Coordination Number

The coordination number of a central metal atom or ion in a complex is the total number of donor atoms directly bonded to it — that is, the total number of coordinate bonds it forms with all of its ligands combined. This is a crucial distinction from simply counting ligands: a monodentate ligand contributes one to the coordination number for every molecule present, but a bidentate ligand contributes two per molecule (since it uses two donor atoms on the same metal at once), and a hexadentate ligand like EDTA$^{4-}$ contributes all six by itself.

For a complex built entirely of monodentate ligands, the coordination number simply equals the number of ligand molecules or ions present. In $[\text{Co}(\text{NH}_3)_6]^{3+}$, six separate $\text{NH}_3$ molecules each donate once, giving a coordination number of 6. In $[\text{Ni}(\text{CO})_4]$, four $\text{CO}$ molecules each donate once, giving a coordination number of 4. In $[\text{Ag}(\text{NH}_3)_2]^+$, two $\text{NH}_3$ molecules give a coordination number of 2.

When bidentate or polydentate ligands are involved, the count must explicitly account for each donor atom. In $[\text{Fe}(\text{C}_2\text{O}_4)_3]^{3-}$, there are three oxalate ions, but oxalate is bidentate, so each contributes two donor atoms to iron: $3 \times 2 = 6$, giving a coordination number of 6, exactly the same as if six separate monodentate ligands were present. Likewise, a single EDTA$^{4-}$ ion in $[\text{Ca}(\text{EDTA})]^{2-}$ contributes all six of its donor atoms by itself, again giving a coordination number of 6. …