The bond length of `C-O` bond in carbon monoxide is `1.128A` The `C-O` bond in `[fe(CO)_(5)]` is .

Options

A. `1.115A`
B. `1.128A`
C. `1.178A`
D. `1.150A`

Explanation

To determine the bond length of the C-O bond in the coordination compound [Fe(CO)5], we can follow these steps:

### Step 1: Understand the Bonding in Carbon Monoxide
The bond length of the C-O bond in carbon monoxide (CO) is given as 1.128 Å. This bond is a result of a triple bond between carbon and oxygen, which consists of one sigma (σ) bond and two pi (π) bonds.

**Hint:** Remember that bond length is influenced by bond order; higher bond order typically means shorter bond length.

### Step 2: Analyze the Coordination Compound [Fe(CO)5]
In the coordination compound [Fe(CO)5], the carbon monoxide acts as a ligand. Here, the central metal ion is iron (Fe). The bonding in this complex involves a phenomenon known as synergic bonding.

**Hint:** Synergic bonding involves both the donation of electron pairs from the ligand to the metal and the back-donation of electron density from the metal to the ligand.

### Step 3: Understand Synergic Bonding
In synergic bonding, the CO ligand donates a lone pair of electrons to the iron atom, while simultaneously, the iron can donate electron density back to the π* (antibonding) orbitals of the CO ligand. This interaction stabilizes the complex but also affects the bond characteristics.

**Hint:** Consider how the interaction between the metal and the ligand can change the effective bond order.

### Step 4: Determine the Effect on Bond Order
The back-donation of electron density from the iron to the π* orbitals of CO increases the number of antibonding electrons. As a result, the bond order of the C-O bond decreases. Bond order is calculated as:
\[ \text{Bond Order} = \frac{1}{2} (\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \]

Since the bond order decreases, the bond length of the C-O bond in [Fe(CO)5] will increase compared to that in free CO.

**Hint:** Recall that a decrease in bond order leads to an increase in bond length.

### Step 5: Estimate the New Bond Length
Given that the bond length in CO is 1.128 Å, and considering the increase in bond length due to the synergic bonding effect, we can estimate that the bond length in [Fe(CO)5] will be slightly longer. It is reasonable to conclude that the bond length will be approximately 1.150 Å.

**Hint:** Use the initial bond length as a reference point and consider how much it might increase due to the effects of synergic bonding.

### Conclusion
The bond length of the C-O bond in [Fe(CO)5] is approximately **1.150 Å**.