If the bond length of \(CO\) bond in carbon monoxide is 1.128 Å, then what is the value of \(CO\) bond length in \(Fe(CO)_5\)?

1.15 Å

The correct answer is option 1. 1.15 Å.

In the complex \( \text{Fe(CO)}_5 \), the CO bonds are influenced by the electronic environment of the iron center. The bonding situation in \( \text{Fe(CO)}_5 \) involves both σ-donation from the CO ligands to the metal and \(\pi \)-backbonding from the metal to the CO ligands.

Factors Affecting CO Bond Length in \( \text{Fe(CO)}_5 \):

1. \(\sigma \)-Donation: CO ligands donate electron density to the metal center through their lone pair on carbon, which stabilizes the metal center but does not significantly affect the CO bond length.

2. \(\pi \)-Backbonding: The metal center can also accept electron density from the CO's \(\pi ^*\) orbitals (antibonding orbitals), which weakens the CO bond in the ligand. This \(\pi \)-backbonding typically results in a longer CO bond length compared to free CO.

Bond Length Comparison:

Free CO: The bond length of CO in free carbon monoxide is approximately 1.128 Å.

In \( \text{Fe(CO)}_5 \): The π-backbonding causes the CO bond length to be longer due to the weakening of the CO bond. Typically, this bond length increases because the bond order of CO decreases in the complex.

In \( \text{Fe(CO)}_5 \), the CO bond length is expected to be longer than that of free CO. Among the given options, the bond length of about 1.15 Å is the most reasonable value for the CO bond in \( \text{Fe(CO)}_5 \).

Conclusion: The CO bond length in \( \text{Fe(CO)}_5 \) is approximately 1.15 Å.