Question

The order of the M–C bond strength in the following species is (Atomic number for Cr = 24, Mn = 25, Ti = 22, Co = 27)
\[ \text{[Cr(CO)}_6] \text{[Mn(CO)}_6]^+ \text{[Ti(CO)}_6]^{2-} \text{[Co(CO)}_6]^+ \]

• A. II > I > IV > III
• B. I > III > II > IV
• C. III > IV > I > II
• D. III > I > II > IV

Hint:

A metal in a lower oxidation state generally has a stronger M–C bond due to greater electron density and enhanced \(\pi\)-back donation to the CO ligands.

Answer 1

The Correct Option is C

To determine the order of the M–C bond strength in the given species \(\text{[Cr(CO)}_6]\), \(\text{[Mn(CO)}_6]^+\), \(\text{[Ti(CO)}_6]^{2-}\), and \(\text{[Co(CO)}_6]^+\), we need to consider the metal-to-carbon monoxide (CO) back-bonding capability, which is influenced by the oxidation state and electronic configuration of the central metal.

1. In organometallic complexes such as these, the strength of the M–C bond is largely dependent on the back-bonding from the metal to the antibonding orbitals of CO (π-backbonding). The greater the extent of back-bonding, the stronger the M–C bond.
2. The back-bonding strength generally increases with the electron density on the metal. Thus, metals with a higher oxidation state will have weaker back-bonding due to reduced electron density.
3. Let's evaluate each complex:
   • \(\text{[Cr(CO)}_6]\): Chromium in \(\text{[Cr(CO)}_6]\) is in the zero oxidation state. Chromium has the electronic configuration \([\text{Ar}] \, 3d^5 4s^1\). Here, \(6 \times \text{CO}\) ligands use the orbitals for back-bonding.
   • \(\text{[Mn(CO)}_6]^+\): Manganese in this complex is in the +1 oxidation state. The loss of one electron reduces the back-bonding ability compared to \(\text{[Cr(CO)}_6]\).
   • \(\text{[Ti(CO)}_6]^{2-}\): Titanium here is in the -2 oxidation state, which facilitates high electron density and strong back-bonding to CO. Titanium's configuration is \([\text{Ar}] \, 3d^2 4s^2\).
   • \(\text{[Co(CO)}_6]^+\): Cobalt in the +1 oxidation state has less electron density for back-bonding, similar to manganese.
4. Based on the above consideration, the complex with titanium having the lowest oxidation number and therefore the greatest electron density for back-bonding is expected to have the strongest M–C bond, followed by cobalt and chromium. Manganese, due to higher oxidation, will have the weakest bond.

Thus, the order of M–C bond strength is: \(\text{[Ti(CO)}_6]^{2-}\) > \(\text{[Co(CO)}_6]^+\) > \(\text{[Cr(CO)}_6]\) > \(\text{[Mn(CO)}_6]^+\).

Therefore, the correct option is: III > IV > I > II.