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Butanol is a somewhat polar molecule, as evident by the presence of its alcohol functional group (-OH), whereas diethyl ether is a non-polar molecule. The stronger intermolecular forces that come along with butanol as a result of its polar nature make it have a higher melting point than diethyl ether.
It's mainly because Butanol has the ability to form hydrogen bonds whereas diethyl ether cannot. This additional bond that butanol can form means it has a higher melting point. Just think of it as more/stronger bonds=harder to break apart and thus higher melting/boiling point.
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