Which of the following has longest `C-O` bond length? (Free `C-O` bond length in CO is `1.128Å`).

Options

A. (a) `[Mn(CO)_6]^(+)`
B. (b) `Ni(CO)_4`
C. (c) `[Co(CO)_4]^(ө)`
D. (d) `[Fe(CO)_4]^(2-)`

Explanation

To determine which of the given compounds has the longest C-O bond length, we need to analyze the bond order of the C-O bond in each compound. The bond order is inversely related to bond length; that is, a higher bond order corresponds to a shorter bond length, and a lower bond order corresponds to a longer bond length.

### Step-by-Step Solution:

1. **Identify the Compounds**: The compounds given are:
- A) Mn(CO)6^+
- B) Ni(CO)4
- C) Co(CO)4^-
- D) Fe(CO)4^2-

2. **Understand Bond Order**: The bond order of the C-O bond in carbon monoxide (CO) is 3 (due to the triple bond). In coordination complexes, the bond order can change due to back-bonding from the metal to the CO ligand.

3. **Assess the Charge on Metal Ions**: The charge on the metal ion affects the extent of back-bonding:
- Mn in Mn(CO)6^+ has a +1 charge.
- Ni in Ni(CO)4 has a 0 charge.
- Co in Co(CO)4^- has a -1 charge.
- Fe in Fe(CO)4^2- has a -2 charge.

4. **Evaluate Back-Bonding**:
- More negative charges on the metal ion lead to increased electron density and stronger back-bonding with CO. This results in a lower bond order for the C-O bond.
- Therefore, the order of back-bonding strength (and thus the effect on bond order) is:
- Fe(CO)4^2- > Co(CO)4^- > Ni(CO)4 > Mn(CO)6^+

5. **Determine Bond Order**:
- For Fe(CO)4^2-, the bond order will be the lowest due to the highest back-bonding, leading to the longest C-O bond.
- For Co(CO)4^-, the bond order will be higher than that of Fe but lower than Ni.
- For Ni(CO)4, the bond order will be higher than Co and Fe.
- For Mn(CO)6^+, the bond order will be the highest due to the least back-bonding.

6. **Conclusion**: Since Fe(CO)4^2- has the lowest bond order due to the highest back-bonding, it will have the longest C-O bond length.

### Final Answer:
The compound with the longest C-O bond length is **D) Fe(CO)4^2-**.