The `pi` acceptor ligands are those which possess vacant `pi-` orbitals in addition to the lone pairs of electrons
Which of the following complex ion has the highest `C-O` bond length ?
(a) `[V(CO)_(6)]^(o+)`
(b) `Ni(CO)_(4)`
(c ) `Fe(CO)_(5)`
(d) `[Mn(CO)_(6)]^(o+)` .

Answer

To determine which complex ion has the highest C-O bond length among the given options, we need to analyze the nature of the bonding in these complexes, particularly focusing on the role of the carbonyl (CO) ligands.

### Step-by-Step Solution:

1. **Understanding Synergic Bonding**:
- Carbonyl ligands (CO) act as π-acceptor ligands. They can donate a pair of electrons from their lone pair to the metal and can also accept electrons into their vacant π* (anti-bonding) orbitals.
- This dual role leads to synergic bonding, which affects the bond order of the C-O bond.

2. **Bond Order Concept**:
- Bond order is defined as the number of bonding electrons minus the number of anti-bonding electrons divided by 2.
- A decrease in bond order results in an increase in bond length. Therefore, the more the synergic bonding, the lower the bond order, and consequently, the longer the bond length.

3. **Analyzing Each Complex**:
- **(a) [V(CO)6]^(1+)**: Vanadium has a +1 oxidation state. The positive charge reduces the electron-donating ability of the metal, leading to less effective synergic bonding.
- **(b) Ni(CO)4**: Nickel in this complex is in the zero oxidation state, which allows for better electron donation to the ligands, enhancing synergic bonding.
- **(c) Fe(CO)5**: Iron has a relatively higher oxidation state compared to nickel, which may reduce the extent of synergic bonding compared to Ni(CO)4.
- **(d) [Mn(CO)6]^(1+)**: Manganese also has a +1 oxidation state, similar to vanadium, which limits its ability to donate electrons.

4. **Comparing Synergic Bonding**:
- The complexes with positive charges ([V(CO)6]^(1+) and [Mn(CO)6]^(1+)) will have reduced synergic bonding due to the decreased ability to donate electrons.
- Between Ni(CO)4 and Fe(CO)5, Ni(CO)4, with its zero oxidation state, will have stronger synergic bonding compared to Fe(CO)5.

5. **Conclusion**:
- Since Ni(CO)4 has the highest synergic bonding, it will have the lowest C-O bond length. Conversely, [V(CO)6]^(1+) and [Mn(CO)6]^(1+) will have higher C-O bond lengths due to their reduced synergic bonding.
- Among the complexes, **Fe(CO)5** will have a higher C-O bond length than Ni(CO)4 but lower than the positively charged complexes. Therefore, the complex with the highest C-O bond length is **[Mn(CO)6]^(1+)**.

### Final Answer:
The complex ion with the highest C-O bond length is **(d) [Mn(CO)6]^(1+)**.