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 need to understand the relationship between octahedral and tetrahedral complexes.

### Step-by-Step Solution:

1. **Identify the Coordination Numbers**:
- The complex \([CoCl_6]^{4-}\) has a coordination number of 6, indicating it is an octahedral complex.
- The complex \([CoCl_4]^{2-}\) has a coordination number of 4, indicating it is a tetrahedral complex.

**Hint**: Coordination number helps determine the geometry of the complex.

2. **Understand Crystal Field Splitting Energy (CFSE)**:
- The CFSE is a measure of the energy difference between the split d-orbitals in a crystal field.
- For octahedral complexes, the CFSE can be calculated using the formula:
\[ \text{CFSE} = \frac{n_t}{2} \Delta - \frac{n_e}{2} \Delta \]
where \(n_t\) is the number of electrons in the t2g orbitals and \(n_e\) is the number of electrons in the eg orbitals.

3. **Relate CFSE of Tetrahedral to Octahedral**:
- The relationship between the CFSE of tetrahedral (\(\Delta_t\)) and octahedral (\(\Delta_o\)) complexes is given by:
\[ \Delta_t = \frac{4}{9} \Delta_o \]
- Here, \(\Delta_o\) is the crystal field splitting energy for the octahedral complex.

4. **Substitute the Given Value**:
- We know that for \([CoCl_6]^{4-}\), \(\Delta_o = 18000 \, \text{cm}^{-1}\).
- Therefore, we can calculate \(\Delta_t\):
\[ \Delta_t = \frac{4}{9} \times 18000 \, \text{cm}^{-1} \]

5. **Calculate \(\Delta_t\)**:
- Performing the calculation:
\[ \Delta_t = \frac{4 \times 18000}{9} = \frac{72000}{9} = 8000 \, \text{cm}^{-1} \]

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

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