Question

List the correct electron and molecular geometries that correspond to each set of electron groups around the central atom of a molecule. \begin{equation}\begin{array}{l}{\text { a. four electron groups overall; three bonding groups and one lone pair }} \\ {\text { b. four electron groups overall; two bonding groups and two lone pair }} \\ {\text { c. five electron groups overall; four bonding groups and one lone pair }} \\ {\text { d. five electron groups overall; three bonding groups and two lone pairs }}\end{array}\end{equation}\begin{equation}\begin{array}{l}{\text { e. five electron groups overall; two bonding groups and three lone pairs }} \\ {\text { f. sixe electron groups overall; five bonding groups and one lone pair }} \\\ {\text { g. six electron groups overall; four bonding groups and two lone pairs }}\end{array}\end{equation}

Short answer

a. Electron Geometry: Tetrahedral, Molecular Geometry: Trigonal Pyramidal; b. Electron Geometry: Tetrahedral, Molecular Geometry: Bent; c. Electron Geometry: Trigonal Bipyramidal, Molecular Geometry: See-Saw; d. Electron Geometry: Trigonal Bipyramidal, Molecular Geometry: T-Shaped; e. Electron Geometry: Trigonal Bipyramidal, Molecular Geometry: Linear; f. Electron Geometry: Octahedral, Molecular Geometry: Square Pyramidal; g. Electron Geometry: Octahedral, Molecular Geometry: Square Planar.

Step-by-step solution

Identify the Geometry for Case a

For four electron groups overall with three bonding groups and one lone pair, the electron geometry is tetrahedral. Because of the lone pair, the molecular geometry will be trigonal pyramidal.

Determine the Geometry for Case b

With four electron groups overall and two bonding groups with two lone pairs, the electron geometry remains tetrahedral. The molecule will have a bent or angular molecular geometry due to the lone pairs.

Figure out the Geometry for Case c

For five electron groups overall including four bonding groups and one lone pair, the electron geometry is trigonal bipyramidal. The molecular geometry becomes a see-saw shape.

Assess the Geometry for Case d

When there are five electron groups overall with three bonding groups and two lone pairs, the electron geometry is still trigonal bipyramidal. The molecular geometry is T-shaped.

Evaluate the Geometry for Case e

Having five electron groups overall with two bonding groups and three lone pairs means the electron geometry is trigonal bipyramidal, but the molecular geometry is linear because there are lone pairs in the equatorial position removing the other positions.

Examine the Geometry for Case f

In the presence of six electron groups overall with five bonding groups and one lone pair, the electron geometry is octahedral. The molecular geometry is square pyramidal due to the lone pair.

Analyze the Geometry for Case g

With six electron groups overall and four bonding groups with two lone pairs, the electron geometry is octahedral. The molecular geometry will be square planar, as the lone pairs arrange themselves to be opposite each other, canceling out their influence and forming a square plane.

Key concepts

Electron Group Arrangement

Understanding the arrangement of electron groups around the central atom of a molecule is key to determining its molecular geometry. An electron group includes not only the bonds shared with adjacent atoms but also any lone pairs of electrons that may exist. The total number of electron groups gives us a foundational shape, known as the electron group geometry.

This arrangement is determined by the principle of electron repulsion, which states that electron groups will arrange themselves as far apart as possible to minimize repulsion between each set of negatively charged electrons. This principle is often referred to as VSEPR theory, or Valence Shell Electron Pair Repulsion theory, and it is the guide we follow to predict the three-dimensional structure of molecules. For instance, when we have four electron groups, they arrange in a way that forms a shape similar to a tetrahedron.

Tetrahedral Geometry

When a molecule has four electron groups surrounding the central atom, the electron geometry is referred to as tetrahedral. In a perfect tetrahedral geometry where all the electron groups are bonding pairs, the atoms are arranged symmetrically around the central atom at approximately 109.5 degrees to one another.

However, if there are lone pairs involved, they will occupy more space than bonding pairs due to their stronger repulsion forces, causing the molecular geometry to adjust. For example, a molecule with three bonding groups and one lone pair (like case a from the exercise) will have a trigonal pyramidal molecular geometry. On the other hand, if there are two bonding groups and two lone pairs (case b), the molecule assumes a bent or angular molecular geometry.

Trigonal Bipyramidal Geometry

If there are five electron groups around the central atom, the electron geometry takes on a trigonal bipyramidal shape. This geometry has a central equatorial plane with three electron groups spaced at 120 degrees and two additional positions called axial positions that are at 90 degrees to the equatorial plane, forming a 3D bipyramid.

The presence of lone pairs changes the molecular geometry from the idealized trigonal bipyramidal shape. For example, with one lone pair and four bonding pairs (case c), the molecular geometry is a see-saw. If there are two lone pairs (case d), the shape is T-shaped. With three lone pairs and two bonding pairs (case e), the molecular geometry simplifies to linear, as the lone pairs spread out within the equatorial plane.

Octahedral Geometry

An octahedral geometry is found in molecules with six electron groups surrounding the central atom. This electron group arrangement positions the atoms at 90-degree angles to each other, forming an octahedron - an eight-faced polyhedron with equal distances between the central atom and the surrounding atoms.

When one of the six groups is a lone pair (as seen in case f), the resulting molecular geometry is square pyramidal, with one atom missing from the octahedral structure, forming a square base and a pyramidal shape with the remaining atoms. If there are two lone pairs (case g), they position themselves opposite from each other, leading to a square planar molecular geometry, flattening the molecule along a plane with four atoms forming the corners of a square.