Of the following complex ions, the one that probably has the largest overall formation constant , `K_(f)`, is

Options

A. `[Co(NH_(3))_(6)]^(3+)`
B. `[Co(H_(2)O)_(6)]^(3+)`
C. `[Co(NH_(3))_(2)(H_(2)O)_(4)]^(3+)`
D. `[Co(en)_(3)]^(3+)`

Explanation

To determine which complex ion has the largest overall formation constant (Kf), we need to analyze the stability of the complexes formed by the ligands involved. The stability of a complex ion is often related to the type of ligands used and their ability to donate lone pairs to the central metal atom.

### Step-by-Step Solution:

1. **Identify the Ligands**:
- We have several complex ions to consider. The ligands mentioned are NH3 (ammonia), H2O (water), and en (ethylene diamine).

2. **Determine the Type of Ligands**:
- NH3 and H2O are both **monodentate ligands**, meaning they can donate only one lone pair of electrons to the central metal atom.
- Ethylene diamine (en) is a **bidentate ligand**, which means it can donate two lone pairs of electrons to the central metal atom.

3. **Consider the Stability of the Complexes**:
- The stability of a complex ion is generally higher when it forms a chelate ring. Bidentate ligands like ethylene diamine can form chelate rings, which enhances the stability of the complex.
- Monodentate ligands do not form such rings and typically result in less stable complexes.

4. **Evaluate the Formation Constants (Kf)**:
- The formation constant (Kf) is larger for more stable complexes. Since ethylene diamine (en) is a bidentate ligand, the complex formed with it is likely to be more stable than those formed with monodentate ligands like NH3 and H2O.

5. **Conclusion**:
- Among the given complex ions, the one with ethylene diamine (en) as a ligand will have the largest overall formation constant (Kf) due to the formation of a stable chelate ring structure.

### Final Answer:
The complex ion that probably has the largest overall formation constant, Kf, is the one that contains ethylene diamine (en) as a ligand.