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When determining how many binding sites a ligand has, the best way to go is drawing the lewis structure out and seeing how many lone pairs would be donated to the metal. For example, ethylenediamine has two lone pairs on each of the nitrogen atoms in the compound, so it would be a bidentate ligand. For carbonate, the lewis structure is attached below. When looking at the structure, there are two oxygens that are bonded to the carbon with single bonds and one oxygen bonded with a double bond. It is most likely that the metal will attach to one or both of the lone pairs on the oxygens that are bonded with single bonds. Also, since the geometry is trigonal planar, you can see how two binding sites is the maximum because of the inability for rotation. Drawing out the complex ion and making lines from the metal to the carbonate ligand helps visualize this.
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