Question

Give the electron-domain and molecular geometries for the following molecules and ions: (a) \(\mathrm{BeF}_{2}\), (b) \(\mathrm{AsCl}_{5}\), (c) \(\mathrm{NO}_{2}^{-}\), (e) \(\mathrm{SF}_{4},(\mathbf{f}) \mathrm{BrF}_{s-}\) (d) \(\mathrm{CS}_{2}\)

Short answer

The electron-domain and molecular geometries for the given molecules and ions are as follows: (a) \(\text{BeF}_{2}\): Electron-domain geometry is linear, and molecular geometry is linear. (b) \(\text{AsCl}_{5}\): Electron-domain geometry is trigonal bipyramidal, and molecular geometry is trigonal bipyramidal. (c) \(\text{NO}_{2}^{-}\): Electron-domain geometry is trigonal planar, and molecular geometry is bent. (d) \(\text{CS}_{2}\): Electron-domain geometry is linear, and molecular geometry is linear. (e) \(\text{SF}_{4}\): Electron-domain geometry is octahedral, and molecular geometry is tetragonal pyramidal (seesaw). (f) \(\text{BrF}_{5}\): Electron-domain geometry is octahedral, and molecular geometry is square pyramidal.

Step-by-step solution

Lewis structure

First, draw the Lewis structure for \(\text{BeF}_2\). We have Be in the center and two F atoms bonded to it with single bonds. Each F atom has six valence electrons, while Be has only two.

Determine Electron-domain Geometry

The central Be atom has two bonded electron pairs with the F atoms. Thus, there is a total of 2 electron domains. According to VSEPR theory, the electron-domain geometry should be linear.

Determine Molecular Geometry

There are no lone pair electrons on the central Be atom, so the molecular geometry will also be linear. (b) \(\text{AsCl}_5\)

Lewis structure

Draw the Lewis structure for \(\text{AsCl}_5\). We have As in the center and five Cl atoms bonded to it with single bonds. Each Cl atom has six valence electrons, and As has five.

Determine Electron-domain Geometry

The central As atom has five bonded electron pairs with the Cl atoms. Thus, there is a total of 5 electron domains. According to VSEPR theory, the electron-domain geometry should be trigonal bipyramidal.

Determine Molecular Geometry

There are no lone pair electrons on the central As atom, so the molecular geometry will also be trigonal bipyramidal. (c) \(\text{NO}_{2}^{-}\)

Lewis structure

Draw the Lewis structure for \(\text{NO}_{2}^{-}\). We have N in the center with single bonds to both O atoms and one extra electron.

Determine Electron-domain Geometry

The central N atom has two bonded electron pairs (with the O atoms) and one lone pair. Thus, there is a total of 3 electron domains. According to VSEPR theory, the electron-domain geometry should be trigonal planar.

Determine Molecular Geometry

Since there is one lone pair of electrons on the central N atom, the molecular geometry will be bent. (d) \(\text{CS}_{2}\)

Lewis structure

Draw the Lewis structure for \(\text{CS}_{2}\). We have C in the center and two S atoms bonded to it with double bonds.

Determine Electron-domain Geometry

The central C atom has two bonded electron pairs with the S atoms. Thus, there is a total of 2 electron domains. According to VSEPR theory, the electron-domain geometry should be linear.

Determine Molecular Geometry

There are no lone pair electrons on the central C atom, so the molecular geometry will also be linear. (e) \(\text{SF}_{4}\)

Lewis structure

Draw the Lewis structure for \(\text{SF}_{4}\). We have S in the center and four F atoms bonded to it with single bonds. There are two lone pair electrons on the central S atom.

Determine Electron-domain Geometry

The central S atom has four bonded electron pairs with the F atoms and two lone pairs. Thus, there is a total of 6 electron domains. According to VSEPR theory, the electron-domain geometry should be octahedral.

Determine Molecular Geometry

There are two lone pairs of electrons on the central S atom, so the molecular geometry will be tetragonal pyramidal (also known as seesaw geometry). (f) \(\text{BrF}_{5}\)

Lewis structure

Draw the Lewis structure for \(\text{BrF}_{5}\). We have Br in the center and five F atoms bonded to it with single bonds. There is one lone pair of electrons on the central Br atom.

Determine Electron-domain Geometry

The central Br atom has five bonded electron pairs with the F atoms and one lone pair. Thus, there is a total of 6 electron domains. According to VSEPR theory, the electron-domain geometry should be octahedral.

Determine Molecular Geometry

There is one lone pair of electrons on the central Br atom, so the molecular geometry will be square pyramidal.

Key concepts

Lewis structure

The Lewis structure is a useful tool for visualizing the distribution of valence electrons in molecules. By representing electrons as dots and chemical bonds as lines, it allows us to see how atoms are connected and how electrons are shared. For example, in the molecule \(\mathrm{BeF}_2\), Beryllium (Be) is at the center, forming single bonds with two Fluorine (F) atoms. Since Beryllium has two valence electrons and bonds with two atoms, each Fluorine atom gets one electron to form a stable bond.
Creating a Lewis structure helps us predict molecular properties and interactions. To draw a correct Lewis structure:

• Count the valence electrons for all atoms involved.
• Use lines to represent bonds between atoms.
• Ensure all atoms have complete outer shells, primarily aiming for octets, except for exceptions like Hydrogen.

Lewis structures are the first step in understanding the geometries and reactivities of molecules, as they lay the groundwork for further theoretical models like VSEPR.

VSEPR theory

VSEPR theory, short for Valence Shell Electron Pair Repulsion theory, is a model that explains the shapes of molecules based on electron pair interactions. It considers that electron pairs around a central atom will arrange themselves to minimize repulsion, resulting in specific geometrical shapes. For instance, in \(\mathrm{BeF}_2\), with two bonded electron pairs, the shape is linear because the electron pairs situate themselves as far apart as possible, leading to a straight line.
The theory allows predictions of the three-dimensional shape of molecules:

• Determine the number of bonding and lone pairs around the central atom.
• Predict the geometry that minimizes repulsions—linear, trigonal planar, tetrahedral, etc.

VSEPR is crucial for understanding molecular geometry and can also predict bond angles and molecular polarity, enriching our comprehension of the molecule's behavior in various situations.

electron-domain geometry

Electron-domain geometry is an extension of VSEPR theory focused on the spatial arrangement of all electron pairs (bonding and non-bonding) around a central atom. It provides an overall picture of the electron densities and their influence on molecular shape. For example, in \(\text{AsCl}_5\), since the central Arsenic (As) atom has five bonded domains, the electron-domain geometry is trigonal bipyramidal.
To find the electron-domain geometry:

• Count all electron domains (both bonding and lone pairs).
• Identify the geometrical arrangement that accommodates those domains.

Understanding this concept helps predict how molecules interact with their environment by identifying the "cloud" of electron domains. This geometry is important in determining molecular interactions and potential reactivity.

lone pair electrons

Lone pair electrons are valence electrons that do not participate in bonding and remain on a single atom. These unshared pairs significantly influence the molecular geometry and properties. For instance, in \(\mathrm{SF}_4\), Sulfur has four bonded pairs and one lone pair, resulting in a seesaw shape due to lone pair-bond pair repulsions.
Lone pairs can:

• Change the bond angles, making them smaller than those predicted by standard geometric models.
• Influence the polarity and reactivity of the molecule since they contribute to electron density asymmetry.

Understanding the role of lone pair electrons is essential for comprehending the actual shape and properties of molecules beyond simple bonding interactions.