Question

(a) An AB \(_{6}\) molecule has no lone pairs of electrons on the A atom. What is its molecular geometry? (b) An AB \(_{4}\) molecule has two lone pairs of electrons on the A atom (in addition to the four B atoms). What is the electron-domain geometry around the A atom? (c) For the AB \(_{4}\) molecule in part (b), predict the molecular geometry.

Short answer

a) The molecular geometry for the AB\(_6\) molecule with no lone pairs of electrons on the A atom is octahedral. b) The electron-domain geometry for the AB\(_4\) molecule with two lone pairs of electrons on the A atom is octahedral. c) The molecular geometry for the AB\(_4\) molecule with two lone pairs of electrons on the A atom is square planar.

Step-by-step solution

Understanding VSEPR theory

VSEPR theory is used to predict the geometry of molecules based on the repulsion between electron pairs. According to this theory, electron pairs in the valence shell of an atom will try to get as far away from each other as possible due to their repulsive forces. As a result, the distribution of electron pairs will determine the molecular geometry.

AB\(_6\) molecule molecular geometry

In the case of the AB\(_6\) molecule, there are 6 bonding pairs of electrons and no lone pairs. According to VSEPR theory, these pairs of electrons will arrange themselves in an octahedral shape. Therefore, the molecular geometry of the AB\(_6\) molecule is octahedral.

Electron-domain geometry of AB\(_4\) molecule

In the case of the AB\(_4\) molecule with two lone pairs of electrons on the A atom, we need to identify the electron-domain geometry. Since there are 4 bonding electron pairs (from the 4 B atoms) and 2 lone electron pairs (on the A atom), there is a total of 6 electron domains. According to VSEPR theory, the electron-domain geometry for 6 electron domains is octahedral.

Molecular geometry of AB\(_4\) molecule with two lone pairs on A atom

Now that we have identified the electron-domain geometry, we can predict the molecular geometry of the AB\(_4\) molecule with two lone pairs of electrons on the A atom. Since there are 4 bonding electron pairs and 2 lone electron pairs, the shape will be determined by the positions of the 4 bonding electron pairs. The positions that minimize repulsions between the lone pairs and the bonding pairs in an octahedral arrangement will result in a square planar molecular geometry. In conclusion: a) The molecular geometry for the AB\(_6\) molecule with no lone pairs of electrons on the A atom is octahedral. b) The electron-domain geometry for the AB\(_4\) molecule with two lone pairs of electrons on the A atom is octahedral. c) The molecular geometry for the AB\(_4\) molecule with two lone pairs of electrons on the A atom is square planar.

Key concepts

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is a fundamental principle in chemistry that explains the shape of molecules. It is based on the idea that groups of electrons, known as electron domains, surrounding a central atom will repel each other and occupy positions in space that minimize this repulsion.

This repulsion leads to a geometric arrangement of electron domains that determines the overall shape of the molecule. The electron domains can consist of lone pairs, single bonds, double bonds, triple bonds, or even free electron pairs that are not involved in bonding.

• Two electron domains: Linear
• Three electron domains: Trigonal planar
• Four electron domains: Tetrahedral
• Five electron domains: Trigonal bipyramidal
• Six electron domains: Octahedral

To predict molecular shape using VSEPR theory, one simply counts the number of electron domains and then uses the corresponding geometric arrangement.

Electron-Domain Geometry

Electron-domain geometry refers to the three-dimensional arrangement of electron domains (bonding and non-bonding electron pairs) around a central atom in a molecule. This geometry only considers the spatial orientation of the electron domains, not the actual positions of the atoms.

Determining the electron-domain geometry is the first step in predicting molecular shape because it accounts for all electron pairs, which ultimately influence the final structure of the molecule. Electron-domain geometries include linear, trigonal planar, tetrahedral, trigonal bipyramidal, and octahedral, corresponding to the number of electron domains surrounding the central atom.

Octahedral Molecular Shape

An octahedral molecular shape is a type of geometric structure that is frequently encountered in molecules with six electron domains surrounding a central atom. In an octahedral arrangement, the six regions of electron density form a shape that resembles two square pyramids joined at their bases.

The term 'octahedral' comes from the geometry having eight faces, where the central atom is positioned at the center of the octahedron and the six ligands (atoms or groups bonded to the central atom) are located at the vertices. These ligands are equidistant from the central atom and achieve a 90-degree angle between each other, resulting in a highly symmetrical shape which is crucial in many chemical and biological processes.

Square Planar Molecular Geometry

The square planar molecular geometry arises when there are four bonding electron pairs and two lone pairs in the electron domain of a molecule with six total electron domains. Here, the central atom lies at the center of a square, and the four atoms it is bonded to occupy the corners of the square.

The unique aspect of the square planar shape is that the two lone pairs are positioned opposite each other in the octahedral electron-domain arrangement. This gives way to a planar, or flat, molecular shape, minimizing the repulsion between these denser electron regions and maintaining the stability of the molecule. This geometry is less common than some other shapes, but is very important in the field of coordination chemistry and is often seen in metal complexes.

Lone Pairs of Electrons

Lone pairs of electrons are pairs of valence electrons that are not involved in chemical bonding. These pairs occupy electron domains around an atom just like bonding pairs but they have no bonding responsibility.

Importantly, lone pairs exert a greater repulsive force on adjacent electron pairs than bonding pairs do. This greater repulsion is due to the lone pair electrons being closer to the nucleus and thus, occupying more space around the central atom. The presence of lone pairs can thus affect the molecular geometry significantly, often leading to shapes that do not conform to the idealized electron-domain geometry. Understanding how lone pairs influence molecular shape is fundamental in predicting a molecule's geometry through VSEPR theory.