MO Theory: Bond Order - Online Tutor, Practice Problems & Exam Prep

Bond order is a key concept in understanding molecular stability and bond strength, indicating the number of chemical bonds between a pair of atoms. A bond order greater than zero suggests a stable molecule, while a bond order of zero implies instability. The bond order can be determined by setting up a molecular orbital diagram and applying the bond order formula:

$\mathrm{bond}\mathrm{order}=\frac{1}{2}(\mathrm{bonding}\mathrm{electrons}-\mathrm{antibonding}\mathrm{electrons})$

The molecular orbital diagram helps distribute electrons into bonding and antibonding orbitals to calculate this value. Additionally, bond order correlates with bond strength and length; as bond order increases, the bond strengthens and shortens. Visually, bond order can be inferred from Lewis structures: a single bond has a bond order of one, a double bond has a bond order of two, and a triple bond has a bond order of three, reflecting the number of shared electron pairs.

MO Theory: Bond Order Concept 1

Molecular orbital diagrams can be used to determine the bond order of a molecule. Now bond order itself is just a measurement of the number of electrons involved in bonds between two elements. We're going to say here a bond order of greater than 0 means that the compound is stable and it exists. And we can also say that as the bond order increases, the stability and strength of a bond also increases.

Now remember there is an inverse relationship between the strength of a bond and the length of a bond. So if your strength is increasing, that means that the length of your bond is decreasing. Now we're also going to say that a bond order of 0 means that the compound is unstable and it doesn't exist.

Now how exactly do we calculate our bond order? Well, we set up a molecular orbital diagram and we distribute our electrons within the bonding molecular orbitals and the anti bonding molecular orbitals. And once we do this, we can use the bond order formula. And here it says that that bond order equals half your bonding electrons, so those electrons found within molecular bonding orbitals minus your antibonding electrons. These are your electrons that are found within your antibonding molecular orbitals.

So again, once you set up your MO diagram, you'd use that to help fill in this bond order formula to find the bond order of any particular molecule.

MO Theory: Bond Order Example 1

Determine the bond order of the no ion. So here, remember we're going to set up our molecular orbital diagram and it'll be based on the less electronegative element. Nitrogen is less electronegative than oxygen. So we're going to use the molecular orbital diagram for nitrogen to set that up. We're going to have here Σ2S, Σ*2S. Then we're going to have π2P and then we're going to have here Σ2P.

Then we're going to have here π*2P and then finally we're going to have up here Σ*2P. Now if we take a look here, nitrogen is in Group 5A, so it has five valence electrons. Oxygen is in Group 6A, so it has six valence electrons. And then -1 means we've gained an additional electron, so that's going to be another electron on top. So this comes out to 12 valence electrons.

So we start filling this in. So it'd be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. So we've filled this in. And remember that the bond order formula, so bond order we're going to abbreviate to Bo, equals half of your bonding electrons minus your anti bonding electrons. So here we'd say half of. So you're bonding. Electrons are 2, 4, 6, 8, so we have 8 minus. Your antibonding are the ones with the stars, so that's going to be 2, 4 antibonding, so that's 8 - 4, which is four. 4 * 1/2 is equal to two. So the bond order here for this particular molecule would be two.

MO Theory: Bond Order Concept 2

Now recall that the bond order can determine how many bonds form between two elements in a compound. And if we have a visual representation of our molecule, we can look at the connections between two elements and simply determine the bond order from that. So if we look at a molecule and we see a single bond between two elements, that means the bond order between them would be one.

If we see a double bond between two elements, then their bond order would be two. So if I gave you for example here I give you carbon triple bonded to nitrogen. We see a triple bond there, so the bond order would simply be 3.

So again, we can calculate bond order by setting up a molecular orbital diagram and then figuring out the number of bonding and antibonding electrons. Or if they give you the actual Lewis dot structure of a molecule, you can look at the bond between the two elements and simply say what the bond order is from that as well.

MO Theory: Bond Order Example 2

Using MO theory and bond order, determine the number of bonds connecting the nitrogen atoms within the N₂^2- ion. All right, so remember we said that if you have a single bond, it's one, if it's double bond, it's two. Here though, we don't have an actual visualization of the bond between the two nitrogens, so we're going to have to use our MO diagram.

