The bond length of `C = O` bond in `CO` is `1.20 Å` and in `CO_(2)` it is `1.34 Å` Then `C = O` bond length in `CO_(3)^(2-)` will be .

Options

A. `1.50Å`
B. `1.34Å`
C. `1.29Å`
D. `0.95Å`

Explanation

To determine the bond length of the C=O bond in \( CO_3^{2-} \), we can follow these steps:

### Step 1: Understand Bond Length and Bond Order
Bond length is inversely proportional to bond order. This means that as the bond order increases (more bonds between atoms), the bond length decreases.

### Step 2: Analyze Given Data
We have the following bond lengths:
- In carbon monoxide (CO), the bond length of the C≡O bond (triple bond) is 1.20 Å.
- In carbon dioxide (CO₂), the bond length of the C=O bond (double bond) is 1.34 Å.

### Step 3: Determine the Bond Order in \( CO_3^{2-} \)
In the carbonate ion \( CO_3^{2-} \), the carbon atom is bonded to three oxygen atoms. The resonance structures of \( CO_3^{2-} \) show that there are three equivalent structures, each contributing to the overall structure. The bond order can be calculated as follows:

\[ \text{Bond Order} = \frac{\text{Number of bonds}}{\text{Number of bond locations}} = \frac{4}{3} \text{ (since there are 3 C=O bonds)} \]

### Step 4: Compare Bond Lengths
Since the bond order in \( CO_3^{2-} \) is \( \frac{4}{3} \), which is less than 2 (the bond order of C=O in CO₂) but more than 1 (the bond order of a single bond), we can infer that the bond length of C=O in \( CO_3^{2-} \) will be longer than 1.34 Å but shorter than 1.20 Å.

### Step 5: Estimate the Bond Length
Given that the bond length increases with decreasing bond order, we can estimate that the bond length of C=O in \( CO_3^{2-} \) will be somewhat longer than that of C=O in CO₂. A reasonable estimate would be around 1.28 Å.

### Final Answer
The bond length of the C=O bond in \( CO_3^{2-} \) is approximately **1.28 Å**.

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