Question

The bond length of $CO$ is $1.128 \mathop A\limits^ \circ$ . What will be the bond length of $CO$ in $Fe{(CO)_5}$ ?
A.$1.158 \mathop A\limits^ \circ$
B.$1.128 \mathop A\limits^ \circ$
C.$1.078 \mathop A\limits^ \circ$
D.$1.118 \mathop A\limits^ \circ$

Answer 1

The bonding present in $CO$ molecules inside the coordination complex of $Fe{(CO)_5}$ is different from its bonding in the isolated state. The change in bonding patterns changes the bond order of a molecule. The bond order and bond length are inversely proportional to each other.

Complete answer:
$Fe{(CO)_5}$ is a coordination complex consisting of iron as the central metal surrounded by five carbonyl ligands. Since carbonyl groups (carbon monoxide) are neutral ligands and there is no overall charge on the coordination sphere, we observe that the central metal has zero oxidation state.
An electropositive metal surrounded by five donor ligands in zero oxidation states tends to have an accumulation of electrons around it. This high electron density around the iron atom gives it a negative formal charge making it extremely unstable.
The neutralization of this negative formal charge can only be achieved by charge dispersal which happens through synergic bonding in metal carbonyl complexes. The carbonyl molecules have empty anti bonding molecular orbitals and highest occupied non-bonding molecular orbitals that have partial anti-bonding character. Therefore, when electrons are added to a carbonyl molecule they enter the anti-bonding molecular orbitals and decrease the bond order of the carbon-oxygen bond and when electrons are removed from the non-bonding orbitals, the bond order increases to some extent due to the partial anti-bonding character of the non-bonding molecular orbitals.
The synergic bonding present in $Fe{(CO)_5}$ involves donating of electrons from carbonyl ligands to iron metal through a coordinate covalent bond and also a back-donation of electrons from the electron dense iron atom to the empty molecular orbitals of carbonyl ligand. This back-donation stabilizes the iron metal in zero oxidation state and reduces the bond order of carbon-oxygen bonds present in $CO$ .
The decreasing bond order results in an increase in bond length and the $CO$ bond gets stretched inside the complex. The bond length of $CO$ becomes longer than its length in an isolated molecule.
Hence, the correct option is (A)

Note:
The formal negative charge is an indicator of the high electron density present around an iron atom but in reality, the metal does not accept electrons to gain a negative charge. The oxidation state of the metal gives us the actual information about the number of electrons being lost or gained by the particular atom.