The hybridisation of Fe in `K_(4)[Fe(CN)_(6)]` is

Options

A. `dsp^(2)`
B. `sp^(3)`
C. `d^(2)sp^(3)`
D. `sp^(3)d^(2)`

Answer

To determine the hybridization of Fe in \( K_4[Fe(CN)_6] \), we can follow these steps:

### Step 1: Determine the oxidation state of iron (Fe)
- In the complex \( K_4[Fe(CN)_6] \), potassium (K) has an oxidation state of +1. Since there are four potassium ions, their total contribution to the charge is \( 4 \times (+1) = +4 \).
- The cyanide ion (CN) is a monodentate ligand with a charge of -1. Since there are six cyanide ions, their total contribution is \( 6 \times (-1) = -6 \).
- The overall charge of the complex is neutral (0). Therefore, we can set up the equation:
\[ +4 + X - 6 = 0 \]
where \( X \) is the oxidation state of Fe.
- Solving for \( X \):
\[ X - 2 = 0 \implies X = +2 \]
- Thus, the oxidation state of Fe in \( K_4[Fe(CN)_6] \) is +2.

### Step 2: Determine the electronic configuration of Fe
- The atomic number of iron (Fe) is 26. The electronic configuration of neutral Fe is:
\[ [Ar] 3d^6 4s^2 \]
- Since Fe is in the +2 oxidation state, it loses two electrons, typically from the 4s orbital first. Therefore, the electronic configuration of \( Fe^{2+} \) is:
\[ [Ar] 3d^6 \]

### Step 3: Identify the type of ligands and their field strength
- Cyanide (CN\(^-\)) is a strong field ligand. Strong field ligands cause pairing of electrons in the d-orbitals.

### Step 4: Fill the d-orbitals considering pairing
- In the presence of a strong field ligand like CN\(^-\), the 3d electrons will pair up. The arrangement of the d-electrons in \( Fe^{2+} \) (3d\(^6\)) will be:
- 3d: ↑↓ ↑↓ ↑ ↑ (pairing occurs)

### Step 5: Determine the hybridization
- With 6 ligands (6 CN\(^-\) ions), the hybridization can be determined as follows:
- 2 electrons from the paired 3d orbitals, 1 from the 4s orbital, and 3 from the 4p orbitals will be used for bonding.
- This leads to the hybridization:
\[ d^2sp^3 \]
- Therefore, the hybridization of Fe in \( K_4[Fe(CN)_6] \) is \( d^2sp^3 \).

### Conclusion
The hybridization of Fe in \( K_4[Fe(CN)_6] \) is \( d^2sp^3 \).

---