Which of the following statements are not correct?

Options

A. All `C-O` bonds in `CO_(3)^(2-)` are equal but not in `H_(2)CO_(3)`
B. All `C-O` bonds in `HCO_(2)^(-)` are equal but not in `HCO_(2)H`
C. `C-O` bond length in `HCO_(2)^(-)` is longer than `C-O` bond length in `CO_(3)^(2-)`
D. `C-O` bond length in `HCO_(2)^(-) and C-O` bond length in `CO_(3)^(2-)` are equal

Explanation

To determine which statements are not correct regarding the structures and bond lengths of CO3²⁻ (carbonate ion) and HCO₂⁻ (formate ion), we will analyze each option step by step.

### Step 1: Draw the Lewis Structures
- **HCO₂⁻ (Formate Ion)**:
- The Lewis structure shows a central carbon atom bonded to two oxygen atoms (one with a double bond and one with a single bond) and one hydrogen atom. The carbon has a formal charge of 0, and the overall charge of the ion is -1.

- **CO3²⁻ (Carbonate Ion)**:
- The Lewis structure shows a central carbon atom bonded to three oxygen atoms, with one double bond and two single bonds. The formal charges are distributed such that the overall charge of the ion is -2.

### Step 2: Analyze Each Statement
- **Option A**: "All CO bonds in CO3²⁻ are equal but not in H2CO3."
- **Analysis**: In CO3²⁻, the resonance structures show that all CO bonds are equivalent due to resonance. In H2CO3, the bonds are not equivalent due to the presence of hydrogen atoms affecting the bond lengths.
- **Conclusion**: This statement is correct.

- **Option B**: "All CO bonds in HCO₂⁻ are equal but not in HCO₂H."
- **Analysis**: In HCO₂⁻, the CO bonds are equal due to resonance. However, in HCO₂H (formic acid), the presence of the hydrogen atom alters the bond lengths, making them unequal.
- **Conclusion**: This statement is correct.

- **Option C**: "CO bond length in HCO₂⁻ is longer than CO bond length in CO3²⁻."
- **Analysis**: The bond order in HCO₂⁻ is 1.5 (due to resonance), while in CO3²⁻, the bond order is 4/3 (approximately 1.33). Since bond order is inversely proportional to bond length, a higher bond order corresponds to a shorter bond length. Therefore, the CO bond length in HCO₂⁻ is shorter than in CO3²⁻.
- **Conclusion**: This statement is incorrect.

- **Option D**: "CO bond length in HCO₂⁻ and CO bond length in CO3²⁻ are equal."
- **Analysis**: As established, the bond lengths are not equal due to different bond orders. HCO₂⁻ has a bond order of 1.5, while CO3²⁻ has a bond order of approximately 1.33, indicating that the bond lengths differ.
- **Conclusion**: This statement is incorrect.

### Final Conclusion
The statements that are not correct are:
- **Option C**: "CO bond length in HCO₂⁻ is longer than CO bond length in CO3²⁻."
- **Option D**: "CO bond length in HCO₂⁻ and CO bond length in CO3²⁻ are equal."