Nernst Equation and Gibbs Energy
Concentration dependence of EMF and relation to ΔG and K. (Chemistry › Electrochemistry, NEET UG syllabus.)
What is Nernst Equation and Gibbs Energy?
An equation that relates the cell potential of an electrochemical cell to its standard cell potential, temperature, and the concentrations/pressures of reactants and products.
Key formula / rule: Nernst Equation (general)
Key points
- State and apply the Nernst equation to calculate cell potentials under non-standard conditions.
- Calculate the reaction quotient (Q) for a given electrochemical reaction.
- Relate Gibbs Free Energy (ΔG) to cell potential (Ecell) and standard cell potential (E°_cell).
- Determine the spontaneity of an electrochemical reaction using Ecell or ΔG.
Common exam trap
Incorrectly determining 'n', the number of electrons transferred in the balanced redox reaction.
Definitions
- Term
Nernst Equation
- Meaning
An equation that relates the cell potential of an electrochemical cell to its standard cell potential, temperature, and the concentrations/pressures of reactants and products.
- Term
Reaction Quotient (Q)
- Meaning
A measure of the relative amounts of products and reactants present in a reaction at any given time, expressed as a ratio of product concentrations to reactant concentrations, each raised to their stoichiometric coefficients.
- Term
Standard Electrode Potential (E°)
- Meaning
The potential of an electrode measured under standard conditions (1 M concentration for ions, 1 atm pressure for gases, 298 K temperature) relative to a standard hydrogen electrode (SHE).
- Term
Gibbs Free Energy (ΔG)
- Meaning
A thermodynamic potential that measures the 'useful' or process-initiating work obtainable from an isothermal, isobaric thermodynamic system. A negative ΔG indicates a spontaneous process.
- Term
Faraday Constant (F)
- Meaning
The amount of electric charge carried by one mole of electrons (approximately 96485 coulombs per mole).
Learning objectives
State and apply the Nernst equation to calculate cell potentials under non-standard conditions.
Calculate the reaction quotient (Q) for a given electrochemical reaction.
Relate Gibbs Free Energy (ΔG) to cell potential (Ecell) and standard cell potential (E°_cell).
Determine the spontaneity of an electrochemical reaction using Ecell or ΔG.
Calculate the equilibrium constant (K) from standard cell potential (E°_cell).
Predict the effect of concentration changes on cell potential.
Formulae
- Name
Nernst Equation (general)
- Note
For non-standard conditions, relates cell potential to concentrations.
- Expression
Ecell = E°_cell - (RT/nF)lnQ
- Name
Nernst Equation (at 298 K, log base 10)
- Note
Simplified form for 25°C, using log base 10.
- Expression
Ecell = E°_cell - (0.0592/n)logQ
- Name
Gibbs Free Energy and Cell Potential
- Note
Relates spontaneity to cell potential.
- Expression
ΔG = -nFEcell
- Name
Standard Gibbs Free Energy and Standard Cell Potential
- Note
For standard conditions.
- Expression
ΔG° = -nFE°_cell
- Name
Standard Cell Potential and Equilibrium Constant
- Note
At equilibrium, Ecell = 0 and Q = K.
- Expression
E°_cell = (RT/nF)lnK
- Name
Standard Gibbs Free Energy and Equilibrium Constant
- Note
Thermodynamic relation between standard free energy and K.
- Expression
ΔG° = -RTlnK
Prerequisites
Basic understanding of redox reactions and balancing.
Knowledge of electrochemical cells (voltaic/galvanic cells).
Concept of standard electrode potentials (E°).
Basic thermodynamics: Gibbs Free Energy (ΔG) and spontaneity.
Understanding of equilibrium constant (K) and reaction quotient (Q).
Common mistakes
Incorrectly determining 'n', the number of electrons transferred in the balanced redox reaction.
Errors in setting up the reaction quotient (Q), especially for gases or omitting pure solids/liquids.
Using log base 10 instead of natural log (ln) or vice versa without the conversion factor (2.303).
Forgetting the negative sign in ΔG = -nFEcell.
Confusing Ecell with E°_cell.
Incorrectly applying units for R, T, and F.
Keywords
Nernst
Gibbs Free Energy
Cell Potential
EMF
Standard Potential
Reaction Quotient
Equilibrium Constant
Spontaneity
Electrochemistry
Faraday Constant
Practice preview
Which of the following represents the Nernst equation at 298 K for a general electrochemical reaction aA + bB → cC + dD?…
easy
Consider a galvanic cell: Zn(s) | Zn²⁺(aq, C₁) || Cu²⁺(aq, C₂) | Cu(s). If the concentration of Zn²⁺ ions (C₁) is increased while keeping Cu²⁺ concentration (C₂) constant, how will the cell potential (E_cell) change?…
easy
For a reaction 2Ag⁺(aq) + Cd(s) → 2Ag(s) + Cd²⁺(aq), the standard cell potential (E°_cell) is +1.20 V at 298 K. Calculate the equilibrium constant (K) for this reaction. (Given: 2.303RT/F = 0.0592 V at 298 K)…
medium