To determine which complex has the highest crystal field splitting energy (Δ), we need to analyze the oxidation states of the central metal atom (cobalt in this case) and the nature of the ligands involved in each complex.
### Step-by-Step Solution:
1. **Identify the complexes and their ligands:**
- **Option A:** Co(NH₃)₅(H₂O)(Cl)₃
- **Option B:** K₃[Co(CN)₆]
- **Option C:** Co(NH₃)₅(Cl)(Cl₂)
- **Option D:** K₂[CuCl₄]
2. **Determine the oxidation state of cobalt in each complex:**
- **Option A:**
- Chlorine (Cl) has a charge of -1, and there are 3 Cl atoms, giving a total of -3.
- Ammonia (NH₃) and water (H₂O) are neutral.
- Therefore, the oxidation state of cobalt (Co) is +3.
- **Option B:**
- Cyanide (CN) has a charge of -1, and there are 6 CN groups, giving a total of -6.
- Potassium (K) has a charge of +1, and there are 3 K atoms, giving a total of +3.
- Hence, the oxidation state of cobalt is +3.
- **Option C:**
- Chlorine (Cl) has a charge of -1, and there is 1 Cl atom, and Cl₂ has a charge of -2, giving a total of -3.
- Ammonia (NH₃) is neutral.
- Therefore, the oxidation state of cobalt is +3.
- **Option D:**
- Chlorine (Cl) has a charge of -1, and there are 4 Cl atoms, giving a total of -4.
- Potassium (K) has a charge of +1, and there are 2 K atoms, giving a total of +2.
- Therefore, the oxidation state of copper (Cu) is +2.
3. **Summarize the oxidation states:**
- Options A, B, and C have cobalt in the +3 oxidation state.
- Option D has copper in the +2 oxidation state.
4. **Consider the ligand strength:**
- The ligands present are:
- Ammonia (NH₃) - moderate field strength
- Water (H₂O) - weak field strength
- Chlorine (Cl) - weak field strength
- Cyanide (CN) - strong field strength
- Among these, CN is the strongest ligand, which leads to a larger crystal field splitting energy (Δ).
5. **Determine which complex has the highest Δ:**
- Since options A, B, and C have cobalt in the +3 oxidation state, we need to compare the ligands.
- Option B has 6 CN ligands, which will provide the highest Δ due to both the strong ligand field and the high oxidation state of cobalt.
### Conclusion:
The complex with the highest crystal field splitting energy (Δ) is **Option B: K₃[Co(CN)₆]**.
