Understanding Gibbs Free Energy at Equilibrium

In the study of thermodynamics and chemical reactions, understanding the concept of equilibrium is crucial. A system reaches equilibrium when the forward and reverse processes occur at equal rates, resulting in no net change in the macroscopic properties of the system over time. This state is associated with a specific thermodynamic potential, which for processes occurring at constant temperature and pressure, is the Gibbs free energy.

What is Gibbs Free Energy?

The Gibbs free energy (denoted by $G$) is a thermodynamic potential that can be used to calculate the maximum reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. It is defined by the equation:

$\qquad G = H - TS$

where:

• $H$ is the enthalpy of the system.
• $T$ is the absolute temperature.
• $S$ is the entropy of the system.

The change in Gibbs free energy ($\Delta G$) for a process indicates whether the process will occur spontaneously under constant temperature and pressure conditions:

• If $\Delta G < 0$, the process is spontaneous (exergonic).
• If $\Delta G > 0$, the process is non-spontaneous (endergonic).
• If $\Delta G = 0$, the process is at equilibrium.

Gibbs Free Energy and the Equilibrium State

A system naturally tends to move towards a state of lower Gibbs free energy. This movement continues until the system reaches a state where the Gibbs free energy cannot decrease any further under the given conditions (constant temperature and pressure). This state is the point of chemical equilibrium.

At equilibrium, the system is in a stable state. Any infinitesimal change away from equilibrium would lead to an increase in the total Gibbs free energy of the system. Therefore, the total Gibbs free energy for all phases in a system at equilibrium is at its lowest possible value under those conditions. It is a minimum.

Consider a simple reaction $A \rightleftharpoons B$. As the reaction proceeds towards equilibrium, the Gibbs free energy of the system changes. It decreases until it reaches a minimum value at the equilibrium composition. At this minimum point, the rate of the forward reaction ($A \to B$) equals the rate of the reverse reaction ($B \to A$), and there is no net change in the amounts of A and B. The system is at thermodynamic equilibrium.

Let's summarise the states based on the change in Gibbs free energy:

Since the system naturally moves towards the state of lowest potential energy, and Gibbs free energy is the relevant potential at constant temperature and pressure, the system settles at the state where the total Gibbs free energy is minimum. This minimum corresponds to the point of equilibrium.

Thus, at equilibrium, the total Gibbs free energy for all phases is minimum.