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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Think about it this way: the greater the length between those two tennis balls (because of your stretching) the lesser amount of energy required to snap that rubber band in half. The same concept applies if you decide to decrease the length by not stretching the tennis balls as wide. There would be more energy required to snap the rubber band. Luckily, we are not concerned about calculating bond length using bond energy. There is a simpler way to determine bond length.
How to Calculate Bond Length
There are three simple steps that can be taken towards calculating bond length:
Draw the Lewis structure of the molecule
Use a chart to identify the radii for each atom bonded within the molecule
Sum the two radii values
Bond length is commonly measured in either angstroms or picometers. There are charts that reveal the estimated bond length (radii in angstroms or picometers) between two given atoms, according to bond type (i.e. single, double, or triple bond). Let's look at an example:
Say you are trying to determine the bond length of hydrogen and chlorine in the molecule hydrochloric acid (HCl):
Step 1: Draw the Lewis structure of HCl
Step 2: Determine the radii for each atom bonded together (using a bond length chart)
H: 31 picometers Cl: 102 picometers
Step 3: Sum the total radii
HCl = 31 + 102 = 133 picometers
This tells you the bond length between hydrogen and chlorine, in a molecule of HCL, is 133 picometers. Now that wasn't too bad, was it? Keep practicing how to calculate bond length. Just remember that bond length plays a large role in the energy and strength of a chemical bond.
Bond length is the measurable distance between two covalently bonded atoms. This measurable distance is an average, as the distance between atoms bounded together can change. Electrostatic forces, where opposites attract, contribute to the strength of a bond. A modified formula of Coulomb's law explains the relationship between bond energy (strength) and bond length. The greater the bond length, the less energy required to break that bond. The shorter the bond length, the more energy required to break the bond.
Three steps can be used to determine bond length:
(1) Drawing of a Lewis structure
(2) Determination of radii (picometers) for each atom bonded
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