[Lewis Thomson (OP)]

Donald would like help answering this question.

"Mixing of two different molecular compounds such as nitrogen and oxygen in our atmosphere is often given as an example of increasing entropy. It is stated that unmixing is possible but vanishingly improbable. Yet examples of spontaneous unmixing occur, such as when water vapor separates from the other gases and falls as rain, or water and oil separates even after violent shaking. Why is this the case? Can thermodynamics explain this?"

Leave your thoughts down in the comments below...

[chiralSPO]

In the case of water condensing, there is also the consideration of enthalpy.

The separation of oil and water is actually driven by entropy! Water molecules at an interface with oil are actually more highly ordered than water molecule surrounded by water, so decreasing the shared surface area between oil and water is entropically favorable, even though there is an entropic cost to unmixing the two!

[alancalverd]

The unmixing of atmospheric water is not spontaneous but dependent on cooling the wet air. You can separate the other gases by a bit more cooling. Oxygen liquefies around 90K, argon at 87K  and nitrogen at 77K

[Bored chemist]

Air liquefies at about 79K.