Have you ever thought about the bond you share with your best friend? When you first met, you probably weren't very close, but as you spent more time together, your friendship became stronger. This is similar to covalent bonds, where the bond length affects the strength of the bond. When the bond length shortens between atoms, the bond energy increases, making it stronger.

So, what exactly is bond length? It's the average distance between the two nuclei of atoms bonded together in a covalent bond. On the other hand, bond energy is how much potential energy is needed to break a covalent bond. Now, let's dive into the formula for bond length and how it's measured. We'll also explore the common trends in bond lengths and how it's reflected in the periodic table. To help us understand this better, we'll take a look at the bond length chart. Lastly, we'll examine the bond length of hydrogen molecules and double bonds in more detail. By understanding bond length and bond energy, we can better understand how atoms form bonds and interact with each other. Plus, it's just really interesting stuff!

What is the Bond Length Formula?

If you've read about Intramolecular Forces and Potential Energy, you should already have a basic understanding of bond length. It's the distance between the two nuclei of covalently bonded atoms when the potential energy of the bond is at its minimum. Bond length is typically measured in picometers (pm) or Angstrom (Å), and two factors that directly affect it are bond order and atomic radius.

It's important to note that bond length and bond energy are inversely related to each other. This means that as bond length decreases, bond energy increases. Coulomb's Law is a formula that proves this relationship. It states that similar forces repel each other, while opposite forces attract one another. Although Coulomb's Law is primarily associated with ionic bonds and their interactions, weak coulombic forces do exist in covalent bonds between the negatively charged electrons and positively charged nuclei of the bonding atoms.

While it's helpful to be familiar with Coulomb's Law, you won't usually need to use it to determine the bond length of covalent bonds. Instead, you can use other methods. Coulomb's formula can be used broadly to prove the relationship between bond strength and bond length, but it's mainly associated with ionic bonds and their interactions. You can learn more about this in Coulomb's Law and Interaction Strength.

The other means of calculating bond length are through potential energy diagrams and an atomic radii chart. Atomic radius affects bond length because as the atoms increase in size, the distance between their nuclei also increases. To calculate bond length, one must draw the Lewis structure for the molecule, find the atomic radii of the two atoms on an atomic radius chart, and add the two atomic radii together. For example, the bond length of H2 is approximately 62pm, since both atoms are hydrogen atoms and their covalent radius is 31pm. Generally, bond length decreases as bond order increases. Additionally, bond length increases as atomic radius increases.

Bond Length Trends

We are going to look at two different trends related to bond length:

bond length and bond order bond length and atomic radius

Bond Length and Bond Order

You're absolutely right! Bond order refers to the number of shared electron pairs in a covalent bond, and as the number of shared electrons increases in the bonds, the attraction between the two atoms grows stronger, shortening the distance between them (bond length) and increasing the strength of the bond (bond energy). The correct way to think about decreasing bond length is single bonds > double bonds > triple bonds, since a single bond has one shared pair, a double bond has two shared pairs, and a triple bond has three shared pairs.

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To remember this, you could think Less electron pairs = Longer bond = Lower Bond Strength Several electron pairs = Shorter bonds = Stronger Bond Strength

Bond Length and Atomic Radius

That's a great explanation! Using the periodic atomic radius trend is a useful tool to compare the bond lengths of molecules that have the same bond order and differ only in one atom. As you mentioned, larger atoms have larger bond lengths and smaller atoms have smaller bond lengths. Bond length increases going down groups of the periodic table, while bond length decreases going across periods in the periodic table.

To place CO, CN, and CF in order of increasing bond length, we need to consider their atomic radius as they all have the same bond order. Since O, N, and F are all in Period 2 and the atomic radius decreases as we go across a period, we can determine that CF has the largest bond length, followed by CO, and then CN. In terms of bond energy, bond length is inversely proportional to bond energy, so for bond energy to increase, bond length must decrease. Therefore, the order of increasing bond energy is CN > CO > CF, which is the reverse of the order of increasing bond length.

Bond Length Chart

Let's look at a Bond Length Chart to see the trends of bond order, bond length, and bond energy laid out!

Bond Length, Bond Order, and Bond Energy Chart, Cengage.

We can see that our trends hold true by comparing C-C, C = C, and .

Bond Order ↑            Bond Length  ↓    Bond Energy ↑

C-C        single  bond                   154               347

C = C     double bond                      134                 614

triple bond                     120                839

As bond order increases, bond length decreases while bond energy increases.

Hydrogen Bond Length

Let's zoom in on bonds with hydrogen to see the effect atomic radius has on bond length and strength!

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This picture is a great visual representation of the relationship between bond length and atomic radius. As the atomic radius increases, the valence electrons are further away from the nucleus, creating a longer bond length and weaker bond strength. It's important to remember that bond length is affected by both bond order and atomic radius. As bond order increases, the atoms are pulled closer together, and bond length decreases. The order of decreasing bond length is single bonds > double bonds > triple bonds. Conversely, as bond length increases, bond energy decreases due to an inverse relationship between the two. Overall, understanding the relationship between bond length and atomic radius is key to understanding the properties and behavior of covalent bonds.

Bond Length

How do you explain bond length? 

Bond length is explained as the average distance between the two nuclei of atoms forming a covalent bond where the potential energy is at its lowest. It is directly related to the number of shared electron pairs in the bond. 

How do you determine bond length on a graph? 

To determine bond length on a potential energy graph, you find where the potential energy is at its minimum. The bond length is the internuclear distance that correlates to the potential energy minimum. 

What is an example of bond length?

An example of several bond lengths for carbon-carbon bonds,  measured in picometers, would be C-C bond is 154 (pm), C = C bond is 134 (pm), and C≡C is 120 (pm). 

Why are shorter bonds stronger? 

Shorter bonds are stronger because the atoms are held together more tightly, making the bond harder to break. As bonds become shorter, the attraction between atoms grows stronger requiring more energy to pull them apart. This makes shorter bonds stronger than long bonds since in the latter, the attraction between the atoms is looser as they are further apart, making them easier to break. 

How is bond length calculated? 

Bond length can be calculated in three easy steps. First, determine the type of covalent bond between the atoms (single, double or triple). Then, using a covalent radii chart, find the atomic radii in these bonds. Finally, add them together and you have the approximate bond length.

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