Which of the following complexes is expected to have lowest `Delta_(0)` value ? [consider only magnitude]

Options

A. `[Co(NH_(3))_(6)]^(3+)`
B. `[Rh(NH_(3))_(6)]^(3+)`
C. `[Ir(NH_(3))_(6)]^(3+)`
D. `[CoF_(6)]^(3-)`

Answer

To determine which complex has the lowest crystal field splitting energy (Δ₀), we need to analyze the given complexes based on the nature of their central metal ions and the ligands involved. The complexes provided are:

1. [Rh(NH₃)₆]³⁺
2. [Co(NH₃)₆]³⁺
3. [Ir(NH₃)₆]³⁺
4. [CoF₆]³⁻

### Step-by-Step Solution:

**Step 1: Identify the central metal ions and their oxidation states.**
- For [Rh(NH₃)₆]³⁺: Rhodium (Rh) is in +3 oxidation state.
- For [Co(NH₃)₆]³⁺: Cobalt (Co) is in +3 oxidation state.
- For [Ir(NH₃)₆]³⁺: Iridium (Ir) is in +3 oxidation state.
- For [CoF₆]³⁻: Cobalt (Co) is in +3 oxidation state.

**Step 2: Determine the electron configurations of the metal ions.**
- Rh³⁺ (Rh: [Kr] 4d⁸ 5s¹) → Configuration: 4d⁶
- Co³⁺ (Co: [Ar] 3d⁷ 4s²) → Configuration: 3d⁶
- Ir³⁺ (Ir: [Xe] 4f¹⁴ 5d⁷ 6s²) → Configuration: 5d⁶ (4f electrons do not participate in bonding)
- Co³⁻ in [CoF₆]³⁻ → Configuration: 3d⁶

**Step 3: Analyze the ligands.**
- NH₃ is a strong field ligand, which causes a larger splitting of the d-orbitals.
- F⁻ is a weak field ligand, which causes a smaller splitting of the d-orbitals.

**Step 4: Compare the crystal field splitting energies (Δ₀).**
- For [Rh(NH₃)₆]³⁺ and [Co(NH₃)₆]³⁺, both have strong field ligands, leading to a higher Δ₀.
- For [Ir(NH₃)₆]³⁺, although it has strong field ligands, the presence of 4f electrons can lead to a lower Δ₀ due to increased shielding.
- For [CoF₆]³⁻, the weak field ligand (F⁻) will result in the lowest Δ₀ due to minimal splitting.

**Step 5: Conclusion.**
Based on the analysis, the complex with the lowest Δ₀ is [CoF₆]³⁻ due to the weak field ligand (F⁻) causing minimal splitting.

### Final Answer:
The complex expected to have the lowest Δ₀ value is **[CoF₆]³⁻**.