Step 1: Understanding the Question:
The question asks to identify a homoleptic coordination complex from the provided options based on the types of ligands attached to the central metal atom.
Step 2: Key Formula or Approach:
Coordination complexes are classified into two structural groups depending on ligand diversity:
Homoleptic complexes: The central metal atom or ion is bound to exactly
one single type of donor ligand group.
Heteroleptic complexes: The central metal atom or ion is bound to
more than one type of donor ligand group.
Step 3: Detailed Explanation:
Let's look at the composition of the inner coordination sphere (inside the square brackets) for each option:
In option (B), $[\text{Co}(\text{NH}_3)_5\text{Cl}]\text{SO}_4$, the Cobalt ion is bound to two different types of ligands: 5 ammine ($\text{NH}_3$) groups and 1 chloride ($\text{Cl}^-$) ion. (Heteroleptic)
In option (C), $[\text{Co}(\text{NH}_3)_4\text{Cl}_2]^+$, the Cobalt ion is bound to 4 ammine groups and 2 chloride ions. (Heteroleptic)
In option (D), $[\text{Co}(\text{H}_2\text{O})(\text{NH}_3)_5]\text{I}_3$, the Cobalt ion is bound to 1 aqua ($\text{H}_2\text{O}$) ligand and 5 ammine groups. (Heteroleptic)
In option (A), $[\text{Co}(\text{NH}_3)_6]^{3+}$, the central Cobalt ion is coordinated exclusively to six identical ammine ($\text{NH}_3$) molecules. Since there is only a single variety of ligand within the coordination sphere, it matches the definition of a homoleptic complex.
Step 4: Final Answer:
The homoleptic complex is $[\text{Co}(\text{NH}_3)_6]^{3+}$, corresponding to option (A).