C-O bond length is minimum in

The correct option is CO.

To determine in which species the C-O bond length is minimum, we can analyze the bond order of the carbon-oxygen bonds in each of the given species. Bond length is inversely proportional to bond order. A higher bond order indicates a stronger, shorter bond.
Let us calculate the bond order for each option:

1. CO (Carbon Monoxide):
In carbon monoxide, there is a triple bond between the carbon and oxygen atoms ($C\equiv O$). Therefore, the bond order of the C-O bond in CO is 3.

2. CO₂ (Carbon Dioxide):
Carbon dioxide has a linear structure where the carbon atom forms double bonds with two oxygen atoms ($O=C=O$). The bond order of each C-O bond in CO₂ is 2.

3. HCOO⁻ (Formate Ion):
The formate ion exhibits resonance between two equivalent structures. The resonance hybrid shares a double bond character over two C-O bonds:
The bond order can be calculated using the formula:
$\text{Bond Order}=\frac{\text{Total number of bonding pairs between C and O}}{\text{Total number of resonating positions}}$
Here, there are 3 bonding pairs distributed over 2 positions:
$\text{Bond Order of HCOO}{⁻}^{}=\frac{3}{2}=1.5$

4. CO₃²⁻ (Carbonate Ion):
The carbonate ion has three resonance structures. The double bond character is distributed over three C-O bonds:
Here, there are 4 bonding pairs distributed over 3 positions:
$\text{Bond Order of CO}{₃}_{}^{\text{2-}}=\frac{4}{3}\approx 1.33$

Comparing the bond orders:
- CO: 3
- CO₂: 2
- HCOO⁻: 1.5
- CO₃²⁻: 1.33

Since carbon monoxide (CO) has the highest bond order (3), it has the strongest and shortest carbon-oxygen bond. Therefore, the C-O bond length is minimum in CO.