The V-C distance in `V(CO)_(5)` and `[V(CO)_(6)]^(-)` are respectively (in pm):

Options

A. 200,200
B. 193,200
C. 200,193
D. 193,193

Answer

To determine the V-C bond lengths in \( V(CO)_5 \) and \( [V(CO)_6]^(-) \), we can follow these steps:

### Step 1: Understand the Concept of Backbonding
Backbonding occurs when there is a donation of electron density from the filled d-orbitals of the metal (in this case, vanadium) to the empty π* orbitals of the carbon monoxide (CO) ligands. This interaction strengthens the bond between the metal and the ligand, leading to shorter bond lengths.

**Hint:** Remember that backbonding is crucial in determining bond lengths in metal-carbon complexes.

### Step 2: Analyze the Number of CO Ligands
In \( V(CO)_5 \), there are 5 CO ligands, while in \( [V(CO)_6]^(-) \), there are 6 CO ligands. The more CO ligands present, the greater the extent of backbonding due to increased overlap between the metal d-orbitals and the π* orbitals of CO.

**Hint:** More ligands generally lead to stronger backbonding, which affects bond lengths.

### Step 3: Compare the Extent of Backbonding
Since \( [V(CO)_6]^(-) \) has one more CO ligand than \( V(CO)_5 \), it will experience greater backbonding. This means that the V-C bond length in \( [V(CO)_6]^(-) \) will be shorter than that in \( V(CO)_5 \).

**Hint:** Consider how the number of ligands influences the strength of the metal-ligand bond.

### Step 4: Determine the Bond Lengths
Based on the analysis:
- The bond length in \( V(CO)_5 \) will be longer due to less backbonding.
- The bond length in \( [V(CO)_6]^(-) \) will be shorter due to increased backbonding.

### Step 5: Choose the Correct Option
From the options provided:
1. 200 pm and 200 pm (not possible, as they cannot have the same bond length)
2. 193 pm and 200 pm (not possible, as \( V(CO)_5 \) should have a longer bond length)
3. 200 pm and 193 pm (this is correct, as \( V(CO)_5 \) has a longer bond length)
4. 193 pm and 193 pm (not possible, as they cannot have the same bond length)

Thus, the correct answer is **200 pm for \( V(CO)_5 \) and 193 pm for \( [V(CO)_6]^(-) \)**.

**Final Answer:** The V-C distances in \( V(CO)_5 \) and \( [V(CO)_6]^(-) \) are 200 pm and 193 pm, respectively.