Question

The coordination number of cobalt in $[\text{Co(NH}_3)_6]^{3+}$ is 

Hint:

Coordination number equals the total number of donor bonds, not the number of ligand molecules -- for a monodentate ligand like $\text{NH}_3$ each one contributes exactly one bond, but a bidentate ligand such as ethylenediamine (en) or oxalate contributes two, so always multiply ligand count by denticity.

Answer 1

Step 1: Concept 
The coordination number of a metal ion in a complex refers to the number of ligand donor atoms directly bonded to it. In coordination complexes, ligands are molecules or ions that donate electron pairs to form coordinate covalent bonds with the central metal ion. 

Step 2: Meaning 
In \([\text{Co(NH}_3)_6]^{3+}\), cobalt (Co) is the central metal ion and ammonia (\(\text{NH}_3\)) molecules act as the ligands. The superscript \(3+\) indicates that the complex ion carries an overall positive charge of three. 

Step 3: Analysis 
To determine the coordination number, we count how many donor atoms from the ligands are directly bonded to the cobalt ion in the complex \([\text{Co(NH}_3)_6]^{3+}\). The chemical formula shows that there are six \(\text{NH}_3\) molecules surrounding the cobalt ion. Ammonia (\(\text{NH}_3\)) is a monodentate ligand because each molecule contains a single nitrogen donor atom that can form exactly one coordinate covalent bond with the metal center. Since there are six monodentate \(\text{NH}_3\) ligands directly bonded to the cobalt ion, the total number of coordinate bonds is: \[6 \times 1 = 6\] 
Step 4: Conclusion 
Therefore, the coordination number of cobalt in this complex is 6

Final Answer: 6

Answer 2

Concept:

• Link the coordination number directly to the geometry and hybridisation of the complex, rather than only counting ligand molecules.

Step 1: Identify the geometry expected for this complex.
In $[\text{Co(NH}_3)_6]^{3+}$, cobalt is in the +3 oxidation state. Complexes of $\text{Co}^{3+}$ with six monodentate ligands like $\text{NH}_3$ characteristically adopt an octahedral geometry, built using $d^2sp^3$ / $sp^3d^2$ hybrid orbitals on the metal.

Step 2: Connect the geometry to the number of bonds.
An octahedral geometry is built from exactly six equivalent hybrid orbitals arranged symmetrically around the metal, pointing toward six vertices. Each hybrid orbital accepts one lone pair of electrons from one $\text{NH}_3$ ligand, forming one coordinate bond per orbital.

Step 3: Count the coordinate bonds.
Since the coordination number equals the number of donor atoms directly bonded to the metal, and there are exactly six hybrid orbitals each forming one bond, the coordination number follows straight from the geometry itself, without needing to separately count the six $\text{NH}_3$ groups in the formula.

Final Answer: The coordination number of cobalt is 6.