The reason that coffee looks brown is because tiny bits of the coffee bean are dissolved in the water. When you evaporate the coffee, only the water evaporates. The boiling point of the coffee bean pieces are WAY higher than the boiling point of the water. That means that you’re left with mostly pure water in the steam with no dissolved coffee.
What you did is called distillation. Basically, you can separate the different parts of a liquid solution by taking advantage of the differing boiling points of its parts.
Water boils at a lower temperature than caffeine and, likely, most of the other stuff in coffee. By heating the coffee up enough to boil the water but not enough to boil that other stuff, the vapor that condenses will be almost entirely water while the rest of the stuff like caffeine will be left behind.
Evaporating water, collecting the steam, and condensing it back into water is known as distillation. By doing this with coffee, you are essentially just separating the coffee from the water – the coffee stays in the cup and the water turns into steam (that you collect and condense back into water). Because the water no longer has the coffee in it, it goes back to being clear.
Your experiment just accidentally invented distillation.
If you have water with stuff in it, when you heat it up, the steam is just pure water. The stuff is left behind when the water evaporates – so when it becomes liquid again, that liquid is just water. You could do this with coffee, tea, juice – or even milk, spaghetti sauce, jam, or yogurt. Anything with water in it. The steam coming off is pure water only.
This effect is why the ocean is so salty. Salt dissolves into rivers and lakes from the ground, and gets carried into the ocean. When the sun evaporates ocean water, the salt is left behind and just accumulates in the ocean.
This can be useful for making drinkable water out of sea water too, just boil or evaporate it and collect the condensation.
You use this effect when cooking every time you “boil down” a sauce or soup to make it thicker. That only happens because it’s not the whole sauce boiling away, it’s only the water *from* the sauce leaving, so the sauce left in the pan gets thicker and more flavourful as you remove water from it.
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