Final answer:
A thermodynamic system reaches equilibrium when its free energy is at a minimum for the specified temperature, pressure, and composition, signifying no net change without extra work, which is consistent with Gibbs energy at equilibrium.
Step-by-step explanation:
To reach a state of equilibrium in a thermodynamic system, the free energy must be a minimum for a specified combination of temperature, pressure, and composition. This condition is crucial because it determines the direction of chemical reactions, and the composition of the system at equilibrium. According to the principles of thermodynamics, at equilibrium, the system's free energy is at its lowest possible value, indicating that no further net change is possible without additional work being done on or by the system. This concept is also tied to Gibbs energy, which predicts the direction of a chemical reaction and the state of the system at constant temperature and pressure. At equilibrium, rates of forward and reverse reactions are equal, rendering the free energy change (ΔG) zero.