In which of the following molecules all A - X bond lengths are identical? [A = central atom and X = surrounding atom]

Options

A. `XeF_4`
B. `PF_5`
C. Both A and B
D. `SF_4`

Answer

To determine which of the given molecules has identical A-X bond lengths, we need to analyze the molecular geometry and hybridization of each molecule.

### Step-by-Step Solution:

1. **Identify the Molecules**: We need to analyze the given molecules (e.g., XeF4, SF4, etc.) to determine their structures.

2. **Determine Valence Electrons**: For each molecule, calculate the total number of valence electrons. For example:
- **XeF4**: Xenon (Xe) has 8 valence electrons, and each fluorine (F) has 7 valence electrons. Thus, total = 8 + (4 × 7) = 36 valence electrons.
- **SF4**: Sulfur (S) has 6 valence electrons, and each fluorine (F) has 7 valence electrons. Thus, total = 6 + (4 × 7) = 34 valence electrons.

3. **Draw the Lewis Structure**: Draw the Lewis structure for each molecule:
- **XeF4**: Place Xe in the center with 4 F atoms around it and 2 lone pairs of electrons on Xe.
- **SF4**: Place S in the center with 4 F atoms around it and 1 lone pair of electrons on S.

4. **Determine Hybridization**: Use the number of bond pairs and lone pairs to determine the hybridization:
- **XeF4**: 4 bond pairs + 2 lone pairs = 6 regions of electron density → Hybridization is sp³d² (octahedral).
- **SF4**: 4 bond pairs + 1 lone pair = 5 regions of electron density → Hybridization is sp³d (trigonal bipyramidal).

5. **Analyze Molecular Geometry**: Identify the molecular geometry based on the hybridization:
- **XeF4**: The molecular geometry is square planar due to the presence of 2 lone pairs.
- **SF4**: The molecular geometry is seesaw due to the presence of 1 lone pair.

6. **Evaluate Bond Lengths**: In the case of XeF4, all bond lengths are identical because the square planar geometry allows for equal bond distances. However, in SF4, the seesaw shape results in different bond lengths (axial vs. equatorial).

7. **Conclusion**: The only molecule where all A-X bond lengths are identical is **XeF4**.

### Final Answer:
**XeF4** has identical A-X bond lengths.