Which of the following complexes has maximum CFSE?

Options

A. `K_(3)[Fe(CN)_(6)]`
B. `K_(3)[Co(Ox)_(3)]`
C. `K_(3)[CoF_(6)]`
D. `K_(3)[Co(CN)_(6)]`

Explanation

To determine which of the following complexes has the maximum Crystal Field Stabilization Energy (CFSE), we will analyze each complex step by step.

### Step 1: Identify the complexes and their oxidation states
We have the following complexes:
1. K3[Fe(CN)6]
2. K3[Co(C2O4)3]
3. K3[CoF6]
4. K3[Co(CN)6]

We need to find the oxidation state of the metal in each complex.

### Step 2: Calculate the oxidation state for each complex
1. **K3[Fe(CN)6]**:
- Let the oxidation state of Fe be \( x \).
- \( 3(+1) + 6(-1) + x = 0 \)
- \( x = +3 \)

2. **K3[Co(C2O4)3]**:
- Let the oxidation state of Co be \( x \).
- \( 3(+1) + 3(-2) + x = 0 \)
- \( x = +3 \)

3. **K3[CoF6]**:
- Let the oxidation state of Co be \( x \).
- \( 3(+1) + 6(-1) + x = 0 \)
- \( x = +3 \)

4. **K3[Co(CN)6]**:
- Let the oxidation state of Co be \( x \).
- \( 3(+1) + 6(-1) + x = 0 \)
- \( x = +3 \)

### Step 3: Determine the electronic configuration of the metal ions
- For **Fe(III)**:
- Electronic configuration: \( [Ar] 3d^5 \)

- For **Co(III)**:
- Electronic configuration: \( [Ar] 3d^6 \)

### Step 4: Determine the ligand field strength
- **CN⁻** is a strong field ligand.
- **C2O4²⁻ (oxalate)** is a weak field ligand.
- **F⁻** is a weak field ligand.

### Step 5: Fill the d-orbitals based on the ligand field strength
1. **K3[Fe(CN)6]** (strong field):
- Configuration: \( t_{2g}^5 \) (all electrons paired in t2g)
- CFSE = \( 5(-0.4\Delta_o) + 0(0.6\Delta_o) = -2.0\Delta_o \)

2. **K3[Co(C2O4)3]** (weak field):
- Configuration: \( t_{2g}^4 e_g^2 \)
- CFSE = \( 4(-0.4\Delta_o) + 2(0.6\Delta_o) = -1.6\Delta_o + 1.2\Delta_o = -0.4\Delta_o \)

3. **K3[CoF6]** (weak field):
- Configuration: \( t_{2g}^3 e_g^3 \)
- CFSE = \( 3(-0.4\Delta_o) + 3(0.6\Delta_o) = -1.2\Delta_o + 1.8\Delta_o = +0.6\Delta_o \)

4. **K3[Co(CN)6]** (strong field):
- Configuration: \( t_{2g}^6 \)
- CFSE = \( 6(-0.4\Delta_o) + 0(0.6\Delta_o) = -2.4\Delta_o \)

### Step 6: Compare the CFSE values
- K3[Fe(CN)6]: CFSE = -2.0Δo
- K3[Co(C2O4)3]: CFSE = -0.4Δo
- K3[CoF6]: CFSE = +0.6Δo
- K3[Co(CN)6]: CFSE = -2.4Δo

### Conclusion
The complex with the maximum CFSE is **K3[CoF6]** with a CFSE of +0.6Δo.