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Hydrogen bonding is a type of dipole-dipole bond, that is stronger than other dipole-dipole bonds, as well as ion-dipole, dipole-induced dipole, and van der Waals / London dispersion forces. Hydrogen bonds can only occur between a hydrogen atom and a N, O, or F atom, because these atoms have very high electronegativities.
Just remember that it only occurs between hydrogen, nitrogen, oxygen or fluorine atoms (H N O F). What is it? Take water molecules for example. 2 hydrogen atoms are bonded with one oxygen atom. The oxygen atoms, because of higher electronegativity, pull the electrons closer to it than the hydrogen atoms. Because the electrons are closer to the oxygen atom, this creates a negative charge around the oxygen atom and positive charge around the hydrogen atoms. When the positive charges attracts a negative charge on another molecule (N O F), this creates a hydrogen bond. It's very important in understanding properties of water and solubility.
Hydrogen bonding is a type of intermolecular force, which means attracting forces between molecules. This is different from intramolecular forces, which happen in the molecule. Hydrogen bonding is very important because it is what gives water it's cohesiveness and adhesiveness.
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