The molecule which is pyramidal in shape is

Options

A. `PCl_(3)`
B. `CO_(3) ^(2-)`
C. `SO_(3)`
D. `NO_(2)^(-)`

Answer

To determine which molecule is pyramidal in shape, we will analyze the given options using the concept of hybridization and steric number. The steric number can be calculated using the formula:

\[ \text{Steric Number} = \frac{1}{2} \left( V + M + \text{Charge (anion)} - \text{Charge (cation)} \right) \]

Where:
- \( V \) = number of valence electrons of the central atom
- \( M \) = number of monovalent atoms attached to the central atom
- Charge is added for anions and subtracted for cations.

Let's evaluate each option step by step:

### Step 1: Analyze PCl3
1. **Identify the central atom**: Phosphorus (P)
2. **Valence electrons (V)**: Phosphorus has 5 valence electrons.
3. **Monovalent atoms (M)**: There are 3 chlorine (Cl) atoms attached.
4. **Calculate steric number**:
\[ \text{Steric Number} = \frac{1}{2} (5 + 3 + 0) = \frac{8}{2} = 4 \]
5. **Determine hybridization**: Since the steric number is 4, the hybridization is \( sp^3 \).
6. **Lone pairs**: With 3 bond pairs and 1 lone pair, the shape is pyramidal.

### Step 2: Analyze CO3^2-
1. **Identify the central atom**: Carbon (C)
2. **Valence electrons (V)**: Carbon has 4 valence electrons.
3. **Monovalent atoms (M)**: There are no monovalent atoms, but we have a charge of -2.
4. **Calculate steric number**:
\[ \text{Steric Number} = \frac{1}{2} (4 + 0 + 2) = \frac{6}{2} = 3 \]
5. **Determine hybridization**: The steric number is 3, leading to \( sp^2 \) hybridization.
6. **Lone pairs**: With 3 bond pairs and 0 lone pairs, the shape is trigonal planar.

### Step 3: Analyze SO3
1. **Identify the central atom**: Sulfur (S)
2. **Valence electrons (V)**: Sulfur has 6 valence electrons.
3. **Monovalent atoms (M)**: There are no monovalent atoms.
4. **Calculate steric number**:
\[ \text{Steric Number} = \frac{1}{2} (6 + 0 + 0) = \frac{6}{2} = 3 \]
5. **Determine hybridization**: The steric number is 3, leading to \( sp^2 \) hybridization.
6. **Lone pairs**: With 3 bond pairs and 0 lone pairs, the shape is trigonal planar.

### Step 4: Analyze NO2^-
1. **Identify the central atom**: Nitrogen (N)
2. **Valence electrons (V)**: Nitrogen has 5 valence electrons.
3. **Monovalent atoms (M)**: There are no monovalent atoms, but we have a charge of -1.
4. **Calculate steric number**:
\[ \text{Steric Number} = \frac{1}{2} (5 + 0 + 1) = \frac{6}{2} = 3 \]
5. **Determine hybridization**: The steric number is 3, leading to \( sp^2 \) hybridization.
6. **Lone pairs**: With 2 bond pairs and 1 lone pair, the shape is bent.

### Conclusion
From the analysis:
- **PCl3** is pyramidal.
- **CO3^2-**, **SO3**, and **NO2^-** are not pyramidal.

Thus, the molecule which is pyramidal in shape is **PCl3**.