Which of the following species has a linear shape?

Options

A. `NO_2^(-)`
B. `SO_2`
C. `NO_2^(+)`
D. `O_3`

Explanation

To determine which of the given species has a linear shape, we will analyze each option using the concept of hybridization and molecular geometry.

### Step-by-Step Solution:

1. **Identify the Species**: The species we need to analyze are NO2-, SO2, NO2+, and O3.

2. **Analyze NO2-**:
- **Valence Electrons**: Nitrogen (N) has 5 valence electrons, and each oxygen (O) has 6 valence electrons. For NO2-, we have:
- Total = 5 + (2 × 6) + 1 (for the negative charge) = 18 valence electrons.
- **Hybridization Calculation**:
- Hybridization = (Number of valence electrons on central atom + Number of monovalent atoms attached - Charge) / 2
- = (5 + 0 - 1) / 2 = 6 / 2 = 3 (sp2 hybridization).
- **Shape**: The presence of a lone pair on nitrogen leads to a bent shape, not linear.

3. **Analyze SO2**:
- **Valence Electrons**: Sulfur (S) has 6 valence electrons, and each oxygen has 6 valence electrons. For SO2, we have:
- Total = 6 + (2 × 6) = 18 valence electrons.
- **Hybridization Calculation**:
- Hybridization = (6 + 0) / 2 = 3 (sp2 hybridization).
- **Shape**: Similar to NO2-, SO2 also has a bent shape due to lone pairs.

4. **Analyze NO2+**:
- **Valence Electrons**: For NO2+, we have:
- Total = 5 + (2 × 6) - 1 (for the positive charge) = 16 valence electrons.
- **Hybridization Calculation**:
- Hybridization = (5 + 0 + 1) / 2 = 6 / 2 = 3 (sp hybridization).
- **Shape**: With no lone pairs on nitrogen, NO2+ has a linear shape.

5. **Analyze O3**:
- **Valence Electrons**: Ozone (O3) has:
- Total = 3 × 6 = 18 valence electrons.
- **Hybridization Calculation**:
- Hybridization = (6 + 0) / 2 = 3 (sp2 hybridization).
- **Shape**: Ozone has a bent shape due to the presence of lone pairs.

6. **Conclusion**:
- The only species that has a linear shape is **NO2+**.

### Final Answer:
The species that has a linear shape is **NO2+**.