Кути при ідеальних зв'язках

Ideal Bond Angles in Chemical Compounds

The ideal bond angles are the angles that would be formed if all of the electron domains surrounding an atom were arranged in a perfectly symmetrical manner. Ultimately, these ideal bond angles are usually not quite correct, because lone electron pairs repel other electron pairs more strongly than bonding electron pairs. However, the ideal bond angles are still usually pretty close to the true bond angles.

If there is $1$ electron domain surrounding an atom, then there are no associated electron domain geometry and ideal bond angles.

If there are $2$ electron domains surrounding an atom, then the electron domain geometry is linear, and the ideal bond angles are $180^{\circ}.$

If there are $3$ electron domains surrounding an atom, then the electron domain geometry is trigonal planar, and the ideal bond angles are $120^{\circ}.$

If there are $4$ electron domains surrounding an atom, then the electron domain geometry is tetrahedral. Doing some geometry, we can find that the ideal bond angles are $\arccos\left(-\frac{1}{3}\right),$ which is approximately $109.5^{\circ}.$

If there are $5$ electron domains surrounding an atom, then the electron domain geometry is trigonal bipyramidal, and the ideal bond angles are $90^{\circ}$ and $120^{\circ}.$ There are two different bond angles in this case because there is no Platonic solid with $5$ vertices, meaning that it is not possible to have all $5$ vertices occupy perfectly symmetrical positions with respect to all adjacent vertices.

If there are $6$ electron domains surrounding an atom, then the electron domain geometry is octahedral, and the ideal bond angles are $90^{\circ}.$

Ideal Bond Angles

(Video) VSEPR Theory - Basic Introduction

By: The Organic Chemistry Tutor

In this video, you will learn about the different types of molecular geometry and their ideal bond angles from VSEPR theory. This video gives examples of different molecules that have different geometries, as well as helps give tips on how to identify the geometry and ideal bond angle of different molecules.

Imagine we have a molecule. It has a central atom. Around the central atom are covalent bonds and lone pairs. These are regions of elevated electron density. What do they want to do? They are all negative charges. So, they repel one another. They want to be as far from each other as possible!

In our last lesson, we started studying VSEPR theory. It helps us determine a molecule's molecular geometry. The model's premise is that electrons repel. But more repulsion amplifies the energy. We know that molecules want to increase their stability. They need to minimize their energy. So, they limit the repulsive forces. How? By having the electrons distributed evenly around the atom. Our goal is to maximize the angle between the electrons.

Steric Numbers

How do we determine the angles? We start with the number of electron domains. Electron domains are the most probable area for finding an electron. In the VSEPR model, that's covalent bonds and lone pairs. The total number of electron domains is the steric number. For multiple bonds, we count them as one electron domain. Why? All the electrons stay localized between two atoms. Any atoms attached to the central atom are called ligands.

For example, let's consider carbon dioxide. The central atom is carbon. It's double-bonded to two oxygen ligands. So, it has two electron domains, and its steric number is two. Let's also consider water. The central oxygen atom is single-bonded to two hydrogens. It also has two lone pairs of electrons. So, its steric number is four.

Ideal Bond Angles

What is a covalent bond? Two atoms share valence electrons. By sharing, each element can complete its octet. In the VSEPR model, we assume bonded electrons are localized. They get attracted to the protons in both nuclei. So, we imagine they get stuck between the atoms. It does not matter if the bond is polar. We ignore electronegativity differences. What about lone pairs? They are only attached to one atom. They have more freedom to move around. So, they take up more space.

Let's imagine a central atom that has zero lone pairs. So, it only has bonds. The bonds will be as far apart as possible. We call this the ideal bond angle. What if we replaced one of the bonds with a lone pair? The lone pair takes up more space. So, we have a deviation from the ideal angle.

The most straightforward geometry is the linear molecule. It always has a steric number of two. The quintessential example is carbon dioxide. The bonds form in a straight line. So, the electron domains are 180 degrees apart.

Molecules with three electron domains are trigonal planar. The model example is borane ($BH_{3}$). Remember, boron only has three valence electrons. So, it's an exception to the octet rule. Each hydrogen atom will spread out evenly. So, the ideal bond angle is 120 degrees.

What about four electron domains? For four, we have to remember that molecules are three-dimensional. So, the ligands can also extend directly above or below the central atom. Four electron domains create a tetrahedral molecule. The best example is methane ($CH_{4}$). One hydrogen points upward. The other three distribute around the base of the carbon. The bond angle is 109.5 degrees.

Trigonal bipyramidal molecules have five bonds! So, they are exceptions to the octet rule. What are some examples? Phosphorous and sulfur can bond to five halogens. Why? Because they have access to the d-orbitals. If you drew a line between the bonded atoms, it would have two three-sided pyramids. One pyramid would point up. The other pyramid would point down. Two atoms point straight up and down. The other three get dispersed around the center. So, it has two bond angles. The center atoms are a trigonal planar shape with 120-degree angles. The up and down ligands are 90 degrees from the center atoms.

Octahedral molecules have six bonds! Two of the bonds are straight up and down. The other four bonds are around the center. An example is sulfur hexafluoride ($SF_{6}$). The bond angle between each fluorine is 90 degrees.

Try It At Home

Are you having a hard time imagining these molecules? It can be hard to visualize molecular geometry. To help you visualize, you have some options. The most fun is using balloons! When we handle balloons, they build up a charge. So, if we tie them together, they act like electrons. They repel each other! Just make sure your balloons are equal in size. The more mundane option is to buy a molecular model kit. If you take organic chemistry, you'll probably have to buy one. They allow you to build molecules from little plastic balls and sticks. It helps with visualization. But it's less fun.