Entropy is a measurement of disorder in a sense mostly related to probability and statistics. A system with greater entropy contains a greater amount of possible microstates. For instance, two gas chambers with the same amount of gas molecules will have different entropy values if one of them contains different types of gases. The molecules in the chamber with more gas types can be displayed in many more ways.
In fact, by understanding entropy one can truly understand the statistical nature of all chemical processes and understand why Gibbs free energy can be seen simply as a measurement of the likeliness of a state existing or not and ΔG can be seen as the likeliness of a process happening or not. This can be shown by an analysis of the famous equation:
ΔG = ΔH – TΔS
We can begin by remembering that ΔH represents the heat exchange involved in a reaction at constant pressure, if it’s negative, the system releases energy and, if it’s positive, the system absorbs energy. Now, enthalpy is “stored” in the form of chemical bonds or interactions that are present in the system and, with the progress of a reaction or other processes like solvation, interactions are formed or broken and this energy is released or absorbed.
And what does –TΔS represents? As an endothermic reaction progresses, heat is transferred to the system from the surroundings, but why does that happen? Why is that spontaneous and not, say, the opposite reaction, which would be exothermic and release heat to the surroundings (supposing the reverse reaction is possible)?
Well, chemists and physicists know that the entropy of the universe always increases (second law of thermodynamics), that is just a way of saying mathematically that all that is most likely to happen will happen. So –TΔS is the term that accounts for the effect that the exchanged heat will have in the system or surroundings when it is transferred.
In the case of an endothermic reversible reaction, we have ΔH > 0, so the reaction can only be spontaneous if TΔS is big enough. That means that the reaction can only be spontaneous if it leads to an increase of disorder in the system (increase in the number of possible microstates of the system) that is big enough to compensate the decrease of disorder in the surroundings, associated to the heat loss by the surroundings, which is accounted for by ΔH.
ΔG will only ever be 0 if the system is in equilibrium and if ΔSu (entropy variation of the universe) is also 0, meaning that the variations of entropy both in the system and in the surroundings caused by the two opposite reactions occurring at the same time are exactly compensated given the constant reaction rates achieved in equilibrium. The system is not only in equilibrium with itself, but also with the surroundings.
The key is to realize that you don’t need to measure the ΔS of the surroundings and yet you obtain information that ultimately depends on it. This is one of the great merits of this equation.
So ΔG can be seen as just a convenient way for chemists to evaluate the balance of factors that “decide” if a process is spontaneous or not, mathematically equivalent to simply checking which processes lead to an increase in the entropy of the universe.