The Nernst Equation

Every electrochemical system has thermodynamic force or a stored energy due to the redox reactions occurring within it. As redox reactions occur, reactants get consumed and products are generated. Depending on whether the reaction is spontaneous or not (based on the sign of its Gibbs free energy change), the reaction may either require external energy (non-spontaneous) or release free energy (spontaneous) that can be used to do work.

Focusing on spontaneous systems where no external energy is needed, electrons move from a species where they are at a higher energy level and less stable, to one where they are at a lower energy level and more stable. The difference in energy creates the driving force for the electrons to move, and is quantified by the change in Gibbs free energy (ΔG). The bigger the energy difference (the more negative ΔG), the stronger the driving force for the forward reaction to proceed. 

As the reaction proceeds, the activities of the reactants decrease, and the activities of the products increase. Gibbs free energy depends on composition, so, the change in activities alters ΔG and therefore changes the driving force of the reaction.

The Gibbs free energy change (ΔG) represents the maximum useful work the reaction can provide under the given reaction conditions. In an electrochemical cell, this useful work appears as electrical work and is measured as the cell potential or voltage.

More interestingly, how the voltage changes as a function of the changing activities of products and reactants is described by an equation known as the Nernst equation. The Nernst equation essentially translates the free energy change at a specific reaction composition into an electrical potential difference.

The Nernst equation is written as:

Where Ecell is the cell potential, Ecell° is the standard potential (measured under standard-state conditions), R is the universal gas constant, T is the temperature, F is Faraday's constant, n is the number of electrons transferred in the reaction, and Q is the reaction quotient.

The reaction quotient is the ratio of the activities of products to reactants, each raised to their stoichiometric coefficients. It represents the thermodynamic state of the reaction mixture by describing its composition at any given moment. In other words, it shows how much product there is relative to reactant, and helps determine how much driving force remains in the system.

A larger reaction quotient (Q>1) indicates a higher relative amount of products compared to reactants. In this situation, ΔG becomes less negative, the driving force for the forward reaction becomes smaller, and the cell voltage decreases.

A smaller reaction quotient (Q < 1) indicates a higher relative amount of reactants compared to products. In this situation, ΔG becomes more negative, the driving force for the forward reaction becomes stronger, and the cell voltage increases.

When the cell is at equilibrium (Q = K, where K is the equilibrium constant), it means the rate of the forward reaction is equal to that of the reverse reaction. In this situation, the Gibbs free energy change is zero, there is no overall push causing electrons to flow, and the voltage is zero.