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

Options

A. `CO_(3)^(2-)ltCO_(2)ltCO`
B. `CO_(2)ltCO_(3)^(2-)ltCO`
C. `COltCO_(3)^(2-)ltCO_(2)`
D. `COltCO_(2)ltCO_(3)^(2-)`

Answer

To determine the correct order of increasing C-O bond length for CO, CO₃²⁻, and CO₂, we need to analyze the bond order for each of these compounds. The bond length is inversely related to bond order; thus, a higher bond order corresponds to a shorter bond length.

### Step-by-Step Solution:

1. **Analyze CO₂ (Carbon Dioxide)**:
- CO₂ has a linear structure with two double bonds (C=O).
- The bond order can be calculated as follows:
- There are 2 bonds between carbon and oxygen.
- Therefore, the bond order for CO₂ = 2.
- Since it has a bond order of 2, it will have a relatively short bond length.

2. **Analyze CO₃²⁻ (Carbonate Ion)**:
- The carbonate ion has resonance structures. The most common resonance structures are:
- O=C(O⁻)-O⁻ (with one double bond and two single bonds).
- The bond order can be calculated:
- There are 3 resonance structures contributing to the bond between C and O.
- Total bonds counted: 4 (2 from the double bond and 2 from the single bonds).
- Bond order = Total bonds / Number of resonance structures = 4 / 3 = 1.33.
- The bond order of 1.33 indicates a longer bond length compared to CO₂.

3. **Analyze CO (Carbon Monoxide)**:
- CO has a triple bond (C≡O).
- The bond order for CO is 3.
- This indicates that CO has the shortest bond length among the three compounds.

4. **Determine the Order of Bond Lengths**:
- Now that we have the bond orders:
- CO: Bond order = 3 (shortest bond length)
- CO₂: Bond order = 2 (intermediate bond length)
- CO₃²⁻: Bond order = 1.33 (longest bond length)
- Therefore, the order of increasing C-O bond length is:
- CO₃²⁻ > CO₂ > CO

### Final Answer:
The correct order of increasing C-O bond length is:
**CO₃²⁻ > CO₂ > CO**