Bond Length: Definition, Formula & Calculation

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  • 0:02 Length of a Chemical Bond
  • 1:37 Coulomb's Law & Bond Length
  • 3:57 How to Calculate Bond Length
  • 5:14 Lesson Summary
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Lesson Transcript
Instructor: Danielle Reid

Danielle has taught middle school science and has a doctorate degree in Environmental Health

Did you know that you could determine the distance between atoms bonded together in a molecule? Complete this lesson to learn more about bond length and how to calculate it.

Do You Know the Length of a Chemical Bond?

Would you be shocked if I told you that two tennis balls hooked to a rubber band is a great example of chemical bonding between atoms? Let me now show you what I mean.

Let's say you use one rubber band and connected it to each tennis ball, then try pulling the balls apart, like image (a). The length of that rubber band will stretch far, eventually breaking.

Suppose you take three rubber bands and connected them to each tennis ball. Now, try pulling them apart, like image (b). Not only is more strength required to pull those tennis balls apart, but the length of the rubber band doesn't stretch very far. More importantly, this shortened length aids in preventing the rubber band from breaking.

Bond length is the measurable distance between atoms covalently bonded together. Measurement of bond length, or distance, is an average. Going back to our tennis ball and rubber band example, we can see why distance is considered to be an average. The tennis balls attached to one rubber band may spring back at a very high speed once pulled apart. Whereas, the tennis balls connected to three rubber bands may take a much longer time to spring back. Relating to chemistry, atoms are not static or stationary. They can bounce or move around when bonded together. Heat and the number of bonds present (single, double, or triple bonds) can influence this movement. However, at some point, equilibrium will be established where the atoms will remain still. It is at this moment that the measurement of bond length (average) is taken. Let's look at how bond length is measured.

Coulomb's Law and Bond Length

If we think about the covalent bond established between two atoms, there is a certain level of attractive force that facilitates this bonding. This force of attraction contributes to bond length through a principle called Coulomb's law. Coulomb's law mathematically describes the strength of this force used to hold two opposite charged atoms together. In this case, think of strength and energy being related: that is, the amount of strength (or energy required) to bond atoms together. The equation of Coulomb's law is shown in Equation 1.

Equation 1: Coulomb's Law

Fe = ke (Q1 * Q2) /r2

Now I know you may be thinking, 'What does charge have to do with covalent bonding?' Always remember that any type of bonding, whether it is covalent or ionic, requires some electrostatic attraction for atoms to link up to each other. When you see the word electrostatic, think opposite charges attract. Applying this concept to covalent bonding, atoms that have a high electronegativity (those who love sharing electrons) will readily participate in this type of bonding. The electrostatic attraction between the positive charge nuclei of one atom and the high electronegativity of another atom bring both of these atoms together like a magnet. They slide right to each other because as we all know, opposites do attract.

Thus, using the modified version of Coulomb's law as shown in Equation 2, we can establish a relationship between the energy of this attraction and bond length. Always keep this in mind: the larger the distance (bond length) the less energy required to break a bond (and vice a versa). I hope you aren't tired of that tennis ball example, but let's use it one more time.

Equation 2: Modified Coulomb's Law

E = (k * Q1 * Q2) / r

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