Unlike the Schrödinger equation, this topic is often very complex to explain. At least there is not something like a cat in a box. I don’t say that the quantum is more easy, of course it isn’t. Let’s start.
Although there are more, we can easily identify three states of matter: solid, liquid and gaseous. These phases may be in some kind of equilibrium between them, for example, liquid water with water vapor (note that we speak of the same substance) for dynamic equilibrium [equal pressures] or a coffee and the container where it is found as a thermal equilibrium (equal temperatures). To comply with the above, the system that is spoken shouldn’t suffer any spontaneous change when it is subject to the conditions of its environment, of course, if you alter some equilibrium system, one of the phases tends to predominate.

Thermal equilibrium is very intuitive, I’m sure you imagine it. The dynamic balance is a bit intuitive, however, it isn’t that complicated. In a container where water and air coexist there is this kind of equilibrium. The water will begin to evaporate until it saturates the air, the molecules of vapor in the air will start to impact the water’s surface and will begin to condesate and return to it’s liquid form, while the water will begin to saturate the air for these portion that it was condensate. Yes, it’s a pretty cicle.

It must be taken into account that evaporation exists without the need to boil the liquid. Have you ever wondered why a puddle evaporates completely without the need for us to live at a temperature of 100 ° C (boiling water temperature) in the environment? Part of the answer is in the last paragraph, we also add the energy input of the heat provided by the sun or as the flame of our stoves when we cook, and do not forget the air currents present in the atmosphere.
All the above will help us to better understand the following. Ok, now the chemical potential makes its appearance. Idealize the change of energy caused by the change in the amount of matter where the volume of the system does not change, whether or not it is in a mixture. Yes, I know, maybe I don’t explain it very well. The chemical potential is the tendency of any substance to escape from one phase to another regardless of whether it is the same phase, as in the following image.

In the next chapter we will discuss more about the chemical potential and thus understand why it is important to know.