The crystal field splitting energy (CFSE) for `[CoCl_(6)]^(4-)` is about `"18000 cm"^(-1)`. What would be the CFSE value for `[CoCl_(4)]^(2-)`?

Answer

To find the crystal field splitting energy (CFSE) for the complex \([CoCl_4]^{2-}\), we can use the relationship between the CFSE of octahedral and tetrahedral complexes.

### Step-by-Step Solution:

1. **Identify the CFSE for \([CoCl_6]^{4-}\)**:
- We are given that the CFSE for \([CoCl_6]^{4-}\) is \(18000 \, \text{cm}^{-1}\). This complex has an octahedral geometry.

2. **Understand the Geometry**:
- The complex \([CoCl_6]^{4-}\) is octahedral, while \([CoCl_4]^{2-}\) is tetrahedral. The splitting energy in octahedral complexes is greater than that in tetrahedral complexes.

3. **Use the Relationship Between Octahedral and Tetrahedral Splitting**:
- The relationship between the crystal field splitting energies of octahedral (\(\Delta_{oct}\)) and tetrahedral (\(\Delta_{tet}\)) complexes is given by:
\[ \Delta_{tet} = \frac{4}{9} \Delta_{oct} \]

4. **Calculate the Tetrahedral Splitting Energy**:
- Substitute the value of \(\Delta_{oct}\) (which corresponds to the CFSE of \([CoCl_6]^{4-}\)):
\[ \Delta_{tet} = \frac{4}{9} \times 18000 \, \text{cm}^{-1} \]
- Calculate:
\[ \Delta_{tet} = \frac{4 \times 18000}{9} = \frac{72000}{9} = 8000 \, \text{cm}^{-1} \]

5. **Conclusion**:
- Therefore, the CFSE for the tetrahedral complex \([CoCl_4]^{2-}\) is \(8000 \, \text{cm}^{-1}\).

### Final Answer:
The CFSE value for \([CoCl_4]^{2-}\) is \(8000 \, \text{cm}^{-1}\).

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