`[Co_2 (CO)_8]` displays :

Options

A. one Co-Co bond, six terminal CO and two bridging CO
B. one Co-Co bond, four terminal CO and four bridging CO
C. no Co-Co bond, six terminal CO and two bridging CO
D. no Co-Co bond, four terminal CO and four bridging CO

Explanation

To analyze the coordination compound \([Co_2(CO)_8]\), we will follow these steps:

### Step 1: Identify the Metal Center and Ligands
The complex contains two cobalt (Co) metal centers and eight carbon monoxide (CO) ligands.

### Step 2: Determine the Electron Count
- Cobalt (Co) has the electronic configuration of \([Ar] 3d^7 4s^2\). In its outermost shell, cobalt contributes 9 valence electrons (7 from 3d and 2 from 4s).
- Each CO ligand donates 2 electrons. Since there are 8 CO ligands, they contribute \(8 \times 2 = 16\) electrons.
- Therefore, the total electron count from the cobalt and CO ligands is:
\[ \text{Total electrons} = 2 \times 9 + 16 = 18 + 16 = 34 \text{ electrons} \]

### Step 3: Apply the 18-Electron Rule
The 18-electron rule states that a stable complex should have a total of 18 valence electrons. In this case, we have 34 electrons, which indicates that the complex is likely stable.

### Step 4: Calculate Metal-Metal Bonds
To find the number of metal-metal bonds, we can use the formula:
\[ \text{Number of metal-metal bonds} = \frac{(18 \times \text{Number of metals}) - \text{Total electrons}}{2} \]
Substituting the values:
\[ \text{Number of metal-metal bonds} = \frac{(18 \times 2) - 34}{2} = \frac{36 - 34}{2} = \frac{2}{2} = 1 \]
Thus, there is 1 metal-metal bond.

### Step 5: Identify the Bonding Mode of CO
In this complex, CO acts as both a terminal and a bridging ligand:
- Terminal CO donates 2 electrons to the metal.
- Bridging CO donates 1 electron to each of the two metal centers it connects.

### Step 6: Count the Electrons for Each Cobalt
For each cobalt:
- Cobalt has 9 of its own electrons.
- It shares 1 electron from the metal-metal bond.
- It receives electrons from the terminal CO ligands and bridging CO ligands.

Assuming there are 2 terminal and 6 bridging CO ligands:
- Each terminal CO contributes 2 electrons (total 4 from 2 terminal CO).
- Each bridging CO contributes 1 electron to each cobalt (total 6 from 6 bridging CO).

Thus, for each cobalt:
\[ \text{Electrons from own} + \text{shared} + \text{from terminal} + \text{from bridging} = 9 + 1 + 4 + 6 = 20 \]
However, since we need to ensure that each cobalt satisfies the 18-electron rule, we can adjust the count based on the actual contribution from the ligands.

### Step 7: Conclusion
The structure of \([Co_2(CO)_8]\) consists of:
- 1 metal-metal bond.
- 2 terminal CO ligands.
- 6 bridging CO ligands.

### Final Answer
The coordination compound \([Co_2(CO)_8]\) displays 1 metal-metal bond, 2 terminal CO bonds, and 6 bridging CO bonds.

---