Question

An \(\mathrm{AB}_{2}\) molecule is described as having a tetrahedral geometry. (a) How many nonbonding domains are on atom A? (b) Based on the information given, which of the following is the molecular geometry of the molecule: (i) linear, (ii) bent, (iii) trigonal planar, or (iv) tetrahedral?

Short answer

(a) There are 2 nonbonding domains on atom A. (b) The molecular geometry of the \(\mathrm{AB}_{2}\) molecule is (iv) tetrahedral.

Step-by-step solution

Identifying the number of nonbonding domains on atom A

In an \(\mathrm{AB}_{2}\) molecule, there are two bonding domains surrounding atom A, as it is connected to two B atoms. Each bonding domain consists of a pair of electrons shared between atom A and one of the B atoms. To determine how many nonbonding domains are present on atom A, we need to find out how many electron pairs are not involved in forming bonds. The molecule is described as having a tetrahedral geometry, which implies that there must be four total domains surrounding atom A (including both bonding and nonbonding domains). Thus, the number of nonbonding domains can be calculated as follows: \[Number\,of\,nonbonding\,domains = Total\,domains - Bonding\,domains\]

Calculate the number of nonbonding domains on atom A

Using the formula from Step 1, we can calculate the number of nonbonding domains on atom A: \[Number\,of\,nonbonding\,domains = 4 - 2\] \[Number\,of\,nonbonding\,domains = 2\] So there are 2 nonbonding domains on atom A. Answer (a): 2

Identifying the molecular geometry of the molecule

Since we know the total domains surrounding atom A and the number of nonbonding domains, we can now identify the molecular geometry of the \(\mathrm{AB}_{2}\) molecule. The molecular geometry can be one of the following based on the information given: (i) linear (ii) bent (iii) trigonal planar (iv) tetrahedral However, recall that we are given that the molecule has a tetrahedral geometry, implying that the molecular geometry must be tetrahedral. In the case of an \(\mathrm{AB}_{2}\) molecule with a tetrahedral geometry, the structure consists of 2 bonding domains and 2 nonbonding domains, and the B-A-B angle would be less than that of a regular tetrahedron, which is 109.5°. Answer (b): (iv) tetrahedral

Key concepts

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. It is determined by considering all electron pairs surrounding a central atom, including both bonding and nonbonding pairs. The concept is crucial because it influences properties like reactivity, polarity, and biological activity.
Different types of molecular geometry include linear, bent, trigonal planar, tetrahedral, and others. The arrangement is predicted using the VSEPR (Valence Shell Electron Pair Repulsion) theory, which states that electron pairs around a central atom tend to orient themselves as far apart as possible to minimize repulsion.
By counting and categorizing the electron pairs (bonding and nonbonding), one can predict the shape or geometry, which dictates molecular function and behavior.

Tetrahedral Geometry

Tetrahedral geometry is a specific type of molecular shape characterized by four electron domains surrounding a central atom. This shape occurs when the central atom forms four bonds with other atoms, or when there are a combination of bonds and lone pairs, totaling four domains.

• The ideal bond angle in a tetrahedral molecule is 109.5°.
• Tetrahedral geometry contributes to the stability and symmetry of many molecular structures.
• Common compounds like methane ( ext{CH}_4) exemplify tetrahedral geometry.

When nonbonding pairs replace some of the bonding pairs in molecules like water ( ext{H}_2 ext{O}), the angle gets distorted from the ideal value. Such variations still arise under the umbrella of tetrahedral electron geometry.

Nonbonding Domains

Nonbonding domains, also known as lone pairs, consist of electron pairs that do not partake in bonding. These pairs are significant as they afford molecules flexibility and influence molecular shape and polarity.
Lone pairs occupy more space than bonding pairs because they are solely influenced by one nucleus. They are key in determining a molecule's geometry alongside bonding domains. For instance, in a water molecule, the two nonbonding domains significantly alter the geometry to a bent shape, although the electron geometry remains tetrahedral.

• Lone pairs can strongly affect molecular angles by repelling bonding pairs.
• They play a crucial role in chemical reactivity and intermolecular interactions.

Bonding Domains

Bonding domains result from electrons shared between atoms, forming a chemical bond. These bonds are essential in dictating the framework of a molecule. In the context of VSEPR theory, bonding domains contribute to the total electron domains around a central atom.
Understanding bonding domains is fundamental in predicting how atoms will organize around a central atom. For example, in an ext{AB}_2 molecule with two bonding domains, like in the linear carbon dioxide molecule, the arrangement creates distinct molecular geometries that impact the molecule's properties.

• Bonding domains typically form bonds such as sigma or pi bonds.
• They are instrumental in determining the basic skeleton and function of molecules in a variety of chemical contexts.

Recognizing the interplay between bonding and nonbonding domains allows for a deeper comprehension of molecular architecture and interactions.