The total crystal field stabilization energy (CFSE) for the complexes `[Co(H_(2)O)_(6)]^(3+)` and `[CoF_(6)]^(3-)` are respectively : (P is the pairing energy)

Options

A. `-24dq+2P" and "-24dq+2P`
B. `-24dq+2P" and "-4.0dq`
C. `-4.0dq" and "-4.0dq`
D. `4.0dq" and "0`

Explanation

To calculate the total crystal field stabilization energy (CFSE) for the complexes \([Co(H_2O)_6]^{3+}\) and \([CoF_6]^{3-}\), we will follow these steps:

### Step 1: Determine the oxidation state and electron configuration of cobalt in both complexes.
- In \([Co(H_2O)_6]^{3+}\), cobalt is in the +3 oxidation state. The electron configuration of cobalt is \([Ar] 3d^7 4s^2\). Therefore, in the +3 state, cobalt has the configuration \(3d^6\).
- In \([CoF_6]^{3-}\), cobalt is also in the +3 oxidation state, so it also has the configuration \(3d^6\).

### Step 2: Identify the nature of the ligands.
- Water (\(H_2O\)) is a strong field ligand, which means it will cause pairing of electrons in the \(d\) orbitals.
- Fluoride (\(F^-\)) is a weak field ligand, which means it will not cause pairing of electrons.

### Step 3: Determine the electron distribution in the \(d\) orbitals for both complexes.
- For \([Co(H_2O)_6]^{3+}\):
- Since \(H_2O\) is a strong field ligand, the \(3d^6\) electrons will pair up in the \(T_{2g}\) orbitals. The configuration will be \(T_{2g}^6 E_g^0\).

- For \([CoF_6]^{3-}\):
- Since \(F^-\) is a weak field ligand, the \(3d^6\) electrons will distribute as \(T_{2g}^4 E_g^2\) without pairing.

### Step 4: Calculate the CFSE for each complex.
- The formula for CFSE is:
\[ \text{CFSE} = \left(-\frac{2}{5} \Delta_o \times \text{(number of electrons in } T_{2g})\right) + \left(\frac{3}{5} \Delta_o \times \text{(number of electrons in } E_g)\right) + \text{(pairing energy)} \]

- For \([Co(H_2O)_6]^{3+}\):
- \(T_{2g} = 6\), \(E_g = 0\), and since all electrons are paired, the pairing energy \(P\) will be counted.
\[ \text{CFSE} = \left(-\frac{2}{5} \Delta_o \times 6\right) + \left(\frac{3}{5} \Delta_o \times 0\right) + 2P \]
\[ \text{CFSE} = -\frac{12}{5} \Delta_o + 2P \]

- For \([CoF_6]^{3-}\):
- \(T_{2g} = 4\), \(E_g = 2\), and there is no pairing, so \(P = 0\).
\[ \text{CFSE} = \left(-\frac{2}{5} \Delta_o \times 4\right) + \left(\frac{3}{5} \Delta_o \times 2\right) + 0 \]
\[ \text{CFSE} = -\frac{8}{5} \Delta_o + \frac{6}{5} \Delta_o = -\frac{2}{5} \Delta_o \]

### Final Results:
- For \([Co(H_2O)_6]^{3+}\): \(\text{CFSE} = -\frac{12}{5} \Delta_o + 2P\)
- For \([CoF_6]^{3-}\): \(\text{CFSE} = -\frac{2}{5} \Delta_o\)