The Nernst Equation: Understanding Cell Potential Beyond Standard Conditions

In electrochemistry, the potential of an electrochemical cell tells us about its ability to do electrical work and is a measure of the spontaneity of its redox reaction. The Standard Cell Potential (E°) is the potential of a cell measured under standard conditions (1 M concentration for solutions, 1 atm pressure for gases, 25°C or 298.15 K). However, real-world electrochemical cells, like batteries, rarely operate under these ideal conditions. The concentrations of reactants and products change as the battery discharges, and the temperature may vary. The Nernst equation is a fundamental equation that relates the cell potential under these non-standard conditions (E) to its standard cell potential (E°).

This calculator is a tool designed to apply the Nernst equation, allowing you to see how changes in temperature and reactant/product concentrations affect the cell potential. It is invaluable for understanding how a battery's voltage drops as it is used up (as reactant concentrations decrease and product concentrations increase), for studying electrolysis, and for understanding bioelectrical phenomena like nerve impulses. It is an essential tool for students of electrochemistry and for engineers designing and analyzing battery systems.

The Nernst Equation Formula

The Nernst equation is expressed as:

E = E° - (RT / nF) * ln(Q)

Where:

E is the cell potential under non-standard conditions (in Volts).
E° is the standard cell potential (in Volts).
R is the ideal gas constant (8.314 J/(mol·K)).
T is the absolute temperature (in Kelvin).
n is the number of moles of electrons transferred in the balanced redox reaction.
F is Faraday's constant (approximately 96,485 C/mol).
Q is the reaction quotient, which has the same form as the equilibrium constant but uses the non-equilibrium concentrations or pressures of the products and reactants. For a reaction aA + bB ⇌ cC + dD, Q = ([C]ᶜ[D]ᵈ) / ([A]ᵃ[B]ᵇ).

Relationship to Gibbs Free Energy and Equilibrium

The Nernst equation is deeply connected to other fundamental concepts in thermodynamics. The cell potential (E) is related to the change in Gibbs Free Energy (ΔG) by the equation ΔG = -nFE. The Nernst equation can be derived from this relationship. When a battery or electrochemical cell reaches equilibrium, its cell potential (E) becomes zero, and it can no longer do work (a 'dead' battery). At this point, the reaction quotient Q is equal to the equilibrium constant K, and the Nernst equation simplifies to show the relationship between the standard cell potential and the equilibrium constant: E° = (RT / nF) * ln(K).

Nernst Equation Calculator