Problem 18 - Chemistry: The Central Science

Question

An \(\mathrm{AB}_{3}\) molecule is described as having a trigonalbipyramidal electron-domain geometry. How many nonbonding domains are on atom A? Explain.

Step-by-Step Solution

Answer

In an AB3 molecule with a trigonal bipyramidal electron-domain geometry, there are a total of 5 electron domains, out of which 3 are bonding domains (as the central atom A is bonded to three B atoms). To find the number of nonbonding domains, we subtract the number of bonding domains from the total number of domains: \(Nonbonding\,electron\,domains = 5 - 3 = 2\). Hence, there are 2 nonbonding electron domains on atom A.

Step 1: Understand the trigonal bipyramidal electron-domain geometry

In a trigonal bipyramidal electron-domain geometry, the central atom (atom A) is surrounded by five electron domains. Three of the domains form an equilateral triangle (trigonal plane) and the other two domains are located above and below the trigonal plane, forming two opposite "pyramidal" parts. The whole structure forms a bipyramid.

Step 2: Analyze the AB3 molecule

In an AB3 molecule, the central atom A is bonded to three other atoms (B atoms). We need to find out how many nonbonding domains are present on atom A in the trigonal bipyramidal geometry.

Step 3: Identify the number of bonding and nonbonding domains on atom A

Since there are three B atoms bonded to the central atom A, we have three bonding electron domains in the trigonal bipyramidal geometry. As there are a total of five electron domains in the trigonal bipyramidal geometry, we can find out the number of nonbonding domains by subtracting the number of bonding domains from the total number of domains. Total electron domains = 5 (trigonal bipyramidal geometry) Bonding electron domains = 3 (AB3 molecule) Nonbonding electron domains = Total electron domains - Bonding electron domains

Step 4: Calculate the number of nonbonding electron domains

Now we can calculate the number of nonbonding electron domains: Nonbonding electron domains = 5 - 3 = 2 Therefore, there are 2 nonbonding electron domains on atom A in the AB3 molecule with a trigonal bipyramidal electron-domain geometry.

Key Concepts

Electron-Domain Geometry

In chemistry, the shape of molecules plays a critical role in understanding how they behave and react with other molecules. The term electron-domain geometry is used to describe the spatial arrangement of electron domains—regions around a central atom where electrons are likely to be found. For a molecule with a central atom, like the AB3 molecule in our example, electron domains can include both bonds to other atoms (bonding domains) and lone pairs of electrons that are not shared (nonbonding domains).

In the case of a trigonal bipyramidal geometry, the central atom is surrounded by five regions of electron density. This geometry is defined by its three equatorial positions forming a plane, and two axial positions above and below this plane. Such arrangements minimize electron repulsion according to the Valence Shell Electron Pair Repulsion (VSEPR) theory, leading to a stable electronic structure for the molecule.

Nonbonding Electron Domains

Nonbonding electron domains, also known as lone pairs, have observable effects on the geometry of a molecule. These lone pairs can cause repulsion that can be stronger than that caused by bonded pairs, altering the angles between bonds. For instance, in the AB3 molecule with trigonal bipyramidal electron-domain geometry, nonbonding domains must be identified to understand the full shape of the molecule.

To calculate the number of nonbonding electron domains, you must first know the total number of electron domains surrounding the central atom, and how many of those domains are occupied by bonds (bonding domains). By subtracting the bonding domains from the total electron domains, you determine the number of nonbonding electron domains. In our exercise, the AB3 molecule has two nonbonding domains. This has implications for the molecular shape, which is influenced by the presence of these lone pairs.

Molecular Geometry

While electron-domain geometry accounts for both bonding and nonbonding electron pairs, the term molecular geometry specifically describes the arrangement of only the atoms in a molecule. A central atom bonded to three other atoms, as in our AB3 molecule example, would ideally form a trigonal planar molecular geometry if there were no lone pairs. However, with nonbonding electron domains present, the shape is altered.

The VSEPR theory predicts that the two nonbonding electron domains in the AB3 molecule with trigonal bipyramidal electron-domain geometry will occupy the equatorial positions, as these offer greater distance from other electron domains and reduce repulsion. As a consequence, the molecular geometry becomes a seesaw shape, due to the presence of those lone pairs pushing down on the bonded atoms.

Chemical Bonding

At the heart of molecular shape and structure lies chemical bonding, the attraction between atoms that allows the formation of chemical substances containing two or more atoms. The bonds between the central atom and surrounding atoms in a molecule are typically covalent, meaning electrons are shared between the atoms. When analyzing an AB3 molecule in terms of trigonal bipyramidal geometry, it's essential to distinguish between the bonding and nonbonding electron pairs.

The three bonds in the AB3 molecule represent areas where electrons are shared between the central atom A and the B atoms. The shared electrons occupy bonding domains and dictate the foundation of the molecule's shape. In our exploration, we've concluded that two additional nonbonding domains complete the five required for a trigonal bipyramidal arrangement, affecting both the electron-domain and molecular geometries through their influence on the spatial distribution of all electron domains.