Question

The bond length of the C-O bond in carbon monoxide is 1.128 $\overset{\circ}{A}$
. The C-O bond length in $Fe{{(CO)}_{5}}$ is-
A. 1.115$\overset{\circ}{A}$
B. 1.128$\overset{\circ}{A}$
C. 1.178$\overset{\circ}{A}$
D. 1.150$\overset{\circ}{A}$

Answer 1

Hint: The length of the bond can be determined by the bond order. The higher the bond order, the stronger the pull between the two atoms and shorter is the bond length. Here, the ligand CO is a $\pi $-acidic ligand i.e. it is a good $\sigma $- donor and $\pi $-acceptor (due to empty pi orbitals). It forms a back bonding with Fe centre.
$\text{Bond order=}\dfrac{\text{electrons in bonding - electrons in antibonding}}{2}$

Complete step by step answer:
 The C-O bond length is 1.128$\overset{\circ}{A}$
 but in $Fe{{(CO)}_{5}}$due to the presence of an iron metal centre and a $\pi $acidic ligand- CO, synergic bonding takes place.
-The ligand (CO) donates its electron lone pair to the vacant d-orbitals of the iron atom and forms the sigma-bond.
-Since the iron atom possesses electrons in its d-orbitals, it forms anti bonding with the molecular orbitals of the ligand, forming a π-bond.
-Due to the p$\pi $-d$\pi$ back bonding the metal-carbon bond strength increases and bond length decreases due to the partial double bond character.
-Due to this anti bonding, the bond order decreases. CO bond order is 3 but in$Fe{{(CO)}_{5}}$, the bond order decreases and therefore the bond length decreases too.
In option [B] the bond length is the same and in option [C] and [D] it has increased.

Therefore, option [A] 1.115$\overset{\circ}{A}$
 where the bond strength has decreased slightly, is the correct answer.
So, the correct answer is “Option A”.

Additional Information:
Synergic bonding is known as pi back bonding, there are two bonding interactions taking place simultaneously. Firstly, the donation of electrons from the ligand to an empty orbital of the metal which gives the ligand-metal bonding interaction. If the metal has filled d orbitals, a second interaction can occur where the electrons are donated from the filled d orbitals on the metal to the empty orbital of the ligand (which is generally the anti-bonding orbital). Together, these two interactions make up synergic bonding.

Note: It is important to note here that the metal atom donates its electron pairs to the antibonding molecular orbital of CO, so the C-O bond is weakened by this synergic bonding, which might increase the C-O bond length. But here the bond order decreases which leads to a decrease in bond length.