In metal carbonyls, the increase in C-O bond length in CO as compared to carbon monoxide is due to :

Options

A. The donation of lone pair of electrons on the carbon into a vacant orbital of the metal atom
B. The donation of a pair of electrons from a filled d-orbital of metal into the vacant antibonding `pi` orbital of carbon monoxide
C. (A) and (B) both
D. None

Explanation

To solve the question regarding the increase in C-O bond length in metal carbonyls compared to carbon monoxide, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Metal Carbonyls**:
- Metal carbonyls are complexes formed between a metal and carbon monoxide (CO) ligands. In these complexes, CO acts as a ligand, coordinating to the metal center.

2. **Synergic Bonding Concept**:
- In metal carbonyls, there is a phenomenon known as synergic bonding. This involves the interaction between the filled d-orbitals of the metal and the vacant anti-bonding π* orbitals of CO.

3. **Electron Donation**:
- The filled d-orbitals of the metal donate a lone pair of electrons to the vacant anti-bonding π* orbital of CO. This process is crucial for the stabilization of the metal-carbonyl bond.

4. **Effect on Bond Order**:
- The bond order of a bond is calculated using the formula:
\[ \text{Bond Order} = \frac{(\text{Number of Bonding Electrons} - \text{Number of Anti-bonding Electrons})}{2} \]
- When electrons are donated to the anti-bonding π* orbital, the number of anti-bonding electrons increases.

5. **Decrease in Bond Order**:
- As the number of anti-bonding electrons increases due to the donation from the metal, the bond order of the C-O bond decreases. A lower bond order indicates a weaker bond.

6. **Relationship Between Bond Order and Bond Length**:
- There is an inverse relationship between bond order and bond length. This means that as the bond order decreases, the bond length increases.

7. **Conclusion**:
- Therefore, the increase in C-O bond length in metal carbonyls as compared to free carbon monoxide is due to the donation of a pair of electrons from the filled d-orbital of the metal into the vacant anti-bonding π* orbital of carbon monoxide, which decreases the bond order and consequently increases the bond length.

### Final Answer:
The increase in C-O bond length in metal carbonyls compared to carbon monoxide is due to the donation of a pair of electrons from the filled d-orbital of the metal into the vacant anti-bonding π* orbital of carbon monoxide.

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