Problem 86 - Chemistry The Central Science In Si Units

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?

Step-by-Step Solution

Answer

(a) Two nonbonding domains on atom A. (b) Bent molecular geometry.

Step 1: Understanding Tetrahedral Geometry

In a tetrahedral geometry, the central atom is surrounded by four electron pairs, distributed in a 3D shape resembling a pyramid. These pairs can be either bonding or nonbonding electron pairs (lone pairs).

Step 2: Identifying Bonding Domains

For a molecule designated as \( \mathrm{AB}_2 \), there are two bonding domains, as the formula indicates that atom A is bonded to two B atoms.

Step 3: Calculating Nonbonding Domains

Since a tetrahedral arrangement involves four electron domains, and we have two bonding domains, the number of nonbonding domains is calculated as: \( 4 - 2 = 2 \). Thus, atom A has two nonbonding domains.

Step 4: Determining Molecular Geometry

The presence of two nonbonding domains and two bonding domains (\( \mathrm{AB}_2 \) with two lone pairs) results in a bent molecular geometry according to VSEPR (Valence Shell Electron Pair Repulsion) theory.

Key Concepts

Tetrahedral Geometry

Tetrahedral geometry is a common molecular shape that involves a central atom connected to four other atoms or groups. Think of it as a structure similar to a pyramid with a triangular base, or a three-dimensional star. This arrangement allows for minimizing the repulsion between electron pairs that surround the central atom. Each of these electron pairs, whether bonding or nonbonding, tries to be as far apart as possible. This is because electrons repel each other due to their like charges. In a tetrahedral arrangement, the angles between electron pairs are about 109.5 degrees, which is the optimal angle for spacing four points evenly around a central point. This geometry is crucial for understanding molecular shapes because even slight changes in angle can lead to different molecular geometries.

Nonbonding Electron Pairs

Nonbonding electron pairs, also known as lone pairs, are electron groups that do not participate in bonding. They are located on the central atom and can have a significant impact on the shape of a molecule. Unlike bonding electron pairs, which are shared between atoms to form a covalent bond, nonbonding pairs are solely associated with one atom.
These pairs still exert repulsive forces on other electron domains (like bonding pairs) but can often push them closer together. This effect can alter the expected geometry of a molecule. For instance, in a tetrahedral arrangement with two bonding and two nonbonding pairs, the nonbonding pairs push the bonding pairs closer together, leading to a bent shape rather than a perfect tetrahedral angle.

Molecular Geometry

Molecular geometry describes the three-dimensional arrangement of atoms within a molecule. This configuration influences physical and chemical properties, such as polarity and reactivity. Molecular geometry is determined by considering both bonding and nonbonding electron pairs around the central atom.
The VSEPR theory, which stands for Valence Shell Electron Pair Repulsion theory, helps predict molecular geometry. VSEPR theory is based on the principle that electron domains, both bonding and nonbonding, repel each other and seek to be as far apart as possible. By assessing the number and types of electron pairs, one can determine the shape of a molecule. For example, even if the electron geometry is tetrahedral, the molecular geometry might be different, such as bent, depending on the number of nonbonding electron pairs.

Bent Geometry

Bent geometry is a common shape that results from the influence of nonbonding electron pairs on a molecule's structure. In the context of VSEPR theory, a bent shape forms when there are two bonding pairs and one or more nonbonding pairs on the central atom.
The nonbonding pairs take up more space than bonding pairs, as they are not shared between atoms. This causes them to push the bonding pairs closer together, resulting in a bent or angular shape. The angle between the bonding pairs in a bent molecule is less than the 109.5-degree angle seen in a perfect tetrahedral geometry; it's typically around 104.5 degrees for water, a classic example of a bent molecule. Bent geometries are important because they often lead to polar molecules, which have significant implications for the molecule's interactions and properties.