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So the real difference between polydentate and chelate is that polydentate may form multiple bonds to either the same or different atoms (does this mean two different atoms in the same molecule, or the central atoms of two different molecules), whereas chelating ligands only form bonds multiple bonds to one central atom?
A chelating ligand should bond more than once to the same metal atom. Therefore, it must be polydentate. However, a regular polydentate ligand does not have to ligate to the same metal and therefore, it is not neccessarily chelating.
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