Problem 78 - A Complete Resource Book in Chemistry for JEE Main

Question

If the bond length of \(\mathrm{CO}\) bond in carbon monoxide is \(1.128 \AA\), then what is the value of \(\mathrm{CO}\) bond length in \(\mathrm{Fe}(\mathrm{CO})_{5} ?\) (a) \(1.15 \AA\) (b) \(1.128 \AA\) (c) \(1.72 \AA\) (d) \(1.118 \AA\)

Step-by-Step Solution

Answer

The CO bond length in Fe(CO)_5 is 1.15 Å.

Step 1: Understanding the Problem

The problem asks us to determine the bond length of the carbon monoxide (CO) when it is a ligand in the compound iron pentacarbonyl, Fe(CO)_5. In its free form, the CO bond length is given as 1.128 Å.

Step 2: Conceptual Insight into CO Bond Length in Metal Carbonyls

In metal carbonyl complexes like Fe(CO)_5, the CO bond length changes due to back-donation. The metal donates electron density into the anti-bonding orbital of CO, which weakens the C-O bond, causing the bond length to increase.

Step 3: Predict the CO Bond Length Change

Knowing that the CO bond length increases when it acts as a ligand in metal complexes, we should expect the CO bond length in Fe(CO)_5 to be longer than in free CO.

Step 4: Evaluate the Options

Among the given options, (a) 1.15 Å seems plausible as it is slightly longer than the free CO bond length 1.128 Å. The obvious increase in length would be expected in a complex due to back-donation.

Key Concepts

Back-donation

Back-donation is a fascinating concept in chemistry, particularly in coordination chemistry involving transition metals. It refers to the transfer of electron density from a metal to a ligand, but in the opposite direction compared to the usual donation from the ligand to the metal. In the context of metal carbonyls, such as iron pentacarbonyl \(Fe(CO)_5\), back-donation plays a crucial role. Here, the metal atom (iron, in this case) donates electron density into the antibonding π* orbitals of the carbon monoxide ligands. This may sound complex, but it essentially means that the metal and the CO are sharing more electrons in a different way than typical ligand-to-metal bonding.

• The back-donation weakens the CO bond because the antibonding orbitals are not meant to hold shared electrons efficiently.
• As a result, back-donation leads to changes in the physical properties of the CO molecule.

Back-donation is an essential concept to understand for predicting changes in molecular geometries and bond strengths in metal complexes.

CO Bond Length

The CO bond length is another key characteristic to explore when discussing metal carbonyls. The bond length of CO is a measure of the distance between the carbon and oxygen atoms within the molecule. In free carbon monoxide, the bond length is quite short, at approximately 1.128 Å, indicative of a strong triple bond composed of one σ bond and two π bonds. However, when CO is a ligand in metal carbonyls like \(Fe(CO)_5\), things change. Due to back-donation:

• Electron donation into the CO antibonding orbitals causes the C-O bond to weaken.
• This weakening reflects in a longer bond length as the atoms aren't held as tightly together.

In the example of \(Fe(CO)_5\), the predicted bond length is approximately 1.15 Å, slightly longer than in free CO. This change is a direct result of the interaction between the metal center and CO ligands.

Iron Pentacarbonyl

Iron pentacarbonyl, or \(Fe(CO)_5\), is a classic example of a metal carbonyl complex. It's made up of an iron atom surrounded by five carbon monoxide molecules. This structure stands out because it showcases the role of back-donation prominently. The iron atom serves as the central metal and can effectively back-donate electron density into the CO ligands. Characteristics:

• The molecular geometry is trigonal bipyramidal, a common shape for five-coordinate metal complexes.
• This allows for efficient back-donation and stabilization of the complex.

Iron pentacarbonyl is significant in research and industrial applications, as understanding its structure can aid in the synthesis and application of other complex organometallic compounds. These fundamental principles help chemists predict how different ligands might interact with metals, influencing everything from reactivity to potential uses in catalysis.