Correct order of bond length is

Options

A. `CO_3^(2-) gt CO_2 gt CO`
B. `CO_2 gt CO gt CO_3^(2-)`
C. `CO gt CO_2 gt CO_3^(2-)`
D. None of the above

Answer

To determine the correct order of bond lengths for the given compounds (CO, CO2, and CO3^2-), we can follow these steps:

### Step 1: Understand Bond Order
Bond order is a measure of the number of chemical bonds between a pair of atoms. It is calculated using the formula:
\[ \text{Bond Order} = \frac{\text{Number of Bonds}}{\text{Number of Resonating Structures}} \]
A higher bond order indicates a stronger bond and a shorter bond length, while a lower bond order indicates a weaker bond and a longer bond length.

### Step 2: Analyze CO (Carbon Monoxide)
For CO:
- The structure is C≡O (triple bond).
- There is only one significant resonance structure.
- Therefore, the bond order is:
\[ \text{Bond Order}_{CO} = \frac{3}{1} = 3 \]

### Step 3: Analyze CO2 (Carbon Dioxide)
For CO2:
- The structure is O=C=O (double bonds).
- There are two significant resonance structures (O=C=O and O^- - C^+ - O).
- Therefore, the bond order is:
\[ \text{Bond Order}_{CO2} = \frac{4}{2} = 2 \]

### Step 4: Analyze CO3^2- (Carbonate Ion)
For CO3^2-:
- The structures include one C=O double bond and two C-O single bonds, with resonance structures.
- There are three significant resonance structures.
- Therefore, the bond order is:
\[ \text{Bond Order}_{CO3^{2-}} = \frac{4}{3} \approx 1.33 \]

### Step 5: Compare Bond Orders
Now we can summarize the bond orders:
- CO: Bond Order = 3
- CO2: Bond Order = 2
- CO3^2-: Bond Order ≈ 1.33

### Step 6: Determine Bond Lengths
Since bond length is inversely proportional to bond order, we can deduce the bond lengths:
- CO has the highest bond order (3) and thus the shortest bond length.
- CO2 has a bond order of 2, which means a longer bond length than CO.
- CO3^2- has the lowest bond order (1.33) and thus the longest bond length.

### Final Order of Bond Lengths
From longest to shortest bond length, the order is:
\[ \text{CO3}^{2-} > \text{CO2} > \text{CO} \]

### Conclusion
The correct order of bond lengths is:
\[ \text{CO3}^{2-} > \text{CO2} > \text{CO} \]

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