Hydrogen bonding occurs when a hydrogen atom is covalently bonded to a highly electronegative atom, such as oxygen, nitrogen, or fluorine, and is attracted to another electronegative atom.
Let's examine the molecules listed:
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Methane (CH₄): Methane does not exhibit hydrogen bonding. It consists of carbon and hydrogen, and the hydrogen atoms are not bonded to a highly electronegative atom.
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Methanol (CH₃OH): Methanol does exhibit hydrogen bonding. The -OH (hydroxyl) group contains an electronegative oxygen atom bonded to hydrogen, allowing it to form hydrogen bonds with other methanol molecules or other compounds that can accept a hydrogen bond.
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Tetraiodomethane (CI₄): Tetraiodomethane does not exhibit hydrogen bonding. While it has several iodine atoms, iodine is not sufficiently electronegative to create hydrogen bonds.
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None of the above: This option is incorrect because methanol does exhibit hydrogen bonding.
In conclusion, the molecule that exhibits hydrogen bonding in your list is methanol.