Which structure is linear ?

Options

A. (a) `SO_2`
B. (b) `CO_2`
C. (c) `CO_3^(2-)`
D. (d) `SO_4^(2-)`

Explanation

To determine which of the given structures is linear, we will analyze each molecule based on its hybridization and geometry. Here’s a step-by-step solution:

### Step 1: Identify the Molecules
The molecules we need to analyze are:
- A) SO2
- B) CO2
- C) CO3²⁻
- D) SO4²⁻

### Step 2: Calculate Hybridization for Each Molecule
We will use the formula for hybridization:
\[ H = \frac{1}{2} \left( V + M - C \right) \]
Where:
- \( V \) = Valence electrons of the central atom
- \( M \) = Number of monovalent atoms attached to the central atom
- \( C \) = Total charge on the molecule (with sign)

#### A) SO2
- Central atom: Sulfur (S)
- Valence electrons (V) = 6 (for S)
- Monovalent atoms (M) = 0 (O is divalent)
- Charge (C) = 0

Calculating hybridization:
\[ H = \frac{1}{2} (6 + 0 - 0) = \frac{6}{2} = 3 \]
Hybridization: **sp²** (Trigonal planar geometry, but shape is bent due to one lone pair).

#### B) CO2
- Central atom: Carbon (C)
- Valence electrons (V) = 4 (for C)
- Monovalent atoms (M) = 0
- Charge (C) = 0

Calculating hybridization:
\[ H = \frac{1}{2} (4 + 0 - 0) = \frac{4}{2} = 2 \]
Hybridization: **sp** (Linear geometry).

#### C) CO3²⁻
- Central atom: Carbon (C)
- Valence electrons (V) = 4 (for C)
- Monovalent atoms (M) = 0
- Charge (C) = -2

Calculating hybridization:
\[ H = \frac{1}{2} (4 + 0 + 2) = \frac{6}{2} = 3 \]
Hybridization: **sp²** (Trigonal planar geometry).

#### D) SO4²⁻
- Central atom: Sulfur (S)
- Valence electrons (V) = 6 (for S)
- Monovalent atoms (M) = 0
- Charge (C) = -2

Calculating hybridization:
\[ H = \frac{1}{2} (6 + 0 + 2) = \frac{8}{2} = 4 \]
Hybridization: **sp³** (Tetrahedral geometry).

### Step 3: Determine the Linear Structure
From our analysis:
- SO2 has a bent shape (due to one lone pair).
- CO2 has a linear shape.
- CO3²⁻ has a trigonal planar shape.
- SO4²⁻ has a tetrahedral shape.

### Conclusion
The molecule that has a linear structure is **CO2**. Therefore, the answer is:
**Option B: CO2**