Problem 43 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Among the following metal carbonyls, the C-O bond order is lowest in (a) \(\left[\mathrm{Mn}(\mathrm{CO})_{6}\right]^{+}\) (b) \(\left[\mathrm{Fe}(\mathrm{CO})_{5}\right]\) (c) \(\left[\mathrm{Cr}(\mathrm{CO})_{6}\right]\) (d) \(\left[\mathrm{V}(\mathrm{CO})_{6}\right]^{-}\)

Step-by-Step Solution

Answer

The C-O bond order is lowest in \\([\mathrm{V}(\mathrm{CO})_{6}]^{-}\\).

Step 1: Bond Order and Back Bonding Basics

The bond order indicates the strength of bonding in a molecule. In metal carbonyls, the metal can donate electron density to the anti-bonding orbitals of CO via back bonding, which decreases the C-O bond order.

Step 2: Analyzing Electron Donation

Back bonding involves donation from a filled metal d orbital to the CO anti-bonding \(*\pi^*\) orbital. The strength of this back bonding reduces the C-O bond order. Typically, metals with higher electron density or negative charge favor this donation.

Step 3: Investigating Each Complex

- (a) \([\mathrm{Mn}(\mathrm{CO})_{6}]^{+}\): Positive charge reduces electron density.- (b) \([\mathrm{Fe}(\mathrm{CO})_{5}]\): Comparatively neutral.- (c) \([\mathrm{Cr}(\mathrm{CO})_{6}]\): Neutral but with high electron donation capacity.- (d) \([\mathrm{V}(\mathrm{CO})_{6}]^{-}\): Negative charge increases electron density for back-bonding.

Step 4: Identifying Strongest Electron Donor

Of the options given, \([\mathrm{V}(\mathrm{CO})_{6}]^{-}\) has a negative charge, increasing electron availability for back-bonding. Thus, it has greater capability to lower the C-O bond order through back-bonding compared to the neutral or positively charged complexes.

Key Concepts

Bond Order

Bond order is a crucial concept in understanding molecular structures, especially in metal carbonyls. It refers to the number of chemical bonds between a pair of atoms. A higher bond order generally indicates a stronger bond. In metal carbonyls, bond order is directly related to the interaction between the metal and the carbonyl (CO) group.
A reduction in bond order suggests a weakening of the bond, which can occur in metal carbonyls due to a phenomenon known as back bonding. The bond order in the carbonyl group can be calculated using molecular orbital theory, where back bonding plays a significant role in reducing it.

Back Bonding

Back bonding, or pi-backbonding, is an essential interaction in transition metal complexes like metal carbonyls. It occurs when a metal donates electrons from its filled d orbitals to the empty anti-bonding \(*\pi^*\) orbitals of the CO ligands. This donation strengthens the metal-carbon (M-C) bond but weakens the carbon-oxygen (C-O) bond.
The most favorable conditions for back bonding are when the metal has high electron density and CO possesses strong \(*\pi^*\) accepting capabilities. This interaction illustrates how metals can redirect electron density, affecting the bond order in these complexes.

Electron Donation

Electron donation is a fundamental part of back bonding. It involves the transfer of electron density from the d orbitals of the metal. Metals with high electron density or negative charge are more effective at donating these electrons.

• Metals in a negatively charged state, such as in \([{\mathrm{V}}(\mathrm{CO})_{6}]^{-}\), are particularly efficient at electron donation.
• This increased electron donation leads to more significant weakening of the C-O bond, resulting in a lower bond order.

Thus, the ability of a metal in a carbonyl to donate electrons is critical in predicting and understanding its structural and bonding properties.

C-O Bond

The carbon-oxygen bond in metal carbonyls, often referred to as the C-O bond, is a key factor in determining the characteristics of these complexes. The strength and length of the C-O bond are influenced by interactions like back bonding.
In the presence of back bonding, the C-O bond becomes weaker as electron density moves away from CO towards the metal. This bond weakening is directly observable as a decrease in bond order.

• For example, in \([\mathrm{V}(\mathrm{CO})_{6}]^{-}\), the C-O bond order is low, due to the negative charge on the vanadium, which enhances electron donation.
• This results in shorter CO-stretching frequencies as observed in spectroscopic studies.

Understanding these interactions is vital in the study of metal carbonyl chemistry.