The molecule of `SO_(2)` has dipole moment. Is the molecule linear or bent ?

Answer

To determine whether the molecule \( SO_2 \) (sulfur dioxide) is linear or bent, we need to analyze its molecular structure and the presence of lone pairs.

### Step 1: Determine the Valence Electrons
Sulfur (S) has 6 valence electrons, and each oxygen (O) has 6 valence electrons. Therefore, for \( SO_2 \):
- Total valence electrons = 6 (from S) + 2 × 6 (from 2 O) = 18 valence electrons.

### Step 2: Draw the Lewis Structure
1. Place the sulfur atom in the center and bond it to two oxygen atoms.
2. Form double bonds between sulfur and each oxygen atom. This uses 4 electrons (2 for each double bond).
3. Distribute the remaining 10 electrons to satisfy the octet rule for oxygen atoms. Each oxygen will have 4 additional electrons (2 lone pairs).
4. Place the remaining 2 electrons as a lone pair on the sulfur atom.

The Lewis structure can be represented as:
```
O
||
S -- O
|
Lone Pair
```

### Step 3: Analyze the Shape
- The presence of the lone pair on sulfur affects the geometry of the molecule. According to the VSEPR (Valence Shell Electron Pair Repulsion) theory, lone pairs occupy more space than bonding pairs, leading to repulsion that alters the shape.
- The molecular geometry is determined by the arrangement of the bonding pairs and lone pairs around the central atom (sulfur).

### Step 4: Determine the Molecular Geometry
- With 2 bonding pairs (from the double bonds to oxygen) and 1 lone pair, the arrangement is trigonal planar, but the presence of the lone pair causes the shape to be bent (or V-shaped).

### Conclusion
Thus, the molecule \( SO_2 \) is bent due to the presence of the lone pair on sulfur, which leads to a net dipole moment in the molecule.