Find the total number of Fe-Fe bonds in `Fe_(3)(CO)_(12)` if it follows EAN rule.

Explanation

To find the total number of Fe-Fe bonds in the coordination compound \( \text{Fe}_3(\text{CO})_{12} \) using the Effective Atomic Number (EAN) rule, we can follow these steps:

### Step 1: Understand the EAN Rule
The EAN rule states that the effective atomic number of a metal in a coordination compound is equal to the atomic number of the metal plus the number of electrons donated by the ligands and the metal-metal bonding electrons.

### Step 2: Identify the Atomic Number of Iron
The atomic number of iron (Fe) is 26.

### Step 3: Determine the Next Stable Noble Gas Configuration
The next stable noble gas configuration after iron is that of krypton, which has an atomic number of 36.

### Step 4: Calculate the Total EAN for the Complex
Since there are three iron atoms in the complex, the total EAN can be calculated as follows:
\[ \text{Total EAN} = 36 \times 3 = 108 \]

### Step 5: Count the Electrons from Ligands
In \( \text{Fe}_3(\text{CO})_{12} \), there are 12 CO ligands. Each CO ligand donates 2 electrons. Therefore, the total number of electrons contributed by the ligands is:
\[ \text{Electrons from ligands} = 12 \times 2 = 24 \]

### Step 6: Determine the Oxidation State of Iron
In this neutral complex, the oxidation state of iron is 0 (since CO is a neutral ligand).

### Step 7: Set Up the EAN Equation
Now we can set up the equation for EAN:
\[ \text{EAN} = \text{Atomic number of Fe} + \text{Electrons from ligands} + \text{Metal-metal electrons} \]
Substituting the known values:
\[ 108 = 26 + 24 + \text{Metal-metal electrons} \]

### Step 8: Solve for Metal-Metal Electrons
Rearranging the equation gives:
\[ \text{Metal-metal electrons} = 108 - 26 - 24 = 58 \]

### Step 9: Calculate the Number of Fe-Fe Bonds
Since each bond is formed by 2 electrons, the number of Fe-Fe bonds can be calculated by dividing the total metal-metal electrons by 2:
\[ \text{Number of Fe-Fe bonds} = \frac{58}{2} = 29 \]

### Conclusion
Thus, the total number of Fe-Fe bonds in \( \text{Fe}_3(\text{CO})_{12} \) is **29**.

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