Why is Gibbs free energy a state function?

Gibbs free energy is a state function because its value depends only on the current state of the system, not its history.

In more detail, a state function is a property of a system that depends only on the current equilibrium state of the system, not on the path by which the system arrived at that state. This means that the value of a state function is determined by the current conditions, such as temperature, pressure, and composition, and not by the process or path taken to reach those conditions.

Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work that a system can perform at constant temperature and pressure. It is defined as G = H - TS, where H is the enthalpy, T is the absolute temperature and S is the entropy of the system. Both enthalpy and entropy are state functions, and the difference between them (which is Gibbs free energy) is also a state function.

This is because the change in Gibbs free energy, ΔG, for a process is given by ΔG = ΔH - TΔS. The changes in enthalpy and entropy (ΔH and ΔS) are state functions, and the difference between them (which is ΔG) is also a state function. This means that the value of ΔG depends only on the initial and final states of the system, not on the path taken to get from one to the other.

In practical terms, this means that if you know the initial and final states of a system, you can calculate the change in Gibbs free energy for the process, regardless of the specific steps or path taken during the process. This is a very useful property in chemistry, as it allows us to calculate the energy changes associated with chemical reactions, phase changes, and other processes, based purely on the initial and final states of the system.