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 solve the problem regarding the complex \( K_2Fe[Fe(CN)_6] \), we will follow these steps:

### Step 1: Determine the oxidation states of iron in the complex
The complex can be represented as \( K_2[Fe^{2+}][Fe^{2+}(CN)_6^{4-}] \).

1. The total charge of the complex must equal zero.
2. Potassium (K) has a charge of \( +1 \), and since there are 2 potassium ions, their total charge is \( +2 \).
3. The cyanide ion (CN) has a charge of \( -1 \), and there are 6 cyanide ions, contributing a total charge of \( -6 \).
4. Let the oxidation state of iron be \( x \). Since there are two iron atoms in the complex, their contribution to the charge is \( 2x \).

Setting up the equation:
\[ 2 + 2x - 6 = 0 \]
\[ 2x - 4 = 0 \]
\[ 2x = 4 \implies x = 2 \]

Thus, both iron atoms are in the \( +2 \) oxidation state.

### Step 2: Determine if the complex is high spin or low spin
1. The electronic configuration of \( Fe^{2+} \) (which has lost two electrons) is \( [Ar] 3d^6 \).
2. In the presence of cyanide (CN), which is a strong field ligand, we expect pairing of electrons to occur.
3. The \( 3d \) orbitals will fill as follows:
- The first five electrons will occupy the five \( 3d \) orbitals singly, and the sixth electron will pair up with one of the existing electrons due to the strong field nature of CN.
4. The configuration will look like this:
- \( \uparrow\downarrow \, \uparrow \, \uparrow \, \uparrow \, \uparrow \) (all paired except for one orbital)

Since all electrons are paired, there are no unpaired electrons.

### Step 3: Determine the hybridization and geometry
1. The coordination number of iron in this complex is 6 (from the 6 cyanide ligands).
2. The hybridization can be determined as \( d^2sp^3 \), which corresponds to an octahedral geometry.

### Conclusion
1. Both iron atoms are in the same oxidation state of \( +2 \).
2. The complex is a low spin complex due to the pairing of electrons caused by the strong field ligand (CN).
3. The coordination number of iron is 6, and the geometry is octahedral.

### Final Answers:
- Both Fe atoms are in the same oxidation state: **True**
- The complex is a high spin complex: **False** (it is a low spin complex)
- The coordination number of iron is 4: **False** (it is 6)
- Both Fe atoms are in different oxidation states: **False** (both are in +2 state)