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, we will follow these steps:

### Step 1: Determine the oxidation number of iron in the coordination sphere (A)

Given the complex formula \( \text{Fe}_4[\text{Fe(CN)}_6]_3 \), we need to find the oxidation state of iron in the coordination sphere.

1. The overall charge of the coordination complex \( [\text{Fe(CN)}_6]^{3-} \) is -4 (since there are 4 Fe ions).
2. Each CN ligand has a charge of -1, and there are 6 CN ligands, contributing a total charge of -6.
3. Let the oxidation state of iron in the coordination sphere be \( x \). The equation can be set up as follows:
\[ x + 6(-1) = -4 \]
\[ x - 6 = -4 \]
\[ x = +2 \]
Thus, \( A = +2 \).

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

The secondary valencies correspond to the number of ligands attached to the central metal ion. In this case, the central iron ion is coordinated by 6 CN ligands.

Thus, \( B = 6 \).

### Step 3: Calculate the effective atomic number of iron in the coordination sphere (C)

The effective atomic number (EAN) can be calculated using the formula:
\[ \text{EAN} = Z + 2L + O \]
where:
- \( Z \) is the atomic number of iron (26),
- \( L \) is the number of ligands (6),
- \( O \) is the oxidation state of the metal ion (+2).

Substituting the values:
\[ C = 26 + 2(6) + (-2) \]
\[ C = 26 + 12 - 2 \]
\[ C = 36 \]

### Step 4: Calculate the value of \( C + A - 2B \)

Now we can substitute the values of \( C \), \( A \), and \( B \) into the expression:
\[ C + A - 2B = 36 + 2 - 2(6) \]
\[ = 36 + 2 - 12 \]
\[ = 26 \]

### Final Answer
The value of \( C + A - 2B \) is \( 26 \).

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