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When water and methanol mix,

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water and methanol are mutually soluble. essentially it is the same thing that happens when you add sulphuric acid to water but with a liquid instead.

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I don't really get what you mean. What does solubility have to do with change in temperature?

well, technically it is the hydration enthalpy. a couple of water molecules will form stronger than average intermolecular bonds with the methanol molecules. the formation of these bonds releases energy which we detect throuhg the temperature rise.

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