The Nernst Equation

A zinc-copper galvanic cell at standard conditions has a cell potential of +1.10 V and a ΔG value of −212 kJ, indicating that it operates spontaneously. However, as the reactant’s concentration changes during the cell’s discharge, it leads to a gradual decrease of cell potential until the reaction stops completely.

Conditions like these are called nonstandard. Here, the established standard values of cell potential, Gibbs free energy, and the equilibrium constant are no longer valid.

Nonstandard conditions are prevalent in many reactions ranging from redox reactions to ion gradients in neuronal membranes. But how is an accurate cell potential determined in such systems?

If the concentration of a reactant is greater, and the concentration of a product is smaller compared to standard conditions, then Le Châtelier’s Principle is used to determine the reaction’s direction qualitatively; however, it cannot be used for quantifying the deviating cell potential.

Thus, this necessitates establishing a relationship between the cell potentials for cells under standard and nonstandard conditions. Recall that the free energy changes under standard and nonstandard conditions are related.

Substituting the equation of change in free energy with the cell potential results in a modified equation known as the Nernst equation. The Nernst equation determines how the cell potential differs from its standard value depending on the number of electrons transferred, temperature, and reaction composition.

The reaction quotient, Q, accounts for the change in free energy due to the difference in the reaction mixtures’ composition. If reactants are solid, Q is omitted.

Under standard state conditions, the value of Q is unity and the concentration of reactants and products is equal. The logarithm of one is zero, so the cell potential equals the standard cell potential.

A Q value less than one indicates a higher concentration of reactants compared to products, which shifts the equilibrium to the right, increasing the cell potential.

A Q value greater than one indicates a higher product to reactant concentration, driving the reaction to the left and lowering the cell potential.

At equilibrium, the Q value is equal to K, and the cell potential becomes zero.

The Nernst equation explains why electrochemical batteries “die” post-discharge: as the reactant concentration decreases, the cell approaches equilibrium conditions and its potential decreases to zero