Problem 15 - Chemistry in 30 days

Question

The structure of \(\mathrm{XeF}_{2}\) is (a) square planar (b) tetrahedral (c) octahedral (d) trigonal bipyramidal

Step-by-Step Solution

Answer

The structure of \(\mathrm{XeF}_{2}\) is (d) trigonal bipyramidal.

Step 1: Identify the central atom

In the molecule \(\mathrm{XeF}_{2}\), the central atom is Xenon (Xe). Fluorine atoms (F) are bonded to the Xenon atom.

Step 2: Count valence electrons

Xenon (Xe) belongs to Group 18 in the periodic table and has 8 valence electrons. Each Fluorine (F) atom has 7 valence electrons, and since there are two fluorine atoms, they contribute a total of 14 valence electrons. Altogether, there are \(8 + 2 \times 7 = 22\) valence electrons in \(\mathrm{XeF}_{2}\).

Step 3: Determine electron pair geometry

Place the 22 valence electrons around Xenon. Two fluorine atoms use a single bond each, consuming 4 electrons. This leaves 18 electrons (9 pairs) around Xe. 3 of these pairs are lone pairs, and they will dictate the overall shape according to the VSEPR theory.

Step 4: Apply VSEPR theory

According to the VSEPR (Valence Shell Electron Pair Repulsion) theory, the presence of 3 lone pairs and 2 bond pairs implies a geometric arrangement around the central atom corresponding to the trigonal bipyramidal arrangement.

Step 5: Identify molecular shape

In a trigonal bipyramidal arrangement, when 3 positions are occupied by lone pairs, the shape adjusts to accommodate minimal repulsion among electron pairs. Two fluorine atoms sitting in the axial positions give \(\mathrm{XeF}_{2}\) a linear molecule shape.

Key Concepts

Electron Pair Geometry

Understanding electron pair geometry is essential for determining the 3D structure of molecules, such as in the case of \( \text{XeF}_2 \). This concept involves arranging electron pairs around a central atom in a way that minimizes repulsion. In a molecule, electrons can be found in bonding pairs or lone pairs, and each type affects the geometry.When electron pairs are arranged, we consider both lone pairs and bond pairs. The arrangement depends on minimizing the repulsion between electron pairs based on their presence around the central atom. This can lead to standard geometrical shapes like linear, trigonal planar, tetrahedral, and more complex arrangements like trigonal bipyramidal or octahedral. The specific shape formed by the electron pairs around the central atom is known as the electron pair geometry and is crucial in predicting the molecular shape.

Valence Electrons

Every atom has valence electrons that play an integral role in bonding. These electrons are located in the outermost shell of an atom and are responsible for chemical reactions and bonding patterns seen in molecules. Understanding valence electrons is vital for determining how atoms interact and combine.Xenon, being a noble gas, possesses 8 valence electrons. However, contrary to what many may think, noble gases like Xenon can form compounds despite their typical inertness, by expanding their octet. In \( \text{XeF}_2 \), each fluorine atom contributes 7 valence electrons, making a total of 22 valence electrons overall for the molecule. This count assists us in predicting how many electron pairs are involved in bonding, helping to sketch possible molecular structures.

Molecular Shape Determination

The determination of a molecule's shape involves understanding the spatial configuration of atoms connected by bonds. The VSEPR (Valence Shell Electron Pair Repulsion) theory aids in predicting these shapes by considering electron pair repulsions.In \( \text{XeF}_2 \), after establishing the electron pair geometry (trigonal bipyramidal due to 5 areas of electron density), the shape of the actual molecule is determined by considering where the lone pairs are positioned. Lone pairs tend to repel more strongly than bonded pairs. Therefore, when these are positioned to minimize this repulsion and occupy equatorial positions in a trigonal bipyramidal setup, the shape of the molecule becomes linear as the two bonded fluorine atoms occupy the less shielded axial positions.

Trigonal Bipyramidal Arrangement

The term "trigonal bipyramidal arrangement" refers to a specific geometrical configuration where five regions of electron density need to be accommodated around a central atom. In VSEPR theory, this configuration arises due to the need for minimizing repulsion between these electron areas.In a trigonal bipyramidal arrangement, atoms or electron pairs are positioned such that three are around the equatorial plane at a 120° angle from each other, while two occupy axial positions, forming a 90° angle with the equatorial plane. This geometry is common in molecules where there are bond pairs and lone pairs and is visualized as a three-sided pyramid (trigonal) with an atom or lone pair at each vertex. This arrangement helps understand the spatial orientation for any given molecule, like \( \text{XeF}_2 \), and how lone pair effects further adjust the observable molecular shape to linear.