Which of the following is (are) V-shaped?

Options

A. `S_(3)^(2-)`
B. `I_(3)^(-)`
C. `N_(3)^(-)`
D. `I_(3)^(+)`

Answer

To determine which of the given molecules are V-shaped, we will analyze their hybridization and molecular geometry using the concept of the steric number (SN). The steric number is calculated as the sum of the number of bonded pairs and lone pairs of electrons around the central atom.

### Step-by-Step Solution:

1. **Identify the Molecules**: The molecules we need to analyze are:
- \( \text{S}_3^{2-} \)
- \( \text{I}_3^{-} \)
- \( \text{N}_3^{-} \)
- \( \text{I}_3^{+} \)

2. **Analyze \( \text{S}_3^{2-} \)**:
- Sulfur (S) has a valency of 6. In \( \text{S}_3^{2-} \), the total number of valence electrons is \( 6 + 2 = 8 \).
- The structure would have 2 double bonds with sulfur and 2 lone pairs.
- **Steric Number (SN)**: 2 (bond pairs) + 2 (lone pairs) = 4.
- **Hybridization**: \( \text{sp}^3 \).
- **Geometry**: Tetrahedral, but with 2 lone pairs, the shape becomes V-shaped.

3. **Analyze \( \text{I}_3^{-} \)**:
- Iodine (I) has a valency of 7. In \( \text{I}_3^{-} \), the total number of valence electrons is \( 7 \times 3 + 1 = 22 \).
- The structure has 2 bond pairs and 3 lone pairs.
- **Steric Number (SN)**: 2 (bond pairs) + 3 (lone pairs) = 5.
- **Hybridization**: \( \text{sp}^3\text{d} \).
- **Geometry**: Trigonal bipyramidal, but with 3 lone pairs, the shape is not V-shaped.

4. **Analyze \( \text{N}_3^{-} \)**:
- Nitrogen (N) has a valency of 5. In \( \text{N}_3^{-} \), the total number of valence electrons is \( 5 \times 3 + 1 = 16 \).
- The structure has 2 bond pairs and no lone pairs.
- **Steric Number (SN)**: 2 (bond pairs) + 0 (lone pairs) = 2.
- **Hybridization**: \( \text{sp} \).
- **Geometry**: Linear, not V-shaped.

5. **Analyze \( \text{I}_3^{+} \)**:
- Iodine (I) has a valency of 7. In \( \text{I}_3^{+} \), the total number of valence electrons is \( 7 \times 3 - 1 = 20 \).
- The structure has 2 bond pairs and 2 lone pairs.
- **Steric Number (SN)**: 2 (bond pairs) + 2 (lone pairs) = 4.
- **Hybridization**: \( \text{sp}^3 \).
- **Geometry**: Tetrahedral, but with 2 lone pairs, the shape becomes V-shaped.

### Conclusion:
The molecules that are V-shaped are:
- \( \text{S}_3^{2-} \)
- \( \text{I}_3^{+} \)

### Summary of Findings:
- **V-shaped Molecules**: \( \text{S}_3^{2-} \) and \( \text{I}_3^{+} \)
- **Not V-shaped**: \( \text{I}_3^{-} \) and \( \text{N}_3^{-} \)