The number of sigma and `pi`-bonds in `Fe_(2)(CO)_(9)`` respectively are .

Options

A. `22sigma` and `15pi`
B. `22sigma` and `16pi`
C. `23sigma` and `15pi`
D. `15sigma` and `8pi`

Answer

To determine the number of sigma (σ) and pi (π) bonds in the complex \( \text{Fe}_2(\text{CO})_9 \), we will follow these steps:

### Step 1: Understand the Structure of the Complex
The complex \( \text{Fe}_2(\text{CO})_9 \) consists of two iron (Fe) atoms and nine carbon monoxide (CO) ligands. Among these CO ligands, one acts as a bridging ligand between the two iron atoms.

### Step 2: Draw the Structure
We can visualize the structure as follows:
- Two iron atoms are connected by one CO ligand (the bridging ligand).
- Each iron atom is also bonded to three additional CO ligands.

### Step 3: Count the Sigma Bonds
- Each CO ligand forms a sigma bond with the iron atoms.
- The bridging CO forms one sigma bond with each iron atom.
- Therefore, the sigma bonds can be counted as follows:
- 3 sigma bonds from CO ligands attached to the first Fe.
- 3 sigma bonds from CO ligands attached to the second Fe.
- 1 sigma bond from the bridging CO ligand connecting the two Fe atoms.

Calculating the total:
- From the first Fe: 3 (from CO) + 1 (bridging CO) = 4 sigma bonds
- From the second Fe: 3 (from CO) + 1 (bridging CO) = 4 sigma bonds
- Total sigma bonds = 4 + 4 = 8 sigma bonds.

However, we must also consider the sigma bonds formed by the CO ligands:
- Each CO ligand forms a sigma bond with the Fe atoms.
- Since there are 9 CO ligands, each contributing 1 sigma bond, we have 9 sigma bonds from CO ligands.

Total sigma bonds = 9 (from CO) + 1 (bridging) = 10 sigma bonds.

### Step 4: Count the Pi Bonds
- Each CO ligand also contributes a pi bond due to the presence of a lone pair on the carbon atom that overlaps with the empty d-orbitals of the iron.
- Since there are 9 CO ligands, and each contributes 1 pi bond, we have a total of 9 pi bonds from the CO ligands.

### Final Count
- Total sigma bonds = 10
- Total pi bonds = 9

### Conclusion
Thus, the number of sigma and pi bonds in \( \text{Fe}_2(\text{CO})_9 \) are:
- Sigma bonds: 10
- Pi bonds: 9