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

Options

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

Answer

To determine the correct order of C-O bond lengths among CO, CO3^(2-), and CO2, we will calculate the bond order for each molecule and then relate it to bond length. The bond length is inversely proportional to bond order; thus, a higher bond order corresponds to a shorter bond length.

### Step 1: Calculate the bond order for CO
- **Molecule:** CO (Carbon Monoxide)
- **Total Electrons:** Carbon has 6 electrons, and Oxygen has 8 electrons, giving a total of 14 electrons.
- **Molecular Orbital Configuration:**
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², (π(2p_x)², π(2p_y)²), σ(2p_z)², (π*(2p_x)¹, π*(2p_y)¹)
- **Bond Order Calculation:**
- Bonding Electrons = 10 (σ and π orbitals)
- Antibonding Electrons = 4 (σ* and π* orbitals)
- Bond Order = (Bonding Electrons - Antibonding Electrons) / 2 = (10 - 4) / 2 = 3

### Step 2: Calculate the bond order for CO2
- **Molecule:** CO2 (Carbon Dioxide)
- **Bonding Structure:** C=O (double bond)
- **Bond Order Calculation:**
- CO2 has a double bond between C and O.
- Bond Order = 2 (since there are 2 bonds between C and O)

### Step 3: Calculate the bond order for CO3^(2-)
- **Molecule:** CO3^(2-) (Carbonate Ion)
- **Resonance Structures:** The carbonate ion has three resonance structures, with one C=O double bond and two C-O single bonds.
- **Bond Order Calculation:**
- Total number of bonds in resonance structures = 4 (1 double bond + 2 single bonds)
- Total number of resonance structures = 3
- Bond Order = Total Bonds / Total Structures = 4 / 3 = 1.33

### Step 4: Compare bond orders and determine bond lengths
- **Bond Orders:**
- CO: 3
- CO2: 2
- CO3^(2-): 1.33
- **Bond Length Order:** Since bond length is inversely proportional to bond order:
- CO (highest bond order) < CO2 < CO3^(2-) (lowest bond order)

### Conclusion
The correct order of C-O bond lengths is:
**CO < CO2 < CO3^(2-)**