔG = -nFEcell.
Definitions
- Term
Gibbs Free Energy Change (ΔG)
- Meaning
The maximum amount of non-expansion work that can be extracted from a closed system at constant temperature and pressure; it determines the spontaneity of a process.
- Term
Electromotive Force (EMF) (Ecell)
- Meaning
The potential difference between the two electrodes of an electrochemical cell when no current is flowing; it represents the driving force of the cell reaction.
- Term
Faraday Constant (F)
- Meaning
The magnitude of electric charge per mole of electrons, approximately 96485 Coulombs per mole.
Learning objectives
To understand the thermodynamic basis of cell potential.
To derive and apply the equation relating ΔG and Ecell.
To predict the spontaneity of a cell reaction using its EMF.
To calculate Ecell from ΔG or vice versa.
Formulae
- Name
Relation between Gibbs Energy Change and EMF
- Note
ΔG is Gibbs free energy change, n is moles of electrons transferred, F is Faraday constant, Ecell is cell EMF.
- Expression
ΔG = -nFEcell
- Name
Relation between Standard Gibbs Energy Change and Standard EMF
- Note
Applies under standard conditions (1 M concentration, 1 atm pressure, 298 K).
- Expression
ΔG° = -nFE°_cell
Prerequisites
Understanding of Gibbs Free Energy and its relation to spontaneity.
Knowledge of electrochemical cells and EMF.
Concept of redox reactions and electron transfer.
Units of energy (Joules) and potential (Volts).
Common mistakes
Forgetting the negative sign in the equation ΔG = -nFEcell.
Using incorrect values for 'n' (number of electrons transferred).
Confusing standard conditions (ΔG°, E°_cell) with non-standard conditions (ΔG, Ecell).
Incorrectly interpreting the sign of ΔG and Ecell in relation to spontaneity.
Keywords
Gibbs Free Energy
EMF
Electrochemical Cell
Spontaneity
Thermodynamics
Faraday Constant
Standard Electrode Potential
Practice preview
What is the relationship between the standard Gibbs energy change (ΔG°) and the standard cell potential (E°_cell) for a spontaneous redox reaction?…
easy
If the standard Gibbs energy change (ΔG°) for a reaction is -19.3 kJ/mol and the number of electrons transferred (n) is 2, what is the standard cell potential (E°_cell)? (Given F = 96500 C/mol)…
easy
If a non-spontaneous reaction is forced to occur by applying an external voltage, what can be inferred about the Gibbs energy change (ΔG) and the cell's EMF (E_cell) during this process?…
hard