Which of the followig statements is/are correct?

Options

A. The carbon-di-oxide molecule behaves as a nonpolar molecule even through two of its resonating structures. `.^(-)O-C-=O^(+) and O^(+)-=C-O^(-)` are dipolar
B. Carbon di-oxide is the anhydride of the unstable dibasic acid `O=C(OH)_(2)`
C. The carbon dioxide molecule is linear because the carbon atom utilizes its sp orbitals to form `sigma` bonds
D. The carbon atom is `sp^(2)`- hybridised in the `CO_(2)` molecule as well as the molecule of its hydrate `H_(2)CO_(3)`

Answer

To determine which statements about carbon dioxide (CO2) are correct, let's analyze each statement step by step.

### Step 1: Analyze the first statement
**Statement:** Carbon dioxide molecule behaves as a nonpolar molecule, even though two of its resonating structures are dipolar.

- **Explanation:** The molecular structure of CO2 is linear, with the formula being O=C=O. The molecule has two polar bonds (C=O), but due to its linear geometry, the dipole moments of these bonds cancel each other out. Therefore, CO2 is a nonpolar molecule.

**Conclusion:** This statement is **correct**.

### Step 2: Analyze the second statement
**Statement:** Carbon dioxide is the anhydride of an unstable dibasic acid, which is C(=O)(OH)2.

- **Explanation:** The compound C(=O)(OH)2 can be identified as carbonic acid (H2CO3). When one molecule of water (H2O) is removed from carbonic acid, we obtain CO2. Hence, CO2 can indeed be considered the anhydride of carbonic acid.

**Conclusion:** This statement is **correct**.

### Step 3: Analyze the third statement
**Statement:** Carbon dioxide molecule is linear because the carbon atom utilizes its sp orbital to form sigma bonds.

- **Explanation:** In CO2, carbon is sp hybridized, forming two sigma bonds with oxygen atoms. The sp hybridization leads to a linear molecular geometry (180° bond angle), confirming that the carbon atom uses its sp orbitals for bonding.

**Conclusion:** This statement is **correct**.

### Step 4: Analyze the fourth statement
**Statement:** The carbon atom is sp2 hybridized in CO2 molecule as well as in its hydrate, which is H2CO3.

- **Explanation:** We already established that the hybridization of carbon in CO2 is sp. For H2CO3 (carbonic acid), the carbon is indeed sp2 hybridized due to the presence of three sigma bonds (two with hydroxyl groups and one double bond with oxygen). Therefore, while the hybridization in H2CO3 is sp2, it is not sp2 in CO2.

**Conclusion:** This statement is **incorrect**.

### Final Conclusion
Based on the analysis above, the correct statements are:
1. Carbon dioxide behaves as a nonpolar molecule despite having dipolar resonating structures.
2. Carbon dioxide is the anhydride of carbonic acid.
3. Carbon dioxide is linear due to the sp hybridization of carbon.

The incorrect statement is regarding the hybridization of carbon in CO2.

### Summary of Correct Statements:
- Statement 1: Correct
- Statement 2: Correct
- Statement 3: Correct
- Statement 4: Incorrect