Nernst Equation and Equilibrium Constant
Derive and utilize the relationship between the standard cell potential (E°cell) and the equilibrium constant (K) of a cell reaction.
What is Nernst Equation and Equilibrium Constant?
An equation that relates the electrode potential of an electrochemical cell to the concentrations of the reactants and products.
Key formula / rule: Nernst Equation
Key points
- Understand the derivation and application of the Nernst equation.
- Relate cell potential to non-standard conditions.
- Calculate the equilibrium constant of a redox reaction from standard cell potential.
- Predict the spontaneity of a reaction using E°cell and K.
Common exam trap
Incorrectly calculating the reaction quotient (Q).
Definitions
- Term
Nernst Equation
- Meaning
An equation that relates the electrode potential of an electrochemical cell to the concentrations of the reactants and products.
- Term
Reaction Quotient (Q)
- Meaning
A measure of the relative amounts of products and reactants present in a reaction at a given time. It has the same form as the equilibrium constant expression but uses non-equilibrium concentrations.
- Term
Equilibrium Constant (K)
- Meaning
The ratio of the concentrations of products to reactants at equilibrium, raised to the power of their stoichiometric coefficients. It indicates the extent to which a reaction proceeds to completion.
- Term
Standard Cell Potential (E°cell)
- Meaning
The potential of an electrochemical cell measured under standard conditions (1 M concentration for solutions, 1 atm pressure for gases, and usually 25°C or 298K).
Learning objectives
Understand the derivation and application of the Nernst equation.
Relate cell potential to non-standard conditions.
Calculate the equilibrium constant of a redox reaction from standard cell potential.
Predict the spontaneity of a reaction using E°cell and K.
Formulae
- Name
Nernst Equation
- Note
Relates cell potential to standard potential and reaction quotient.
- Expression
Ecell = E°cell - (RT/nF)lnQ
- Name
Nernst Equation (at 298K)
- Note
Simplified form at standard temperature.
- Expression
Ecell = E°cell - (0.0592/n)logQ
- Name
Relationship between E°cell and K
- Note
Connects standard cell potential to equilibrium constant.
- Expression
E°cell = (RT/nF)lnK
- Name
Relationship between E°cell and K (at 298K)
- Note
Simplified form at standard temperature.
- Expression
E°cell = (0.0592/n)logK
Prerequisites
Understanding of electrochemical cells (anode, cathode, cell potential).
Knowledge of redox reactions and balancing them.
Basic thermodynamics (Gibbs free energy, spontaneity).
Concept of equilibrium and equilibrium constant (K).
Common mistakes
Incorrectly calculating the reaction quotient (Q).
Using concentrations instead of activities (though often approximated).
Forgetting to balance the redox reaction to find 'n'.
Confusing Ecell with E°cell.
Keywords
Nernst Equation
Cell Potential
Standard Cell Potential
Equilibrium Constant
Reaction Quotient
Electrochemistry
Redox Reaction
Thermodynamics
Practice preview
For a general electrochemical cell reaction, the relationship between the standard cell potential (E°cell) and the equilibrium constant (K) is given by:…
easy
If the equilibrium constant (K) for a cell reaction is very large (K >> 1), what can be inferred about the standard cell potential (E°cell)?…
easy
At 298 K, for a cell reaction, if E°cell = 0.1 V, what is the approximate value of the equilibrium constant (K)? (Given R = 8.314 J K⁻¹ mol⁻¹, F = 96485 C mol⁻¹)…
medium