How many metal-metal bonds are present in `Co_(4)(CO)_(12)` ?

Answer

To determine the number of metal-metal bonds in the coordination compound \( Co_4(CO)_{12} \), we can follow these steps:

### Step 1: Identify the central metal and its electronic configuration
The central metal in this compound is cobalt (Co). The valence electronic configuration of cobalt is \( 3d^7 4s^2 \). This means cobalt has a total of 9 valence electrons.

### Step 2: Calculate the total number of valence electrons from cobalt
Since there are 4 cobalt atoms in the compound, the total number of valence electrons contributed by cobalt is:
\[ 9 \text{ (valence electrons per Co)} \times 4 \text{ (number of Co)} = 36 \text{ electrons} \]

### Step 3: Determine the contribution of the ligands
The ligands present in this compound are carbonyl (CO) ligands. Each carbonyl ligand donates 2 electrons. There are 12 carbonyl ligands, so the total contribution from the ligands is:
\[ 2 \text{ (electrons per CO)} \times 12 \text{ (number of CO)} = 24 \text{ electrons} \]

### Step 4: Calculate the total number of electrons
Now, we can find the total number of electrons in the coordination complex:
\[ \text{Total electrons} = \text{Electrons from Co} + \text{Electrons from CO} = 36 + 24 = 60 \text{ electrons} \]

### Step 5: Apply the EAN rule
According to the Effective Atomic Number (EAN) rule, for a complex with \( n \) metal atoms, the total number of electrons should equal \( 18n \). Here, \( n = 4 \) (since there are 4 cobalt atoms), so we expect:
\[ 18 \times 4 = 72 \text{ electrons} \]

### Step 6: Set up the equation for metal-metal bonds
Let \( x \) be the number of metal-metal bonds. Each metal-metal bond contributes 2 electrons. Therefore, the equation can be set up as follows:
\[ 2x + 60 = 72 \]

### Step 7: Solve for \( x \)
Rearranging the equation gives:
\[ 2x = 72 - 60 \]
\[ 2x = 12 \]
\[ x = 6 \]

### Conclusion
Thus, the number of metal-metal bonds present in \( Co_4(CO)_{12} \) is **6**.

---