In the complex `K_2Fe[Fe(CN)_6]`

Options

A. the complex is high spin complex
B. both Fe atoms are in the same oxidation state
C. the coordination number of iron is 4
D. both Fe atoms are in different oxidation state

Answer

To analyze the complex \( K_2Fe[Fe(CN)_6] \) and evaluate the provided statements, we will follow these steps:

### Step 1: Determine the oxidation states of iron in the complex
The complex \( K_2Fe[Fe(CN)_6] \) contains two potassium ions (K), which have an oxidation state of +1 each. The ferrocyanide ion \( [Fe(CN)_6]^{4-} \) has a charge of -4.

Let the oxidation state of iron in the complex be \( x \). The overall charge of the complex must equal the sum of the charges of the components:

\[ 2(+1) + x + (-4) = 0 \]

This simplifies to:

\[ 2 + x - 4 = 0 \implies x - 2 = 0 \implies x = +2 \]

Thus, both iron atoms in the complex are in the +2 oxidation state.

### Step 2: Analyze the nature of the ligands
The ligand \( CN^- \) is known to be a strong field ligand. Strong field ligands cause a large splitting of the d-orbitals, which can lead to pairing of electrons.

### Step 3: Determine the electron configuration of iron
For \( Fe^{2+} \), the electron configuration is:

\[ [Ar] 3d^6 \]

### Step 4: Determine the spin state of the complex
In the presence of strong field ligands like \( CN^- \), the splitting energy (Δ) is greater than the pairing energy. Thus, the six electrons in the \( 3d \) orbitals will pair up:

\[ \text{Electron configuration: } \uparrow\downarrow \uparrow\downarrow \uparrow\downarrow \]

This results in no unpaired electrons, indicating that the complex is a low-spin complex.

### Step 5: Determine the coordination number of iron
In the complex \( [Fe(CN)_6]^{4-} \), there are six cyanide ligands coordinating to the iron atom. Therefore, the coordination number of iron is 6.

### Step 6: Evaluate the statements
1. **The complex is high-spin**: **False** (it is low-spin due to strong field ligands).
2. **Both iron atoms are in the same oxidation state**: **True** (both are +2).
3. **The coordination number of iron is 4**: **False** (the coordination number is 6).
4. **Both iron atoms are in different oxidation states**: **False** (both are +2).

### Conclusion
The only correct statement about the complex \( K_2Fe[Fe(CN)_6] \) is that both iron atoms are in the same oxidation state (+2).

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