To determine which of the given molecules is linear, we will analyze each molecule's structure based on the valence electrons, steric number, hybridization, and molecular geometry.
### Step-by-Step Solution:
1. **Analyze ICl2- (Iodine Dichloride Ion)**:
- **Valence Electrons**: Iodine has 7 valence electrons, and with a -1 charge, it gains 1 electron, giving a total of 8 valence electrons. Each chlorine contributes 1 electron, so 2 chlorines contribute 2 electrons. Total = 8 + 2 = 10 valence electrons.
- **Steric Number**: The steric number is calculated as the number of bonding pairs plus the number of lone pairs. ICl2- has 2 bonding pairs (I-Cl) and 3 lone pairs on iodine. Therefore, the steric number = 2 + 3 = 5.
- **Hybridization**: With a steric number of 5, the hybridization is sp³d.
- **Geometry**: The geometry is trigonal bipyramidal, but due to the presence of 3 lone pairs, the shape is linear.
2. **Analyze SO3^2- (Sulfite Ion)**:
- **Valence Electrons**: Sulfur has 6 valence electrons, and each oxygen has 6. The sulfite ion has a -2 charge, so total = 6 + (3 × 6) + 2 = 26 valence electrons.
- **Steric Number**: There are 3 bonding pairs (S-O) and 1 lone pair on sulfur. Therefore, the steric number = 3 + 1 = 4.
- **Hybridization**: The hybridization is sp³.
- **Geometry**: The geometry is tetrahedral, and due to the lone pair, the shape is trigonal pyramidal.
3. **Analyze SO3 (Sulfur Trioxide)**:
- **Valence Electrons**: Sulfur has 6, and each of the 3 oxygens has 6. Total = 6 + (3 × 6) = 24 valence electrons.
- **Steric Number**: There are 3 bonding pairs (S=O) and no lone pairs. Therefore, the steric number = 3.
- **Hybridization**: The hybridization is sp².
- **Geometry**: The geometry is trigonal planar, and the shape is also trigonal planar.
4. **Analyze SO2 (Sulfur Dioxide)**:
- **Valence Electrons**: Sulfur has 6, and each oxygen has 6. Total = 6 + (2 × 6) = 18 valence electrons.
- **Steric Number**: There are 2 bonding pairs (S=O) and 1 lone pair. Therefore, the steric number = 2 + 1 = 3.
- **Hybridization**: The hybridization is sp².
- **Geometry**: The geometry is trigonal planar, but due to the lone pair, the shape is bent.
### Conclusion:
From the analysis, the only molecule that has a linear shape is **ICl2-**.
