`Fe_(4)[Fe(CN)_(6)]_(3)` a blue coloured complex. Average oxidation number of Fe in `Fe_4[Fe(CN)_6]_3` is 'a', oxidation number of central iron atom 'b', oxidation number of counter iron atom 'c', a, b, c are respectively:

Options

A. `+5/2, +2, +3`
B. `+5/2, +3, +2`
C. `+(18)/(7), +2, +3`
D. `+(18)/(7), +3, +2`

Answer

To find the average oxidation number of iron (Fe) in the complex \( \text{Fe}_4[\text{Fe(CN)}_6]_3 \), we will follow these steps:

### Step 1: Identify the components of the complex
The complex consists of:
- 4 iron (Fe) atoms in total.
- One central iron atom in the complex ion \( [\text{Fe(CN)}_6]^{3-} \).
- Three \( [\text{Fe(CN)}_6]^{3-} \) complexes.

### Step 2: Determine the charge of the complex ion
The charge of the complex ion \( [\text{Fe(CN)}_6]^{3-} \) is -3. Since there are three of these complex ions in the formula, the total negative charge contributed by them is:
\[ 3 \times (-3) = -9 \]

### Step 3: Determine the charge of the counter ions
The overall charge of the entire complex \( \text{Fe}_4[\text{Fe(CN)}_6]_3 \) must be neutral. Therefore, the total positive charge from the 4 iron atoms must balance the -9 charge from the complex ions.

Let the oxidation number of the counter iron atoms be \( c \) and the oxidation number of the central iron atom be \( b \).

### Step 4: Assign oxidation states
1. For the central iron atom in \( [\text{Fe(CN)}_6]^{3-} \):
- Each cyanide ion (CN) has a charge of -1.
- Therefore, for 6 CN ions, the total charge is \( -6 \).
- Let the oxidation state of the central iron atom be \( b \). The equation for the charge balance is:
\[ b + (-6) = -3 \implies b - 6 = -3 \implies b = +3 \]

2. For the counter iron atoms:
- There are 3 counter iron atoms, and we denote their oxidation state as \( c \).
- The total charge from the 4 iron atoms must balance the -9 charge from the complex ions:
\[ 3c + b = +9 \]
Substituting \( b = +3 \):
\[ 3c + 3 = 9 \implies 3c = 6 \implies c = +2 \]

### Step 5: Calculate the average oxidation number of iron
The average oxidation number \( a \) can be calculated using the total oxidation states of all iron atoms:
- Total oxidation state from 1 central iron atom: \( +3 \)
- Total oxidation state from 3 counter iron atoms: \( 3 \times +2 = +6 \)

Thus, the total oxidation state of all iron atoms is:
\[ 3 + 6 = 9 \]
Since there are 4 iron atoms in total, the average oxidation number \( a \) is:
\[ a = \frac{9}{4} = 2.25 \]

### Summary of Results
- Average oxidation number of Fe, \( a = 2.25 \)
- Oxidation number of the central iron atom, \( b = +3 \)
- Oxidation number of the counter iron atoms, \( c = +2 \)

### Final Answers
- \( a = 2.25 \)
- \( b = +3 \)
- \( c = +2 \)