How do you calculate the Gibbs free energy change at equilibrium?

At equilibrium, the Gibbs free energy change (∆G) is zero.

In more detail, the Gibbs free energy change is a measure of the maximum reversible work a system can perform at constant temperature and pressure. It is given by the equation ∆G = ∆H - T∆S, where ∆H is the change in enthalpy, T is the absolute temperature and ∆S is the change in entropy.

However, at equilibrium, the system is in a state of maximum stability and no further work can be done. This means that the Gibbs free energy change is zero (∆G = 0). This is a fundamental principle of thermodynamics and is true for all systems at equilibrium, regardless of the specific values of ∆H, T and ∆S.

This principle can also be understood in terms of the reaction quotient Q and the standard Gibbs free energy change ∆G°. The relationship between these quantities is given by the equation ∆G = ∆G° + RTlnQ, where R is the gas constant and ln is the natural logarithm. At equilibrium, the reaction quotient Q is equal to the equilibrium constant K, and so the equation becomes ∆G = ∆G° + RTlnK.

However, we know that ∆G = 0 at equilibrium, and so we can rearrange this equation to find that ∆G° = -RTlnK. This equation tells us that the standard Gibbs free energy change is negative when the equilibrium constant is greater than 1 (i.e., the reaction is product-favoured), and positive when the equilibrium constant is less than 1 (i.e., the reaction is reactant-favoured).

In summary, the Gibbs free energy change at equilibrium is zero, reflecting the fact that the system is in a state of maximum stability. The standard Gibbs free energy change, on the other hand, provides information about the direction in which the system tends to move when it is not at equilibrium.