Question

Use VSEPR theory to predict the probable geometric structures of the molecules (a) \(\mathrm{O}_{2} \mathrm{XeF}_{2} ;\) (b) \(\mathrm{O}_{3} \mathrm{XeF}_{2}\) (c) OXeF \(_{4}\).

Short answer

\(\mathrm{O}_{2} \mathrm{XeF}_{2}\) has a square planar geometry, \(\mathrm{O}_{3} \mathrm{XeF}_{2}\) has a square pyramidal geometry, and OXeF \(_{4}\) is octahedral.

Step-by-step solution

Identifying the Central Atom

Identify the central atom in each molecule. This is usually the atom with the least electronegativity or the single unique atom in the molecules. In \(\mathrm{O}_{2} \mathrm{XeF}_{2}\), \(\mathrm{O}_{3} \mathrm{XeF}_{2}\), and OXeF \(_{4}\), the central atom is Xenon (Xe).

Determine the Electron Pair Geometry

Count the number of bonding pairs (BP) and non-bonding pairs (lone pairs, LP) of electrons around the central atom. In \(\mathrm{O}_{2} \mathrm{XeF}_{2}\), we have 4 BP and 2 LP; in \(\mathrm{O}_{3} \mathrm{XeF}_{2}\), we have 5 BP and 1 LP; and in OXeF \(_{4}\), we have 5 BP and no LP.

Predict the Molecular Geometry

Using VSEPR theory and the number of BP and LP, we can predict the molecular geometry: \(\mathrm{O}_{2} \mathrm{XeF}_{2}\) has a square planar geometry due to 4 BP and 2 LP around the central atom. \(\mathrm{O}_{3} \mathrm{XeF}_{2}\) has a square pyramidal geometry due to 5 BP and 1 LP around the central atom. OXeF \(_{4}\) is octahedral because it has 6 BP (5 bonded with F and 1 bonded with O) around the central atom and no LP.

Key concepts

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. This geometry significantly affects the molecule's physical and chemical properties. VSEPR (Valence Shell Electron Pair Repulsion) theory is a tool used to predict molecular shapes. It assumes that electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsion.

For instance, in the molecule \(\mathrm{O}_{2} \mathrm{XeF}_{2}\), there are four bonding pairs and two lone pairs of electrons around xenon. This leads to a square planar shape, with lone pairs positioned opposite each other to reduce repulsion. Meanwhile, \(\mathrm{O}_{3} \mathrm{XeF}_{2}\) has five bonding pairs and one lone pair, creating a square pyramidal shape. Finally, \(\mathrm{OXeF}_{4}\) forms an octahedral shape due to its six bonding pairs, allowing an optimal spatial distribution with minimal electron repulsion.

• Square planar: Four bonding pairs and two lone pairs.
• Square pyramidal: Five bonding pairs and one lone pair.
• Octahedral: Six bonding pairs.

Electron Pair Geometry

Electron pair geometry considers both the bonding pairs and lone pairs around a central atom. It's essential for understanding the inherent shape of the electron cloud before lone pairs and bonded atoms refine it into the final molecular shape.

The VSEPR theory is applied to predict this geometry. When analyzing \(\mathrm{O}_{2} \mathrm{XeF}_{2}\), we see four bonding pairs and two lone pairs, indicating an octahedral electron pair geometry, the blueprint for the square planar shape.

• In \(\mathrm{O}_{3} \mathrm{XeF}_{2}\), the five bonding pairs and one lone pair also suggest an octahedral electron pair geometry, although the final molecular shape is square pyramidal.
• For \(\mathrm{OXeF}_{4}\), the absence of lone pairs means the electron pair geometry directly corresponds to the molecular geometry, which is octahedral.

Understanding electron pair geometry helps us appreciate how lone pairs influence molecular conformation by pushing bonding pairs into specific positions. This critical step aids in determining the exact molecular geometry later.

Xenon Compounds

Xenon, a noble gas, is usually inert, but it can form stable compounds like \(\mathrm{O}_{2} \mathrm{XeF}_{2}\), \(\mathrm{O}_{3} \mathrm{XeF}_{2}\), and \(\mathrm{OXeF}_{4}\). These compounds are fascinating due to their unusual electron arrangements and geometries.

In xenon fluoride compounds, xenon acts as the central atom. This is due to xenon's ability to expand its octet, accommodating more than the typical noble gas electron count.

• With \(\mathrm{O}_{2} \mathrm{XeF}_{2}\), xenon forms a compound with two oxygen atoms and two fluorine atoms, presenting a unique electron arrangement that leads to a square planar structure.
• The \(\mathrm{O}_{3} \mathrm{XeF}_{2}\) structure includes more oxygen, influencing its molecular and electron pair geometry, creating a square pyramidal shape.
• \(\mathrm{OXeF}_{4}\) showcases xenon's full versatility, bonding with four fluorines and one oxygen, leading to an octahedral structure.

These xenon compounds illustrate the principle that even typically non-reactive elements can form complex structures under the right conditions, showcasing the diversity of chemical bonding.