Assertion: `C_(3)O_(2)` has linear structure.
Reason: Each carbon atom in `C_(3)O_(2)` in `sp` -hydridized.

Options

A. If assertion is true but the reason is false
B. If assertion is false but reason is true
C. If both assertion and reason are true and the reason is the correct explanation of assertion
D. If both assertion and reason are true and the reason is not the correct explanation of assertion

Answer

To analyze the given assertion and reason statements regarding \( C_3O_2 \), we will break down the problem step by step.

### Step 1: Understand the Assertion
The assertion states that \( C_3O_2 \) has a linear structure. To verify this, we need to examine the molecular structure of \( C_3O_2 \), which is known as carbon suboxide.

### Step 2: Draw the Structure of \( C_3O_2 \)
The structure of \( C_3O_2 \) can be represented as follows:
- The molecule consists of three carbon atoms and two oxygen atoms.
- The arrangement is: \( O=C=C=C=O \).
- This indicates that the carbon atoms are connected by double bonds, and the terminal carbon atoms are each double-bonded to an oxygen atom.

### Step 3: Determine the Hybridization of Carbon Atoms
Next, we analyze the hybridization of the carbon atoms in \( C_3O_2 \):
- Each carbon atom is involved in two sigma bonds (one with the adjacent carbon and one with the oxygen).
- The presence of double bonds means that there are also pi bonds, but these do not contribute to hybridization.
- Therefore, each carbon atom has a steric number of 2 (2 sigma bonds), which indicates that they are \( sp \)-hybridized.

### Step 4: Confirm the Structure
Since each carbon atom is \( sp \)-hybridized and there are no lone pairs on the carbon atoms, the molecular geometry is linear. This confirms the assertion that \( C_3O_2 \) has a linear structure.

### Step 5: Analyze the Reason
The reason states that each carbon atom in \( C_3O_2 \) is \( sp \)-hybridized. We have established that this is indeed true, as each carbon atom has a steric number of 2.

### Step 6: Conclusion
Both the assertion and the reason are true:
- Assertion: \( C_3O_2 \) has a linear structure (True).
- Reason: Each carbon atom in \( C_3O_2 \) is \( sp \)-hybridized (True).

Furthermore, the reason correctly explains the assertion because \( sp \)-hybridization leads to a linear geometry.

### Final Answer
Both the assertion and reason are true, and the reason correctly explains the assertion.

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