In which of the following carbonyls, the bond length of CO is the highest ?

Options

A. `[V(CO)_6]^-`
B. `[Cr(CO)_6]`
C. `[Mn(CO)_6]^+`
D. `[Fe(CO)_4]^(2-)`

Answer

To determine which carbonyl has the highest CO bond length, we need to analyze the bond order of the carbonyl complexes given. The bond length of CO is inversely proportional to its bond order; therefore, a lower bond order corresponds to a longer bond length.

### Step-by-Step Solution:

1. **Understanding Bond Order and Bond Length**:
- Bond order is defined as the number of chemical bonds between a pair of atoms. A higher bond order means a stronger bond and a shorter bond length.
- Conversely, a lower bond order results in a weaker bond and a longer bond length.

2. **Identifying the Carbonyl Complexes**:
- We need to consider the metal center in each carbonyl complex and its oxidation state, as this affects the electron density and consequently the bond order of the CO bond.

3. **Analyzing the Given Carbonyls**:
- Let's denote the carbonyls as follows:
- A: Co(CO)₄
- B: Cr(CO)₆
- C: Mn(CO)₅⁺
- D: Fe(CO)₄²⁻

4. **Determining the Charge on the Metal**:
- Co in A: 0 (neutral)
- Cr in B: 0 (neutral)
- Mn in C: +1
- Fe in D: -2

5. **Evaluating the Electron Density**:
- The higher the positive charge on the metal, the lower the electron density, which leads to less π back-bonding with CO.
- Conversely, a lower positive charge (or a negative charge) on the metal increases the electron density, enhancing π back-bonding and increasing the bond order of CO.

6. **Comparing the Bond Orders**:
- For Co(CO)₄ (neutral): Moderate π back-bonding.
- For Cr(CO)₆ (neutral): Moderate π back-bonding.
- For Mn(CO)₅⁺ (+1): Weaker π back-bonding due to +1 charge.
- For Fe(CO)₄²⁻ (-2): Strong π back-bonding due to -2 charge.

7. **Conclusion on Bond Order**:
- The bond order of CO will be lowest in the case of Fe(CO)₄²⁻ due to the strong π back-bonding, which means the bond length of CO will be the highest in this complex.

### Final Answer:
The carbonyl with the highest CO bond length is **Fe(CO)₄²⁻**.