The correct order of increasig `C-O` bond length of `CO, CO_(3)^(2-), CO_(2)` is

Options

A. `CO_(3)^(2-) lt CO_(2) lt CO`
B. `CO_(2) lt CO_(3)^(2-) lt CO`
C. `CO lt CO_(3)^(2-) lt CO_(2)`
D. `CO lt CO_(2) lt CO_(3)^(2-)`

Answer

To determine the correct order of increasing `C-O` bond length for `CO`, `CO3^(2-)`, and `CO2`, we need to analyze the bond order of each compound. The bond length is inversely related to bond order; that is, a higher bond order corresponds to a shorter bond length.

### Step-by-Step Solution:

1. **Analyze Carbon Monoxide (CO)**:
- Carbon monoxide (CO) has a triple bond between carbon and oxygen.
- The bond order for CO is 3 (since a triple bond consists of three shared pairs of electrons).
- Higher bond order means a shorter bond length.

2. **Analyze Carbon Dioxide (CO2)**:
- Carbon dioxide (CO2) has a double bond between carbon and each oxygen atom.
- The structure can be represented as O=C=O.
- The bond order for each `C=O` bond is 2.
- This bond order is lower than that of CO, indicating a longer bond length than CO.

3. **Analyze Carbonate Ion (CO3^(2-))**:
- The carbonate ion (CO3^(2-)) has resonance structures. The most significant resonance structures include one C=O bond and two C-O bonds.
- The bond order can be calculated as follows:
- Total number of bonds in all resonance structures = 4 (considering the three resonance structures).
- Total number of resonance structures = 3.
- Therefore, the bond order = Total bonds / Total structures = 4 / 3 ≈ 1.33.
- This bond order is lower than that of CO2, indicating that the `C-O` bond length in CO3^(2-) is longer than in CO2.

4. **Compare Bond Lengths**:
- Now we can summarize the bond orders:
- CO: Bond order = 3 (shortest bond length)
- CO2: Bond order = 2 (longer than CO)
- CO3^(2-): Bond order ≈ 1.33 (longest bond length)
- Therefore, the order of increasing `C-O` bond length is:
- CO3^(2-) > CO2 > CO

### Final Answer:
The correct order of increasing `C-O` bond length is:
**CO3^(2-) > CO2 > CO**