Which of the following species has a linear shape?

Options

A. `SO_(2)`
B. `NO_(2)^(+)`
C. `O_(3)`
D. `NO_(2)^(-).`

Explanation

To determine which of the following species has a linear shape, we will analyze the molecular geometry of each given species step by step.

### Step 1: Analyze SO2 (Sulfur Dioxide)
- **Valence Electrons**: Sulfur (S) has 6 valence electrons, and each oxygen (O) has 6 valence electrons. Therefore, SO2 has a total of 6 + 2(6) = 18 valence electrons.
- **Lewis Structure**: In SO2, sulfur forms double bonds with each oxygen atom. There is one lone pair of electrons on the sulfur atom.
- **Molecular Geometry**: The presence of the lone pair causes the molecule to adopt a bent shape rather than linear.

**Conclusion**: SO2 is not linear.

### Step 2: Analyze NO2+ (Nitronium Ion)
- **Valence Electrons**: Nitrogen (N) has 5 valence electrons, and each oxygen (O) has 6 valence electrons. The positive charge indicates the loss of one electron. Therefore, NO2+ has a total of 5 + 2(6) - 1 = 14 valence electrons.
- **Lewis Structure**: In NO2+, nitrogen forms double bonds with both oxygen atoms. There are no lone pairs on the nitrogen atom.
- **Molecular Geometry**: The absence of lone pairs and the presence of two double bonds lead to a linear shape.

**Conclusion**: NO2+ is linear.

### Step 3: Analyze O3 (Ozone)
- **Valence Electrons**: Each oxygen has 6 valence electrons. Therefore, O3 has a total of 3(6) = 18 valence electrons.
- **Lewis Structure**: In O3, one oxygen forms a double bond with another oxygen, while the third oxygen is connected via a single bond and has a lone pair.
- **Molecular Geometry**: The presence of a lone pair results in a bent shape.

**Conclusion**: O3 is not linear.

### Step 4: Analyze NO2- (Nitrite Ion)
- **Valence Electrons**: Nitrogen has 5 valence electrons, and each oxygen has 6 valence electrons. The negative charge indicates the addition of one electron. Therefore, NO2- has a total of 5 + 2(6) + 1 = 18 valence electrons.
- **Lewis Structure**: In NO2-, nitrogen forms one double bond with one oxygen and a single bond with the other oxygen, while there is one lone pair on the nitrogen atom.
- **Molecular Geometry**: The presence of the lone pair results in a bent shape.

**Conclusion**: NO2- is not linear.

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

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