Which of the following have a linear structure?

Options

A. `HgCl_(2)`
B. `SnCl_(2)`
C. `ICl_(2)^(-)`
D. `CS_(2)`

Answer

To determine which of the given compounds have a linear structure, we will analyze each option based on their hybridization and molecular geometry.

### Step-by-Step Solution:

1. **Identify the Compounds:**
- Option 1: HgCl2
- Option 2: SnCl2
- Option 3: ICl2^-
- Option 4: CH2 (assuming this refers to CS2, as CH2 is not a stable molecule)

2. **Analyze HgCl2:**
- **Valence Electrons:** Mercury (Hg) has 2 valence electrons, and each chlorine (Cl) has 1 valence electron.
- **Hybridization Calculation:**
\[ \text{Hybridization} = \frac{\text{Valence electrons of central atom} + \text{Monovalent atoms} + \text{Negative charge} - \text{Positive charge}}{2} \]
\[ = \frac{2 + 2 + 0 - 0}{2} = \frac{4}{2} = 2 \quad (\text{sp hybridization}) \]
- **Geometry:** sp hybridization indicates a linear structure with a bond angle of 180°.

3. **Analyze SnCl2:**
- **Valence Electrons:** Tin (Sn) has 4 valence electrons, and there are 2 chlorine atoms.
- **Hybridization Calculation:**
\[ = \frac{4 + 2 + 0 - 0}{2} = \frac{6}{2} = 3 \quad (\text{sp}^2 \text{ hybridization}) \]
- **Geometry:** sp² hybridization indicates a bent structure due to the presence of a lone pair.

4. **Analyze ICl2^-:**
- **Valence Electrons:** Iodine (I) has 7 valence electrons, and there are 2 chlorine atoms, plus 1 negative charge.
- **Hybridization Calculation:**
\[ = \frac{7 + 2 + 1 - 0}{2} = \frac{10}{2} = 5 \quad (\text{sp}^3\text{d hybridization}) \]
- **Geometry:** sp³d hybridization indicates a linear structure due to the presence of 3 lone pairs and 2 bonding pairs, leading to a bond angle of 180°.

5. **Analyze CS2:**
- **Valence Electrons:** Carbon (C) has 4 valence electrons and sulfur (S) has 6 valence electrons, with 2 sulfur atoms.
- **Hybridization Calculation:**
\[ = \frac{4 + 0 + 0 - 0}{2} = \frac{4}{2} = 2 \quad (\text{sp hybridization}) \]
- **Geometry:** sp hybridization indicates a linear structure with a bond angle of 180°.

### Conclusion:
The compounds with a linear structure are:
- **Option 1: HgCl2**
- **Option 3: ICl2^-**
- **Option 4: CS2**

### Final Answer:
The compounds that have a linear structure are **HgCl2, ICl2^-, and CS2**.