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# Bond Length

Imagine the relationship between you and your best friend. You two probably weren’t very close when you first met, and your bond wasn’t that strong. But as you got closer and closer, your bond as friends became stronger and stronger. Believe it or not, this is a simple way to think about bond length in covalent bonds - as bond length shortens between atoms, the strength of the bond (also known as bond energy) increases!

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Bond Length is the average distance between the two nuclei of atoms bonded together in a covalent bond.

Bond Energy is the potential energy required to break a covalent bond.
• To begin with, we will learn the formula for bond length and how it is measured.
• Then, we will look at the common trends in bond lengths and see how this is reflected in the periodic table.
• Afterwards, we will familiarize ourselves with the bond length chart.
• Finally, we will look in detail at the bond length of hydrogen molecules and double bonds.

## What is the Bond Length Formula?

If you’ve read Intramolecular Forces and Potential Energy, you should have a basic understanding of bond length as the distance between the two nuclei of covalently bonded atoms when the potential energy of the bond is at a minimum. But let’s very briefly review some foundational principles to keep in mind about bond length before we dive into specifics.

• Bond length is usually measured in a unit called picometers (pm) or Angstrom (Å).
• The factors that directly affect the bond length are bond order and atomic radius.
• Bond length and bond energy are inversely related to one another.

As we saw in the friendship metaphor, this last point about bond length and bond energy being inversely related to each other means that as bond length decreases, bond energy increases. The formula that proves this relationship is known as Coulomb's Law.

Coulomb's Law states that similar forces repel each other while opposite forces attract one another.

The formula associated with Coulomb's Law is:

$F=k\frac{{q}_{1}{q}_{2}}{{r}^{2}}$

In this case, k is the Coulomb constant, q refers to the electrostatic charge of the atoms, r refers to the atomic radius, and F refers to the electric force which is equivalent to the bond energy.

Coulomb's Law is primarily associated with ionic bonds and their interactions but weak coulombic forces do exist in covalent bonds between the negatively charged electrons and positively charged nuclei of the bonding atoms. While it helps to be familiar with Coulomb's law, as it mathematically proves the inverse relationship between bond length and strength, you will use other means to determine the bond length of covalent bonds.

Coulomb's formula can be used to prove the relationship between bond strength and bond length broadly but is usually associated with ionic bonds and their interactions. This is discussed in detail in Coulomb's Law and Interaction Strength.

So, what other means are there to calculate bond length?

The more common ways of calculating the bond length of covalent bonds are through potential energy diagrams and an atomic radii chart. We will concentrate on atomic radii; check out Chemical Potential Energy Diagrams for more on determining bond length from an energy diagram.

It’s quite simple. As the atoms increase in size, the distance between their nuclei also increases. With this knowledge in mind, we can follow these three steps to calculate bond length:

1. ALWAYS draw the Lewis structure for the molecule and determine the bond order.

2. Find the atomic radii of the two atoms on an atomic radius chart.

Let's do a simple example and try to calculate the approximate bond length of H2.

First, sketch out a quick Lewis structure for the H2 bond.

You should have drawn a single bond:$\mathrm{H}-\mathrm{H}$

Next, let's reference the small portion of the covalent radii chart attached below:

 Atomic number Element Covalent radii Single bonds Double bonds Triple bonds 1 H 31 - - 2 He 28 - - 3 Li 128 124 - 4 Be 96 90 85

As we can see, the covalent radius for a hydrogen atom is 31 pm.

Finally, we add the sum of the atomic radii of both atoms in the molecule together. Since both atoms are hydrogen atoms, the bond length is 31 pm + 31 pm, approximately 62 pm.

It’s important to understand the general trends associated with bond length, as you will often need to know how to order the bond length of molecules based on bond order or atomic radius.

## Bond Length Trends

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

1. bond length and bond order

2. bond length and atomic radius

You should know by now that bond order refers to the number of shared electron pairs in a covalent bond.

Single bonds = 1 shared pair

Double bonds = 2 shared pairs

Triple bonds = 3 shared pairs

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). This also increases the strength of the bond (bond energy) because the attraction between the atoms is stronger, making them harder to pull apart.

The correct way to think about decreasing bond length is Single bonds > Double bonds > Triple bonds.

Fig.1-Single, double, and triple carbon-carbon bonds

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

We have also mentioned the relationship between bond length and atomic radius.

• Larger atoms will have a larger bond length
• Smaller atoms will have smaller bond lengths

The trend is helpful because we can use the periodic atomic radius trend to figure out bond length!

• Bond length increases going down groups of the periodic table.
• Bond length decreases going across periods in the periodic table.

Using this trend allows us to correctly compare the bond lengths of molecules that have the same bond order and only differ in one atom such as CO, CN, and CF!

Let's place CO, CN, and CF in order of increasing bond length? What about bond energy?

What do you think the first step is?

We always need to draw a Lewis structure to determine the bond order (of course, in this case we know they are all single bonds but best to make a habit out of drawing them!)

Since the bond order is the same, we know it comes down to atomic radius. Let's locate O, N, and F on the periodic table.

Fig.2- The Periodic Table

Fig.3-Bond length increasing down a group

We can see that O, N, F are all in Period 2. As we go across a period, what happens to the atomic radius and in turn, bond length?

It decreases! So, we just need to place the three molecules in the opposite order they are in the period to display increasing bond length which would be:

CF > CO > CN

But what about increasing bond energy?

Well, we know the bond length is inversely proportional to bond energy, so for bond energy to increase, bond length must decrease...we flip it!

CN > CO > CF

Check out Periodic Trends if you want a refresher on atomic radius trends!

## 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 Bond Type Bond Length (pm) Bond Energy (kJ/mol) C-C Single 154 347 C=C Double 134 614 $\mathrm{C}\equiv \mathrm{C}$ Triple 120 839 C-O Single 143 358 C=O Double 123 745 C-N Single 143 305 C=N Double 138 615 $\mathrm{C}\equiv \mathrm{N}$ Triple 116 891

We can see that our trends hold true by comparing $\mathrm{C}-\mathrm{C},\mathrm{C}=\mathrm{C},\mathrm{C}\equiv \mathrm{C}$.

 Bond Representation Bond Order ↑ Bond Length ↓ Bond Energy ↑ C-C Single bond 154 347 C = C Double bond 134 614 $\mathrm{C}\equiv \mathrm{C}$ 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!

Fig.3-Bond length increasing down a group

This picture helps us visualize what is happening to the bond length as we go down a group on the periodic table and why. These are all single bonds, so the bond order is the same. This means the difference is in the 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.

## Bond Length - Key takeaways

• Bond Length is the average distance between the two nuclei of atoms bonded together in a covalent bond.
• It is affected by bond order and atomic radius.
• As bond length increases, bond energy decreases due to an inverse relationship between the two.
• As bond order increases, the atoms are pulled closer together and bond length decreases.
• Single bonds > Double bonds > Triple Bonds
• As the atomic radius increases, the nuclei end up further from the valence electrons and bond length increases.

## References

1. Brown, Theodore L, H E. LeMay, Bruce E. Bursten, Catherine J. Murphy, Patrick M. Woodward, and Matthew Stoltzfus. Chemistry: The Central Science. , 2018. Print.

#### Flashcards in Bond Length 14

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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.

## Test your knowledge with multiple choice flashcards

As bond length ______, bond strength _______

Single bonds are the longest bonds and triple bonds are the shortest bonds.

Describe how the atomic radius trend on the periodic table and bond length trend are related?

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