Question

The structure of $[XeF_8]^{2-} $ is

• A. cubic
• B. hexagonal bipyramid
• C. square antiprism
• D. octagonal

Answer 1

The Correct Option is C

$\text{1. Determine the Valence Electron Count}$

The structure is determined using the VSEPR (Valence Shell Electron Pair Repulsion) theory. First, calculate the total number of valence electrons around the central atom, Xenon ($\text{Xe}$).

$\text{Xenon} (\text{Group } 18): 8 \text{ valence electrons}$

$\text{Fluorine} (8 \text{ atoms} \times 7 \text{ valence electrons/atom}): 56 \text{ valence electrons}$

$\text{Charge} (2-): 2 \text{ additional electrons}$

$$\text{Total Valence Electrons} = 8 + 56 + 2 = 66$$

$\text{2. Determine the Number of Electron Pairs}$

The total number of electron pairs around the central atom is found by dividing the total valence electrons by 2:

$$\text{Total Electron Pairs} = \frac{66}{2} = 33$$

$\text{3. Determine the Number of Bond Pairs (BP) and Lone Pairs (LP)}$

The $8$ Fluorine atoms form $8$ single bonds with the central $\text{Xe}$ atom.

$\text{Number of Bond Pairs (BP)} = 8$

$\text{Number of Lone Pairs (LP)}$ on $\text{Xe}$ = $\text{Total Electron Pairs} - (\text{Lone Pairs on F} + \text{Bond Pairs})$

Each $\text{F}$ atom uses $1$ pair for bonding, leaving $3$ lone pairs per $\text{F}$. $\text{LP on F} = 8 \times 3 = 24$.

$\text{LP on Xe} = 33 - (24 + 8) = 33 - 32 = 1 \text{ lone pair}$

The number of electron domains (steric number, $\text{SN}$) around the central $\text{Xe}$ atom is:

$$\text{Steric Number } (\text{SN}) = \text{BP} + \text{LP} = 8 + 1 = 9$$

$\text{4. Determine the Electron Geometry and Molecular Structure}$

Based on the $\text{SN}$ of $9$ ($\text{AX}_8\text{E}_1$), the electron pair geometry is based on a $\mathbf{\text{non-ideal tri-capped trigonal prism}}$.

However, for a coordination number of 8 (8 $\text{F}$ atoms surrounding $\text{Xe}$), two common stable geometries minimize repulsion: the square antiprism and the dodecahedron.

For the $\mathbf{[\text{XeF}_8]^{2-}}$ ion, experimental data (specifically, X-ray diffraction of its salts, such as the $\text{NO}_2^+$ salt) show that it adopts a highly symmetric $\mathbf{\text{square antiprism}}$ geometry in the solid state.

The $\text{Xe}-\text{F}$ bond lengths are all approximately equal, consistent with a uniform, high-symmetry structure like the square antiprism. ^{2-}$]

$\text{Conclusion}$

The structure of $[\text{XeF}_8]^{2-}$ is square antiprism.