Which of the following has all equal bond lengths?

Options

A. `SF_(4)`
B. `lCl_(3)`
C. `PCl_(3)`
D. `lCl_(2)^(+)`

Explanation

To determine which of the given compounds has all equal bond lengths, we will analyze each option step by step.

### Step 1: Analyze SF4
1. **Determine the hybridization**:
- Sulfur (S) has a valency of 6 and forms bonds with 4 fluorine (F) atoms.
- Total valence electrons = 6 (S) + 4 (F) = 10.
- Steric number = 10 / 2 = 5.
- Hybridization = sp³d.

2. **Shape of SF4**:
- The molecular geometry is trigonal bipyramidal.
- In this structure, there are 2 axial and 3 equatorial positions.
- The bond lengths will be different: axial bonds are longer than equatorial bonds due to lone pair repulsion.

**Conclusion for SF4**: Not all bond lengths are equal.

### Step 2: Analyze ICl3
1. **Determine the hybridization**:
- Iodine (I) has a valency of 7 and forms bonds with 3 chlorine (Cl) atoms.
- Total valence electrons = 7 (I) + 3 (Cl) = 10.
- Steric number = 10 / 2 = 5.
- Hybridization = sp³d.

2. **Shape of ICl3**:
- The molecular geometry is also trigonal bipyramidal.
- Similar to SF4, there are 2 axial and 3 equatorial positions.
- The bond lengths will differ: axial bonds are longer than the equatorial bond.

**Conclusion for ICl3**: Not all bond lengths are equal.

### Step 3: Analyze PCl3
1. **Determine the hybridization**:
- Phosphorus (P) has a valency of 5 and forms bonds with 3 chlorine (Cl) atoms.
- Total valence electrons = 5 (P) + 3 (Cl) = 8.
- Steric number = 8 / 2 = 4.
- Hybridization = sp³.

2. **Shape of PCl3**:
- The molecular geometry is tetrahedral.
- There are 3 Cl atoms and 1 lone pair on phosphorus.
- All bond lengths (P-Cl) are equal due to the symmetrical tetrahedral shape.

**Conclusion for PCl3**: All bond lengths are equal.

### Step 4: Analyze ICl2⁺
1. **Determine the hybridization**:
- Iodine (I) has a valency of 7 and forms bonds with 2 chlorine (Cl) atoms.
- Since it has a positive charge, we subtract 1 electron.
- Total valence electrons = 7 (I) + 2 (Cl) - 1 = 8.
- Steric number = 8 / 2 = 4.
- Hybridization = sp³.

2. **Shape of ICl2⁺**:
- The molecular geometry is also tetrahedral.
- There are 2 Cl atoms and 2 lone pairs on iodine.
- Due to lone pair-lone pair repulsion, the bond lengths will not be equal.

**Conclusion for ICl2⁺**: Not all bond lengths are equal.

### Final Answer
The compound that has all equal bond lengths is **PCl3**.