In complexes off wea field ligands, `Delta_(o) lt P` (pairing energy), the energy difference between `t_(2g) and e_(g)` sets is relatively less. Under the unfluence of strong field ligands, `Delta_(O) gt p` (Pairing energy), the energy difference between `t_(2g) and e_(g)` sets is relatively high.
Q. Which of the following is correct statement?

Options

A. Complex `[Co(H_(2)O)_(6)]^(2+)` is more stable than `[Co(H_(2)O)_(6)]^(3+)`
B. All compounds of `Ni(II)` are bound to be outer-d-orbital complexes
C. Stability constant for `[Ni(en)_(3)]^(2+)` is greater than stability constant for `[Ni(NH_(3))_(6)]^(2+)`
D. `Delta_(oct)` for `[Cr(H_(2)O)_(6)]^(3+)` is greater than `Delta_(oct)` for `[Cr(NH_(3))_(6)]^(3+)`

Answer

To solve the question regarding the stability of complexes with weak and strong field ligands, we will analyze the provided statements step by step.

### Step-by-Step Solution:

1. **Understanding Ligands and Splitting Energy**:
- Weak field ligands cause a smaller splitting of the d-orbitals, which means that the energy difference between the \( t_{2g} \) and \( e_g \) sets is relatively small. This results in less energy required for pairing of electrons.
- Strong field ligands, on the other hand, cause a larger splitting of the d-orbitals, leading to a higher energy difference between \( t_{2g} \) and \( e_g \) sets. This means that the energy required for pairing electrons is greater.

2. **Analyzing the Statements**:
- **Statement 1**: "The stability of \( [Co(H_2O)_6]^{2+} \) is more than \( [Co(H_2O)_6]^{3+} \)".
- This statement is incorrect. The \( [Co(H_2O)_6]^{3+} \) complex has a higher oxidation state, which generally increases stability due to increased positive charge attracting the ligands more strongly.

- **Statement 2**: "All compounds of \( Ni^{2+} \) are bound to be outer d orbital complexes".
- This statement is also incorrect. While \( Ni^{2+} \) typically has a configuration of \( 3d^8 \), it can form inner d orbital complexes in the presence of strong field ligands, leading to pairing of electrons.

- **Statement 3**: "The stability constant for \( [Ni(en)_3]^{2+} \) is greater than that of \( [Ni(NH_3)_6]^{2+} \)".
- This statement is correct. Ethylenediamine (en) is a stronger field ligand compared to ammonia (NH₃), leading to a higher stability constant for the \( [Ni(en)_3]^{2+} \) complex.

- **Statement 4**: "The octahedral complex \( [Cr(H_2O)_6]^{3+} \) is more stable than the given complex".
- This statement is incorrect. \( [Cr(H_2O)_6]^{3+} \) involves weak field ligands, and if compared with a strong field ligand complex, it would generally be less stable.

3. **Conclusion**:
- Based on the analysis, the only true statement is Statement 3. Therefore, the correct answer to the question is:
- **Option C**: "The stability constant for \( [Ni(en)_3]^{2+} \) is greater than that of \( [Ni(NH_3)_6]^{2+} \)".