Step 1: Understanding the Concept:
The Effective Atomic Number (EAN) rule states that in many coordination complexes, the central metal atom tends to surround itself with enough ligands so that the total number of electrons around it matches the atomic number of the nearest noble gas.
Step 2: Key Formula or Approach:
The formula to calculate EAN is:
\[ \text{EAN} = Z - X + Y \]
Where \( Z \) is the atomic number of the central metal atom, \( X \) is the number of electrons lost in forming the ion (oxidation state), and \( Y \) is the number of electrons gained from the ligands (usually \( 2 \times \text{Coordination Number} \)).
Step 3: Detailed Explanation:
For the complex ion \( [\text{Fe}(\text{CN})_6]^{4-} \):
The atomic number of Iron (\( \text{Fe} \)) is \( Z = 26 \).
Let the oxidation state of Fe be \( x \).
The cyanide ligand (\( \text{CN}^- \)) has a charge of -1.
Since the overall charge of the complex is -4, we have:
\[ x + 6(-1) = -4 \implies x = +2 \]
Thus, Fe is in the +2 oxidation state, meaning it has lost 2 electrons (\( X = 2 \)).
There are 6 \( \text{CN}^- \) ligands, and each ligand donates a pair of electrons.
Electrons from ligands \( Y = 6 \times 2 = 12 \).
Now, calculate the EAN:
\[ \text{EAN} = 26 - 2 + 12 = 36 \]
This matches the atomic number of the noble gas Krypton (\( \text{Kr} \)).
Step 4: Final Answer:
The Effective Atomic Number of Iron is 3
6.