The correct order of increasing `C-O` bond lengths in `CO, CO_3^(2-)` and ` CO_2` is :

Options

A. `CO_2 lt CO_3^(2-) lt CO`
B. `CO lt CO_3^(2-) lt CO_2`
C. `CO_3^(2-) lt CO_2 lt CO`
D. `CO lt CO_2 lt CO_3^(2-)`

Explanation

To determine the correct order of increasing C-O bond lengths in CO, CO₃²⁻, and CO₂, we will follow these steps:

### Step 1: Determine the Bond Order of Each Molecule
- **CO (Carbon Monoxide)**: CO has a triple bond between carbon and oxygen, which means it has a bond order of 3.

- **CO₂ (Carbon Dioxide)**: CO₂ has a double bond between carbon and each oxygen atom. Thus, the bond order for each C-O bond in CO₂ is 2.

- **CO₃²⁻ (Carbonate Ion)**: In CO₃²⁻, carbon is bonded to three oxygen atoms with a resonance structure. The effective bond order can be calculated as follows: there are 3 bonds (one for each C-O) and the overall charge is -2, which gives a bond order of 2 (since the total number of bonds is divided by the number of bond pairs).

### Step 2: Compare the Bond Orders
- CO: Bond Order = 3
- CO₂: Bond Order = 2
- CO₃²⁻: Bond Order = 2

### Step 3: Analyze the Bond Lengths
Bond length is inversely related to bond order. Therefore:
- The molecule with the highest bond order (CO) will have the shortest bond length.
- CO₂ and CO₃²⁻ both have a bond order of 2, but we need to consider their stability to determine which has a longer bond length.

### Step 4: Stability Consideration
- CO is a neutral molecule and is very stable.
- CO₂ is also a neutral molecule and quite stable.
- CO₃²⁻ is an ion and generally less stable than neutral molecules.

Since CO₂ is more stable than CO₃²⁻, we can conclude that:
- CO₂ will have a shorter bond length than CO₃²⁻.

### Conclusion: Order of Increasing C-O Bond Lengths
Based on the bond orders and stability:
1. CO (shortest bond length)
2. CO₂
3. CO₃²⁻ (longest bond length)

Thus, the correct order of increasing C-O bond lengths is:
**CO₃²⁻ > CO₂ > CO**