Among the following metal carbonyls, the `C-O` bond order is lowest in

Options

A. `[Mn(CO)_(6)]^(+)
B. `[Fe(CO)_(5)]
C. `(Cr(CO)_(6)]`
D. `(V(CO)_(6)]^(-)`

Answer

To determine which metal carbonyl has the lowest C-O bond order among the given options, we need to analyze the concept of back-bonding and the oxidation states of the metals involved. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Concept of Back-Bonding
Back-bonding occurs when the metal donates electron density to the empty π* (pi star) orbitals of the CO ligand. This interaction strengthens the metal-carbon bond and affects the C-O bond order.

**Hint:** Remember that back-bonding increases with the electron density on the metal.

### Step 2: Identify the Oxidation States of the Metals
The oxidation state of the metal influences its electron density. A lower oxidation state typically means higher electron density, which enhances back-bonding. The metals in the carbonyl complexes will have different oxidation states:

- For example, consider the following metals:
- Vanadium (V) in -1 oxidation state
- Chromium (Cr) in 0 oxidation state
- Iron (Fe) in 0 oxidation state
- Manganese (Mn) in +1 oxidation state

**Hint:** The lower the oxidation state, the more electron density the metal has.

### Step 3: Analyze the Back-Bonding Strength
- Vanadium in -1 oxidation state will have the highest electron density, leading to strong back-bonding and thus a stronger metal-CO bond. This results in a longer C-O bond length and a lower C-O bond order.
- Manganese in +1 oxidation state will have the least electron density, resulting in weak back-bonding. This leads to a shorter C-O bond length and a higher C-O bond order.

**Hint:** Strong back-bonding means a stronger metal-CO bond, which inversely affects the C-O bond order.

### Step 4: Compare the Bond Orders
Given the trend:
- Vanadium (-1) > Chromium (0) > Iron (0) > Manganese (+1) in terms of back-bonding strength.
- Therefore, the C-O bond order will be lowest in the carbonyl complex with Vanadium because it has the highest back-bonding.

**Hint:** The more back-bonding, the lower the C-O bond order.

### Conclusion
Among the given metal carbonyls, the C-O bond order is lowest in the carbonyl complex with Vanadium (V) in the -1 oxidation state.

**Final Answer:** The metal carbonyl with the lowest C-O bond order is that of Vanadium (-1 oxidation state).