Question

Shown below are dot diagrams for some simple molecules and polyatomic ions: \(: \ddot{B r}-\dot{S}_{\cdots}^{\prime \prime}-\vec{B}_{r}^{\prime \prime}\) (a) Draw the three-dimensional shape for each molecule. Use lines, solid wedges, and dashed wedges as necessary. Indicate the numeric value of all bond angles. (b) For each species, name both the electrongroup geometry around the central atom and the molecular shape.

Short answer

The three-dimensional shape of the \(Br-S-Br\) molecule can be represented as: Br | S - Br | with two lone pairs on the top and bottom of the sulfur atom, and a bond angle of \(109.5^\circ\). The electron group geometry is tetrahedral, while the molecular shape is bent.

Step-by-step solution

Draw the Lewis structure

First, we need to draw the Lewis structure for the molecule. For this, we need to know the valence electrons of each atom. We have the following valence electrons: - Bromine (Br): 7 valence electrons - Sulfur (S): 6 valence electrons The Lewis structure would be: \(Br - S - Br\) with two lone electron pairs on the sulfur atom (S).

Draw the three-dimensional structure

Since there are two bonded atoms and two lone pairs around the central sulfur atom, we consider the electron group geometry as tetrahedral. It is essential for drawing the three-dimensional structure to represent the molecules in space. (a) The three-dimensional shape of the molecule can be represented as: Br | S - Br | and the two lone pairs would be on the top and bottom of the sulfur atom. The bond angle in a tetrahedral electron group geometry is \(109.5^\circ\).

Determine the electron group geometry

Since there are four electron groups around the central sulfur atom (two bonding groups and two lone pairs), the electron group geometry is tetrahedral. (b) Electron group geometry: Tetrahedral

Determine the molecular shape

To find the molecular shape, we need to consider the bonded atoms only. In this case, there are 2 bonded atoms and 2 lone pairs around the central sulfur atom. This results in a bent molecular shape. (b) Molecular shape: Bent

Key concepts

Three-Dimensional Molecular Shape

Understanding the three-dimensional molecular shape of compounds is integral in studying chemistry, as it can influence both physical and chemical properties. To visualize the three-dimensional shape, we must first know the Lewis structure, as it informs us about the electron and bonding arrangements.

For instance, considering a molecule with a central sulfur atom bonded to two bromine atoms, we begin by drawing lines connecting the sulfur to each bromine, indicating a chemical bond. To represent the three-dimensional aspect, solid wedges are used to show bonds that project out of the page towards the viewer, while dashed wedges represent bonds going behind the page.

In our example, sulfur has two electron pairs that are not involved in bonding, known as lone pairs. These lone pairs affect the spatial arrangement, causing the molecule to adopt a bent shape rather than a linear one. The molecule's shape is pivotal as it determines reactivity, polarity, and several other properties relevant in chemical reactions and material behavior.

Electron Group Geometry

Electron group geometry refers to the spatial arrangement of all electron regions (domains) around the central atom, regardless of whether they are bonds or lone pairs. The basic geometries one needs to know are linear, trigonal planar, tetrahedral, trigonal bipyramidal, and octahedral.

In analyzing the electron group geometry, we look at the Lewis structure and count both the bonding pairs and lone pairs of electrons. For instance, a sulfur atom with two bonding pairs and two lone pairs has four electron groups in total. This number aligns with a tetrahedral electron group geometry, which has a characteristic angle of approximately 109.5 degrees. This geometry arises due to the electron pairs repelling each other, both bonding and non-bonding, trying to maximize their distance apart to minimize repulsion.

It's important to note that the electron group geometry itself is not always the same as the visible molecular shape. Lone pairs are 'invisible' when determining the molecular shape, but they have a significant impact on the geometry, pushing the bonded atoms to certain positions.

Bond Angles

Bond angles are the angles between adjacent lines representing bonds that emanate from a central atom. These angles are a direct outcome of the electron group geometry and are crucial in defining the shape of the molecule.

In a molecule where the electron group geometry is tetrahedral, such as our sulfur-bromine example, the ideal bond angle is approximately 109.5 degrees. However, the presence of lone pairs can cause deviations from this idealized angle. Lone pairs are slightly more repulsive than bonded pairs, as they occupy more space. Therefore, in cases where lone pairs are present, as in the case of the bent shape of our example, the bond angles are slightly less than 109.5 degrees due to the extra repulsion exerted by the lone pairs.

Knowing the bond angles is integral in predicting the molecule's behavior. For instance, molecules with perfect tetrahedral angles might be nonpolar, but the bent shape with different angles results in a polar molecule, which will have different solubilities and reactivities compared to nonpolar molecules.