Which of the following has a bond angle of `109^(@)`?

Options

A. `CO_(2)`
B. `H_(2)O`
C. `CH_(4)`
D. `SO_(2)`

Explanation

To determine which of the given molecules has a bond angle of approximately 109°, we need to analyze the molecular geometries of the compounds based on the VSEPR (Valence Shell Electron Pair Repulsion) theory. The ideal bond angle for a tetrahedral geometry is 109.5°.

### Step-by-Step Solution:

1. **Identify the Molecules**:
We need to look at the given options. Let's assume we have the following molecules: CO2, H2O, and CH4.

2. **Analyze CO2**:
- **Valence Electrons**: Carbon has 4 valence electrons, and each oxygen has 6, so CO2 has a total of 16 valence electrons.
- **Steric Number Calculation**: The central atom (carbon) has 0 lone pairs and is bonded to 2 oxygen atoms.
- **Steric Number**: \( \text{Steric Number} = \frac{(4 + 0)}{2} + 2 = 2 \) (2 bonds, no lone pairs).
- **Hybridization**: This indicates sp hybridization, which corresponds to a linear geometry.
- **Bond Angle**: The bond angle is 180°, not 109°.

3. **Analyze H2O**:
- **Valence Electrons**: Oxygen has 6 valence electrons, and each hydrogen has 1, giving a total of 8 valence electrons.
- **Steric Number Calculation**: The central atom (oxygen) has 2 lone pairs and is bonded to 2 hydrogen atoms.
- **Steric Number**: \( \text{Steric Number} = \frac{(6 + 0)}{2} + 2 = 4 \) (2 bonds and 2 lone pairs).
- **Hybridization**: This indicates sp³ hybridization, which corresponds to a tetrahedral geometry.
- **Bond Angle**: However, due to the presence of lone pairs, the bond angle is less than 109.5°.

4. **Analyze CH4**:
- **Valence Electrons**: Carbon has 4 valence electrons, and each hydrogen has 1, giving a total of 8 valence electrons.
- **Steric Number Calculation**: The central atom (carbon) has 0 lone pairs and is bonded to 4 hydrogen atoms.
- **Steric Number**: \( \text{Steric Number} = \frac{(4 + 0)}{2} + 4 = 4 \) (4 bonds, no lone pairs).
- **Hybridization**: This indicates sp³ hybridization, which corresponds to a tetrahedral geometry.
- **Bond Angle**: The bond angle is approximately 109.5°.

5. **Conclusion**:
Among the given options, **CH4 (methane)** has a bond angle of approximately 109.5° and is the correct answer.