Identify the most stable complex.

The correct answer is option 3. \([Co(en)_3]Cl_3\)

To determine the stability of the complexes, we can consider the nature of the ligands, their arrangement around the central metal ion, and the overall charge on the complex.

1. \([Co(NH_3)_6]Cl_3\):

This is a hexaamminecobalt(III) chloride complex. Ammonia (NH₃) is a strong field ligand. The coordination number is 6, and the complex has an overall charge of +3.

2. \([CoCl_2(en)_2]Br\):

This is a dichloro-bis(ethylenediamine)cobalt(III) bromide complex. Ethylenediamine (en) is a strong field ligand. The coordination number is 4, and the complex has an overall charge of +1.

3. \([Co(en)_3]Cl_3\):

This is a tris(ethylenediamine)cobalt(III) chloride complex. Ethylenediamine (en) is a strong field ligand. The coordination number is 6, and the complex has an overall charge of +3.

4. \(K[CoCl_4(en)]\):

This is a potassium tetrachloroethylenediaminecobaltate(III) complex. Ethylenediamine (en) is a strong field ligand. The coordination number is 4, and the complex has an overall charge of -1.

In general, stability is influenced by factors such as the nature of ligands and the coordination number. Strong field ligands tend to form more stable complexes. Additionally, a higher coordination number often leads to greater stability.

Considering these factors, the most stable complex is likely to be \([Co(en)_3]Cl_3\) (Option 3) because it has a higher coordination number (6) and involves strong field ligands (ethylenediamine).