Problem 22 - Chemistry The Central Science

Question

Describe the characteristic electron-domain geometry of each of the following numbers of electron domains about a central atom: \((a) 3,(b) 4,(c) 5,(d) 6\)

Step-by-Step Solution

Answer

For different numbers of electron domains about a central atom, the characteristic electron-domain geometries are as follows: (a) For 3 electron domains, the geometry is trigonal planar, with 120° angles between the domains. (b) For 4 electron domains, the geometry is tetrahedral, with 109.5° angles between the domains. (c) For 5 electron domains, the geometry is trigonal bipyramidal, having three equatorial domains with 120° angles and two axial domains at 90° to the equatorial plane. (d) For 6 electron domains, the geometry is octahedral, with each domain having 90° angles from the others.

Step 1: Case A: 3 electron domains

Using VSEPR theory, when the central atom has 3 electron domains, this means that the electron groups will try to stay as far apart as possible to minimize electron repulsion. In this case, the characteristic electron-domain geometry is trigonal planar. The three electron domains are located at 120° angle from each other in a planar arrangement.

Step 2: Case B: 4 electron domains

If the central atom has 4 electron domains, VSEPR theory tells us that these electron groups will maintain a tetrahedral shape to minimize electron repulsion. In this case, the characteristic electron-domain geometry is tetrahedral. Each of the four electron domains is at a 109.5° angle from the others, forming a tetrahedron around the central atom.

Step 3: Case C: 5 electron domains

With 5 electron domains surrounding the central atom, VSEPR theory indicates that the electron groups will adopt a trigonal bipyramidal configuration for minimal electron repulsion. In this case, the characteristic electron-domain geometry is trigonal bipyramidal. Three of the electron domains are located in an equatorial plane (120° angle from one another) and the other two are at the axial positions (90° angle from the equatorial plane and 180° from each other).

Step 4: Case D: 6 electron domains

When there are 6 electron domains around the central atom, VSEPR theory suggests that the electron groups will arrange themselves into an octahedral shape to reduce electron repulsion. In this case, the characteristic electron-domain geometry is octahedral. Here, the six electron domains are organized in such a way that each has a 90° angle from the others, forming an octahedron around the central atom.

Key Concepts

Electron-Domain Geometry

Electron-domain geometry gives us a meticulous arrangement of electron pairs around a central atom. The positions of these pairs are determined using the Valence Shell Electron Pair Repulsion (VSEPR) Theory. This theory helps us understand the 3D structure of the molecule by focusing on minimizing electron repulsion.

By analyzing the number of these electron domains, we can identify the most stable geometry for a molecule.

• Each lone pair or bond (single, double, triple) counts as one domain.
• The geometry influences molecular shape, bond angles, and overall reactivity.

The goal is always to achieve a configuration where electron repulsion is at its lowest, providing a stable structure for the molecule.

Trigonal Planar

When a central atom is surrounded by three electron domains, the geometry is termed trigonal planar. In this structure, the electron domains spread out evenly at angles of 120° in a single plane.

This arrangement minimizes repulsion by maximizing the distance between each domain.

• Commonly seen in molecules like boron trifluoride ( BF_3)
• This geometry is flat because all atoms remain in a single plane.

Even though it seems straightforward, this configuration significantly influences the chemical properties and reactions of the molecule.

Tetrahedral Geometry

With four electron domains, a molecule adopts a tetrahedral geometry. This configuration creates a three-dimensional shape with angles of 109.5° between each domain.

Imagine a pyramid with a triangular base; that's the essence of tetrahedral.

• Methane ( CH_4) is a classic example of tetrahedral geometry.
• This shape allows for an even distribution in 3D space, minimizing repulsion.

Such a structure not only influences physical properties but also dictates how molecules interact in chemical reactions.

Trigonal Bipyramidal

In molecules with five electron domains, the geometry is trigonal bipyramidal. This configuration is slightly more complex, with three domains in an equatorial plane and two in axial positions.

• The angle between equatorial domains is 120°, and the angle between equatorial and axial domains is 90°.
• Phosphorus pentachloride ( PCl_5) showcases this geometry.

This diverse arrangement allows for different interactions and flexibility in chemical reactions, adding a layer of complexity to its chemical behavior.

Octahedral Geometry

When a central atom is surrounded by six electron domains, the resulting geometry is octahedral. This 3D shape is akin to two four-sided pyramids sharing a base.

In this arrangement, all domains are equivalent, with 90° angles between each.

• Sulfur hexafluoride ( SF_6) is a prime example of octahedral geometry.
• This shape provides maximum symmetry and minimal repulsion across all domains.

The octahedral arrangement leads to unique chemical properties and interactions, making it a fascinating area of study in molecular chemistry.