What does ∆G° equal when an electrochemical cell is at equilibrium?

When an electrochemical cell is at equilibrium, the change in Gibbs free energy (∆G°) equals zero. This is a fundamental principle in thermodynamics, indicating that at equilibrium, there is no net change in the concentrations of reactants and products, and thus no spontaneous work can be done by the system.

In the context of electrochemistry, the relationship between Gibbs free energy and the equilibrium constant (K) is expressed by the equation ∆G° = -RT ln(K). Here, R is the universal gas constant, T is the temperature in Kelvin, and K is the equilibrium constant for the reaction. This equation reflects that when the system is at equilibrium, the Gibbs free energy change (∆G°) is zero, which coincides with the definition of the equilibrium constant (K) where Q (the reaction quotient) equals K.

Therefore, at equilibrium, while ∆G° equals zero, it is important to understand that the relationship among ∆G°, K, and RT ln(K) reflects the state of the system, confirming that no net reaction occurs, and thus we derive the relationship that connects these thermodynamic concepts, though the assertion itself of K will ultimately lead to that equilibrium point being reached.