How is a hydrogen bond different from a chemical bond?

Hydrogen bonds are powerful bonds; they're still weaker than ionic and covalent bonds but are considerably stronger than the other intermolecular forces. They occur when a strongly electronegative atom (specifically O, F and Cl) is bonded to hydrogen. The electron-pulling power of the O, F or Cl atom is so strong that the H is left almost bare; the positive charge, then, of the H is strongly attracted to the negatively charged O, F or Cl in another molecule.

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