A covalent bond will be formed by the overlapping of atomic orbitals having single electron of opposite spin, according to the overlapping of atomic orbitals the covalent bond may be of two types :
(i) Sigma bond `(sigma) " " (ii) ` Pi bond `(pi)`
Sigma bond is stronger bond than the Pi-bond. If atomic orbitals overlap about the nuclear axis then sigma bond is formed but when atomic orbitals overlap sideway then Pi-bond is formed.
The correct order of increasing 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 the compounds CO (carbon monoxide), CO₃²⁻ (carbonate), and CO₂ (carbon dioxide), we need to analyze the bond orders of each compound and understand how bond order relates to bond length.

### Step-by-Step Solution:

1. **Identify the Compounds**: We have three compounds to analyze:
- Carbon monoxide (CO)
- Carbonate ion (CO₃²⁻)
- Carbon dioxide (CO₂)

2. **Determine the Bond Order for Each Compound**:
- **Carbon Monoxide (CO)**:
- CO has a triple bond (one sigma bond and two pi bonds).
- The bond order is 3.

- **Carbonate Ion (CO₃²⁻)**:
- In the carbonate ion, there are three oxygen atoms bonded to carbon.
- The resonance structures show that one oxygen forms a double bond with carbon and the other two form single bonds.
- The average bond order can be calculated as follows:
- Total bonds = 4 (2 double bonds and 2 single bonds)
- Number of bonds = 3 (to 3 oxygen atoms)
- Bond order = Total bonds / Number of bonds = 4 / 3 = 1.33.

- **Carbon Dioxide (CO₂)**:
- CO₂ has a double bond between carbon and each oxygen (linear structure).
- The bond order is 2.

3. **Relate Bond Order to Bond Length**:
- Bond order is inversely related to bond length. Higher bond order means shorter bond length.
- Therefore, we can summarize 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)

4. **Establish the Order of Increasing Bond Length**:
- Since bond length increases as bond order decreases, we can arrange the compounds in order of increasing bond length:
- CO < CO₂ < CO₃²⁻
- Thus, the order of increasing C-O bond length is:
- CO < CO₂ < CO₃²⁻

5. **Final Answer**:
- The correct order of increasing C-O bond length is: CO < CO₂ < CO₃²⁻.