Which of the following compounds has the smallest bond angle?

Options

A. `OH_(2)`
B. `SH_(2)`
C. `NH_(3)`
D. `SO_(2)`

Answer

To determine which of the given compounds has the smallest bond angle, we need to analyze the molecular geometry and hybridization of each compound. Let's break it down step by step.

### Step 1: Analyze Water (H₂O)
- **Valence Electrons**: Oxygen (O) has 6 valence electrons. Each hydrogen (H) contributes 1 electron, giving a total of 8 electrons.
- **Lone Pairs**: Water has 2 lone pairs and 2 bond pairs (O-H bonds).
- **Steric Number**: The steric number is 4 (2 bond pairs + 2 lone pairs).
- **Hybridization**: The hybridization is sp³.
- **Bond Angle**: The ideal bond angle for sp³ is 109.5°, but due to lone pair-lone pair repulsion, the bond angle is reduced to approximately 104.5°.

### Step 2: Analyze Hydrogen Sulfide (H₂S)
- **Valence Electrons**: Sulfur (S) has 6 valence electrons. Each hydrogen contributes 1 electron, giving a total of 8 electrons.
- **Lone Pairs**: H₂S has 2 lone pairs and 2 bond pairs (S-H bonds).
- **Steric Number**: The steric number is 4.
- **Hybridization**: The hybridization is sp³.
- **Bond Angle**: The ideal bond angle for sp³ is 109.5°, but due to lone pair-bond pair repulsion, the bond angle is reduced to approximately 92°.

### Step 3: Analyze Ammonia (NH₃)
- **Valence Electrons**: Nitrogen (N) has 5 valence electrons. Each hydrogen contributes 1 electron, giving a total of 8 electrons.
- **Lone Pairs**: NH₃ has 1 lone pair and 3 bond pairs (N-H bonds).
- **Steric Number**: The steric number is 4.
- **Hybridization**: The hybridization is sp³.
- **Bond Angle**: The ideal bond angle for sp³ is 109.5°, but due to lone pair-bond pair repulsion, the bond angle is approximately 107°.

### Step 4: Analyze Sulfur Dioxide (SO₂)
- **Valence Electrons**: Sulfur (S) has 6 valence electrons, and oxygen contributes 6 electrons (2 O atoms), giving a total of 18 electrons.
- **Lone Pairs**: SO₂ has 1 lone pair and 2 bond pairs (S=O bonds).
- **Steric Number**: The steric number is 3.
- **Hybridization**: The hybridization is sp².
- **Bond Angle**: The ideal bond angle for sp² is 120°, but due to lone pair-bond pair repulsion, the bond angle is approximately 119.5°.

### Conclusion
Now, comparing the bond angles:
- H₂O: 104.5°
- H₂S: 92°
- NH₃: 107°
- SO₂: 119.5°

The compound with the smallest bond angle is **Hydrogen Sulfide (H₂S)** with a bond angle of approximately **92°**.

### Final Answer
**Hydrogen Sulfide (H₂S) has the smallest bond angle of approximately 92°.**

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