A blue colour complex is obtained in the analysis of `Fe^(+3)` having formula `Fe_(4)[Fe(CN)_(6)]_(3)`
Let a= oxidation number of Iron in the corrdination sphere
b= no. of secondary valencies of central iron ion.
c=Effective atomic number of Iron in the coordination sphere.
Then find the value of (c+a-2b)

Answer

To solve the problem step by step, let's break down the components of the complex \( Fe_4[Fe(CN)_6]_3 \) and find the values of \( a \), \( b \), and \( c \).

### Step 1: Determine the oxidation number of Iron in the coordination sphere (a)

The complex has the formula \( Fe_4[Fe(CN)_6]_3 \).

1. The cyanide ion \( CN^- \) is a monodentate ligand with a charge of -1.
2. In the coordination sphere \( [Fe(CN)_6]^{3-} \), the overall charge is -3.
3. Since there are 6 cyanide ligands, their total contribution to the charge is \( 6 \times (-1) = -6 \).
4. Let the oxidation state of the iron in the coordination sphere be \( x \). The equation can be set up as follows:

\[ x + (-6) = -3 \]

5. Solving for \( x \):

\[ x - 6 = -3 \implies x = +3 \]

Thus, the oxidation number of iron in the coordination sphere \( a = +3 \).

### Step 2: Determine the number of secondary valencies of central iron ion (b)

The secondary valency corresponds to the coordination number of the central iron ion in the complex.

1. In the complex \( [Fe(CN)_6]^{3-} \), there are 6 cyanide ligands coordinated to the iron ion.
2. Therefore, the coordination number (or secondary valency) \( b = 6 \).

### Step 3: Calculate the Effective Atomic Number (EAN) of Iron in the coordination sphere (c)

To find the Effective Atomic Number (EAN), we use the formula:

\[ \text{EAN} = Z + 2 \times \text{Coordination Number} - \text{Oxidation State} \]

Where:
- \( Z \) is the atomic number of iron, which is 26.
- The coordination number is 6 (from step 2).
- The oxidation state is +3 (from step 1).

Substituting the values into the formula:

\[ \text{EAN} = 26 + 2 \times 6 - 3 \]

Calculating this gives:

\[ \text{EAN} = 26 + 12 - 3 = 35 \]

Thus, the Effective Atomic Number \( c = 35 \).

### Step 4: Calculate the final expression \( c + a - 2b \)

Now we can substitute the values of \( a \), \( b \), and \( c \) into the expression:

\[ c + a - 2b = 35 + 3 - 2 \times 6 \]

Calculating this gives:

\[ c + a - 2b = 35 + 3 - 12 = 26 \]

### Final Answer

The value of \( c + a - 2b \) is \( 26 \).

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