Problem 9 - Chemistry in 30 days

Question

The structure of \(\mathrm{XeO}_{2} \mathrm{~F}_{2}\) is (a) Plane triangular (b) Trigonal bipyramidal (c) Square planar (d) Tetrahedral

Step-by-Step Solution

Answer

The structure of \( \mathrm{XeO}_{2} \mathrm{~F}_{2} \) is Square planar (Option c).

Step 1: Determine the Number of Electron Pairs

Xenon (Xe) is the central atom. In the molecule \(\mathrm{XeO}_{2}\mathrm{~F}_{2}\), Xe has 8 valence electrons. Xe forms 4 bonds with 2 oxygen atoms and 2 fluorine atoms. Thus, the number of bonding pairs is 4.

Step 2: Calculate the Lone Pairs

Since Xe has 8 valence electrons and uses 4 for bonding (one with each oxygen and fluorine), there are 4 - 4 = 0 lone pairs on Xe.

Step 3: Determine the Molecular Geometry

The central atom Xe is surrounded by 4 bonds (2 from O and 2 from F) and no lone pairs. According to VSEPR theory, 4 bonds with no lone pairs correspond to a trigonal bipyramidal electron geometry. In \(\mathrm{XeO}_2\mathrm{F}_2\), the shape forms a square planar arrangement due to the positions of the bonds.

Key Concepts

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is a model used to predict the geometry of individual molecules. It is based on the idea that electron pairs around a central atom will arrange themselves to minimize repulsion. This results in the atoms forming distinct geometrical shapes. In the VSEPR model:

• Electron pairs include both bonding pairs (shared between atoms) and lone pairs (non-bonding pairs).
• The shape of the molecule is determined by the number of electron pairs, their repulsions, and spatial arrangement.
• Different numbers of electron pairs lead to varying shapes, such as linear, trigonal planar, tetrahedral, and more.

For instance, a molecule like \( \mathrm{XeO}_{2} \mathrm{~F}_{2} \), as discussed, forms a square planar geometry due to no lone pairs on the central atom, following the VSEPR theory.

Valence Electrons

Valence electrons are the electrons in the outermost shell of an atom that are involved in forming bonds. They are crucial for determining how an atom interacts with others in a molecule.

• The number of valence electrons dictates the type and number of bonds an atom can form.
• The more valence electrons, the greater the ability of an atom to engage in chemical bonding.

In the molecule \( \mathrm{XeO}_{2} \mathrm{~F}_{2} \), Xenon (Xe) has 8 valence electrons. Being able to use all these electrons in bonding is key for determining the overall structure and properties of the molecule. It's how Xe can form up to four bonds with oxygen and fluorine atoms without having any lone pairs left.

Electron Pair Geometry

Electron pair geometry considers the spatial arrangement of both bonding and lone electron pairs around a central atom. It plays a pivotal role in determining the three-dimensional shape of a molecule.

• Bonding pairs are electron pairs that participate in covalent bonds.
• Lone pairs are those that do not participate in bonding but still affect the molecule's shape due to their spatial requirements.

For \( \mathrm{XeO}_{2} \mathrm{~F}_{2} \), the electron pair geometry around Xenon includes four bonds. Such a geometry typically results as trigonal bipyramidal. However, the molecular shape modifies to square planar due to the positions and interactions of these bonds, with no lone pairs to alter the basic geometry.

Lone Pairs

Lone pairs refer to pairs of valence electrons that are not shared with another atom and therefore not involved in bonding. They have significant effects on molecular geometry:

• Such electron pairs occupy space around the central atom, exerting repulsive forces.
• They can modify the angles between bonds, affecting overall molecular shape.

In the case of \( \mathrm{XeO}_{2} \mathrm{~F}_{2} \), no lone pairs are present on the central xenon atom. This absence allows the binds from oxygen and fluorine to assume the square planar shape without interference from any positioned lone pairs. Usually, lone pairs would push nearby bonds away, altering geometries into other shapes.