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

Short answer

The electron-domain geometries of a central atom with different numbers of electron domains are as follows: (a) For 3 electron domains, the geometry is Trigonal Planar. (b) For 4 electron domains, the geometry is Tetrahedral, with bond angles of 109.5º. (c) For 5 electron domains, the geometry is Trigonal Bipyramidal, with 120º and 90º angles between electron domains. (d) For 6 electron domains, the geometry is Octahedral, with 90º angles between each pair of electron domains.

Step-by-step solution

Identify the number of electron domains

We are told that there are 3 electron domains surrounding the central atom. This implies that there are three regions of electron density around the central atom.

Determine the electron-domain geometry

Since the repulsion between the 3 electron domains wants to be minimized, they'd occupy positions as far apart as possible in space. Thus, they form an equilateral triangle with the central atom in the middle, creating a total angle of 360º. This geometry is called Trigonal Planar. #b) 4 Electron Domains#

Identify the number of electron domains

We are told that there are 4 electron domains surrounding the central atom. This implies that there are four regions of electron density around the central atom.

Determine the electron-domain geometry

For the 4 electron domains to minimize repulsion, they'd occupy positions as far apart as possible in space. They will form a regular tetrahedron with the central atom in the middle, creating a geometry called Tetrahedral, which has bond angles of 109.5º between each pair of electron domains. #c) 5 Electron Domains#

Identify the number of electron domains

We are told that there are 5 electron domains surrounding the central atom. This implies that there are five regions of electron density around the central atom.

Determine the electron-domain geometry

To minimize repulsion for the 5 electron domains surrounding the central atom, they will form an arrangement known as Trigonal Bipyramidal. In this geometry, three of the electron domains form an equilateral triangle at the central atom's plane, creating a 120º angle, and the other two domains are positioned above and below the triangle, 180º apart and forming 90º angles with the domains in the plane. #d) 6 Electron Domains#

Identify the number of electron domains

We are told that there are 6 electron domains surrounding the central atom. This implies that there are six regions of electron density around the central atom.

Determine the electron-domain geometry

To minimize repulsion between the 6 electron domains surrounding the central atom, they will adopt an octahedral arrangement. In an Octahedral geometry, all six domains are arranged in a way that forms the vertices of a regular octahedron, with the central atom in the middle. Every pair of electron domains are 90º apart.

Key concepts

Trigonal Planar

Understanding Trigonal Planar electron-domain geometry is crucial for students studying molecular shapes. When a central atom is surrounded by three regions of electron density, these domains will arrange themselves as far apart as possible to reduce repulsion. This results in a flat, triangular shape where the central atom lies in the middle, much like the Mercedes-Benz logo. Each angle within this triangle, or plane, is 120 degrees, providing the molecule with an even, three-sided distribution of its electron clouds.

To visualize this, think about placing three dots equally apart on the edge of a circle with a dot at the center; that center dot represents the central atom and the outer dots are the electron domains. This configuration is not only aesthetically pleasing but also an energetically favorable arrangement for molecules with three electron domains, such as BF₃ (boron trifluoride).

Tetrahedral

When we step up to four electron domains around a central atom, enter the Tetrahedral shape. Aiming for maximum separation, the domains will form what can be imagined as a pyramid with a triangular base. Each corner of the base and the peak of the pyramid form the points where the electron domains reside. This structure creates bond angles of about 109.5 degrees between any two electron clouds.

Consider the shape of a classic gaming die; the central atom would be at the center, while the corners of the die are where the electron domains push out to. Methane (CH₄) is a prime example of a molecule sporting this geometric figure. Four hydrogen atoms are linked to a central carbon atom, all equally spread out in three-dimensional space to keep the negative charge from the electrons as distant as possible from each other.

Trigonal Bipyramidal

Moving into a more complex terrain, the Trigonal Bipyramidal geometry comes into play with five electron domains around a central atom. Picture a tripod: three of these domains lay out in a horizontal plane, forming 120-degree angles with each other. This 'tripod' supports two more electron domains, one shooting up and the other directly down, forming straight lines with the central atom, 90 degrees apart from the plane.

Such an arrangement is like having two pyramids base-to-base, with the central atom marking the meeting point. A real-world molecule with trigonal bipyramidal geometry is phosphorus pentafluoride (PF₅), where three fluorine atoms spread out in one plane and the remaining two stake out positions above and below this plane.

Octahedral

The Octahedral geometry illustrates the electron-domain structure for six electron clouds surrounding a central atom. An octahedron is like two square-based pyramids attached at their bases; the electron domains reside at the six corners of the pyramid bases. Here, each electron cloud is perfectly 90 degrees apart from its neighbors, making it a highly symmetrical shape.

One way to depict this is imagining a box where each corner is an electron domain, and the central atom is floating right at the heart of the box. All angles are squared-off, creating an overall shape that has eight faces—hence the prefix 'octa-' in octahedral. A typical molecule with such geometry is sulfur hexafluoride (SF₆), exhibiting this six-sided electron domain distribution surrounding a central sulfur atom.