Is the Co-ordination number of Cobalt always 6 in every co-ordination compound?

Question

For example in the following compounds

1. CoCl₃.6H₂O
2. CoCl₃.6NH₃
3. CoCl₃.5NH₃
4. CoCl₃.4NH₃

in all of these complexes, we took the

a)oxidation state of Cobalt as +3 ( since there are 3 Cl^- ions and NH₃ and H₂O are neutral ligands )

b) Co-ordination number of Cobalt as 6

and the answer to writing the compounds was:

1.[Co(H₂O)₆]Cl₃ or [Co(H₂O) ₅Cl]Cl₂.H₂O

2. [Co(NH₃)₆]Cl₃

3. [Co(NH₃)₅Cl]Cl₂

4. [Co(NH₃)₄Cl₂]Cl

My question is this: Why do we take the co-ordination number of Cobalt always six?

Can't Co take other co-ordination numbers like 4? or 5?

So for the following compound

CoCl₃.4NH₃

Can't we write it as [Co(NH₃)₄]Cl₃ instead of

[Co(NH₃)₄Cl₂]Cl

Also how to predetermine the C.N of the central metal atom just by looking at anions and ligands? (cases when no coordination sphere is marked like in my above examples)

Answer 1

With these compounds, you have coordination number $6$, but like other transition metals cobalt can have different coordination numbers with the right ligands. In this answer the $\ce{CoO4^{3-}}$ ion is discussed as an example of a tetrahedral complex with the rare case of high spin despite the central ion having an oxidation state of $+5$. (The tetrahedral geometry and strongly pi-donating ligands favor the high-spin electron confuguration.) Five-coordination is seen in Co(II) complexes with pi-accepting organic ligands such as $\ce{o-(C6H4)(SCH3)(P(C6H5)2)}$ [1].

1. Geoffrey Dyer and Devon W. Meek (1967). "Five-coordination. VI. Low-spin cobalt(II) complexes with with bidentate ligands". J. Am. Chem. Soc. 89, 16, 3983–3987. https://doi.org/10.1021/ja00992a006