Which of the following complex is most stable ?

Options

A. `[M(NH_(3))_(6)]^(2+)`
B. `[M(NH_(3))_(6)]^(3+)`
C. `[M(en)_(2)(NH_(3))_(2)]^(3+)`
D. `[M(en)_(3)]^(3+)`

Answer

To determine which complex is the most stable among the given options, we need to analyze the types of ligands present in each complex and their coordination properties.

### Step-by-Step Solution:

1. **Identify the Ligands and Their Types:**
- The complexes mentioned in the question include ammonia (NH3) and ethylenediamine (EN).
- Ammonia is a **monodentate ligand**, meaning it binds to the central metal atom through one donor atom (the nitrogen atom).
- Ethylenediamine (EN) is a **bidentate ligand**, meaning it binds through two donor atoms (the two nitrogen atoms).

2. **Analyze the Given Complexes:**
- **Option A:** Metal with 6 ammonia ligands and a +2 charge.
- **Option B:** Metal with 6 ammonia ligands and a +3 charge.
- **Option C:** Metal with 2 ethylenediamine ligands and 2 ammonia ligands, with a +3 charge.
- **Option D:** Metal with 3 ethylenediamine ligands and a +3 charge.

3. **Determine Stability Based on Ligand Type:**
- Complexes with **chelation** (bidentate ligands) are generally more stable than those with only monodentate ligands due to the formation of ring structures that stabilize the complex.
- Therefore, options containing ethylenediamine (EN) will be more stable than those containing only ammonia (NH3).

4. **Compare the Options:**
- **Options A and B** contain only monodentate ligands (NH3), thus they are less stable.
- **Option C** has 2 bidentate ligands (EN) and 2 monodentate ligands (NH3). While it has some stability, it is still less stable than a complex with only bidentate ligands.
- **Option D** contains 3 bidentate ligands (EN), which will provide maximum stability due to the chelation effect.

5. **Conclusion:**
- The complex with the most stability is **Option D**, which consists of a metal with 3 ethylenediamine ligands and a +3 charge. This complex benefits from the chelation effect, making it the most stable among the options provided.

### Final Answer:
**Option D** is the most stable complex.