If melting points and freezing points are the same, what state is pure equilibrium?

Question

If melting points and freezing points are the same, what state is pure equilibrium?

I understand melting points and freezing points are the same; adding or removing temperature of melting points for specific variables, like water at $\pu{0^\circ C}$ will melt or freeze them. Then, I have to ask the question, what is in between freezing and melting? What is that state? What is the behavior of the atoms if you somehow managed a perfect system where there wasn't extra heat being added nor removed and equilibrium was exact.

Answer 1

At the melting point there is a change of state. This means that solid is transformed in liquid or viceversa. For this process you need energy which is supplied or withdrawn in the form of heat. The whole process occurs at constant temperature, which is precisely the melting point.

Adding or removing temperature has no sense. It is heat what is added or removed. The temperature is just a result of the state. When you have a mixture of solid and liquid in equilibrium, this temperature is defined, is the same in the whole system and is the melting point.

Since it is state change, both solid and liquid are present and the temperature will not change while both are there in any quantity and if the system is in equilibrium. The quantities of solid and liquid will not vary until there is some heat flow. However, on the microscopic level, the molecules are still moving and some will migrate from the solid to the liquid while others (the same amount) will go from the liquid to the solid. This results in that, even if the system is in equilibrium, the small crystals will dissolve while the bigger ones will grow bigger.

Answer 2

The other answer is right but I just wish to clarify a point because I see this error all over the place.

There is a strong misconception that melting point and freezing point happen at the same temperature. It all practicality they do, in almost all practical experimentation they should be treated as such, and 99.9999% of the time its the same.

However, when we get away from bulk chemistry and get to the small scale, there can be variations, see this paper for example.

Also, I did read about one super cooled bulk material that had a difference in intermediate crystal structures going from liquid to solid vs solid to liquid that actually resulted in a difference in the two temperatures. I can not find that article now, but it's out there somewhere.

Again, these are extreme examples, but to truly say melting and freezing point are the same is technically wrong. I just needed to put this out there now.

It's also an important distinction because there is a directional component to the energy vector by saying either melting point or freezing point. (endothermic vs exothermic), although I guess "point" implies otherwise, but I find differentiating the two helps when understanding which state you started from.