Question

A molecule with the formula \(A B_{3}\) has a trigonal pyramidal geometry. How many electron groups are on the central atom (A)?

Short answer

There are 4 electron groups on the central atom (A).

Step-by-step solution

Identify the Number of Bonding Groups

The molecular formula given is \(AB_3\), which means there are three bonding groups attached to the central atom A.

Identify the Electron Group Geometry

Given the molecule has a trigonal pyramidal geometry, this means that, in addition to the bonding groups, there must be one lone pair of electrons on the central atom to account for the pyramidal shape, as opposed to a trigonal planar shape which would have no lone pairs.

Calculate the Total Number of Electron Groups

Add the number of bonding groups (3) to the number of lone pairs (1) on the central atom to determine the total number of electron groups. Therefore, there are 3 + 1 = 4 electron groups on the central atom (A).

Key concepts

Molecular Geometry

Understanding molecular geometry is crucial for students as it helps in predicting the shape of a molecule. The shape of a molecule is determined by the positions of the nuclei and the electron pairs surrounding the central atom. In our particular exercise, with a formula of \(AB_3\), the molecule is described as having a trigonal pyramidal geometry.

This essentially means the central atom A is at the apex of a pyramid with the three B atoms forming the base of the pyramid. The molecular geometry is influenced not only by the atoms but also by any lone pairs of electrons that are present on the central atom. For instance, when lone pairs are present, as in the case of a trigonal pyramidal geometry, they push the bonding groups slightly closer together, altering the shape from what would be predicted if we only considered the atoms themselves.

Electron Group

Electron groups around a central atom include both bonding pairs of electrons, which may be found in single, double, or triple bonds, as well as lone pairs, which are pairs of valence electrons not involved in bonding. In our exercise, the central atom A has three bonding groups or pairs of electrons that connect to the three B atoms. It is essential for students to recognize that all these groups, whether they're forming bonds or present as lone pairs, occupy space and repel each other. This mutual repulsion is what determines the final geometry of the molecule.

These groups want to be as far apart as possible, leading to specific molecular shapes. For instance, if there were only bonding groups and no lone pairs, the molecule might adopt a different shape.

Lone Pair

A lone pair refers to a pair of valence electrons that are not shared with another atom and hence do not participate in bonding. Lone pairs have a significant impact on a molecule's shape because they take up more space around the central atom compared to bonding pairs. This is due to the lack of contraction from bonding, which lone pairs do not experience. In the exercise example, we deduce that there must be one lone pair on the central atom A in order to create a trigonal pyramidal geometry. The presence of this lone pair pushes the bonding groups together, creating a three-dimensional shape rather than a flat one.

Lone pairs are crucial in VSEPR theory as they can often be the deciding factor in the molecular shape, which is why identifying their presence is an essential step in predicting molecular geometry.

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is a model used in chemistry to predict the geometry of individual molecules based on the number of electron groups surrounding their central atoms. According to the VSEPR theory, electron groups will arrange themselves to minimize the repulsion between them.

The way these electron groups can be lone pairs, bonding pairs, or even multiple bonds is important because they all influence the molecular geometry. For a molecule with the formula \(AB_3\), which displays a trigonal pyramidal geometry, the VSEPR theory helps us conclude that there must be four electron groups in total. Three are bonding pairs connecting the central atom to the three peripheral atoms, and one is a lone pair. This lone pair causes the bonding pairs to adopt a geometry that has a non-planar shape, hence the term 'pyramidal'.

By applying VSEPR theory, students can predict the molecular shape of most simple molecules and polyatomic ions by knowing the number of electron groups around the central atom.