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In what extreme circumstance would alcohol not be soluble in water?

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Alcohol is mostly soluble in water. However, the only way would be to solidify it. That would mean that the alcohol has to be frozen at -114 degrees C.

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I thought of that as well, but wouldnt there be some (talking micro level) melting going on in the water? Because the water would have to be above freezing.

Another thought I had was maybe the carbon chain attached to an alcohol would eventually make it insoluble? I know at 5-11 carbons alcohol gets ioly, and at 12+ it becomes a waxy soild.

Anyone have an insight? Thanks.
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I was thinking if alcohol evaporates, wouldn't that gas be insoluble in water
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