Since we're dealing with nitrogen, remember that would be what? σ2s σstar2S? π2P, σ2P, πstar2P and then finally σstar2P. Here nitrogen's in Group 5 ACO. It has five valence electrons and there are two nitrogen, so that's 5 * 2 which is 10. And then we have an additional 2 electrons, so add 2 to this. This is 12. So all we got to do now is fill in those electrons 1 2 3 4 5 6 7 8 9 10 11 and then 12.

And then remember here bond order which we're going to abbreviate as Bo, equals half of your bonding electrons. So your bonding electrons would be 2 4 6 8. So you have 8 bonding electrons minus your antibonding electrons, the ones with the star S 2 4. So we do 8 - 4 which is 4 * 1/2 gives me two. So the bond order between the two nitrogens would be two.

And if we wanted, if I wanted to show you what this would look like, it looks like this, this is what the ion actually looks like. And we can clearly see that there's a double bond between the nitrogens. So this visualization is definitely reinforced by the fact that we find a bond order of two. So that means there's a double bond between the two nitrogens, right. So we'd say determine the number of bonds be connecting the two nitrogens. We'd say that they're connected by a double bond.

Apply Molecular Orbital Theory to determine the bond order of HHe⁺ ion.

• A. 2
• B. 1.5
• C. 4
• D. 3
• E. 1

Apply molecular orbital theory to predict which species has the strongest bond. 

a) O₂                             b) O₂^–                           c) O₂⁺                          d) All the bonds are equivalent 

• A. O₂
• B. O₂^-
• C. O₂⁺
• D. All the bonds are equivalent

Using Molecular Orbital Theory, answer the following questions dealing with carbon mononitride, CN. 

• A. CN is diagmagnetic
• B. CN– is paramagnetic
• C. If an electron is removed to give CN+, the bond length decreases.
• D. The π*2p orbital is the highest energy orbital containing an electron in CN.
• E. If an electron is added to give CN–, the bond order increases.

Here’s what students ask on this topic:

How do you calculate bond order?

Bond order is a way to determine the stability and strength of a chemical bond. It is calculated by taking the difference between the number of bonding electrons and the number of antibonding electrons, then dividing that number by two. Here's a step-by-step guide:

1. Draw the Lewis structure for the molecule.
2. Determine the number of bonding electrons (these are typically the electrons shared between atoms in a bond).
3. Determine the number of antibonding electrons (these are electrons in antibonding orbitals, often denoted by an asterisk, like σ* or Π*).
4. Subtract the number of antibonding electrons from the number of bonding electrons.
5. Divide the result by two.

The formula for bond order (BO) is:

$\mathrm{BO}=\frac{(\text{Number of bonding electrons}-\text{Number of antibonding electrons})}{2}$

For example, in a diatomic nitrogen (N≡N) molecule, there are three bonds (six bonding electrons) and no antibonding electrons, so the bond order is 3. Higher bond orders indicate stronger, shorter bonds between atoms.

What is bond order?

Bond order is a concept in molecular chemistry that represents the number of chemical bonds between a pair of atoms. In essence, it indicates the stability of a bond. For a simple molecule like diatomic nitrogen ($N_2$), where two nitrogen atoms are connected by a triple bond, the bond order is three. This is calculated by taking the number of bonding electrons (in this case, six for the three bonds) and subtracting the number of anti-bonding electrons (which is zero for $N_2$), then dividing by two.

Bond order can also be fractional when considering resonance structures. For example, in benzene ($C_6{H}_6$), each carbon-carbon bond has a bond order of 1.5 due to the delocalization of electrons across the ring structure.

Higher bond orders generally mean stronger, shorter bonds. A bond order of zero implies that no bond exists between the atoms, and typically, a molecule with such a bond order is not stable. Understanding bond order is crucial for predicting molecular stability, reactivity, and the strength of bonds within different molecules.

What does bond order mean?

Bond order refers to the number of chemical bonds between a pair of atoms in a molecule. It is a way of expressing the stability and strength of the bond. In simple terms, the higher the bond order, the stronger and more stable the bond between the atoms. For example, a single bond has a bond order of 1, a double bond has a bond order of 2, and a triple bond has a bond order of 3.

To calculate the bond order in molecular orbital theory, you subtract the number of electrons in antibonding orbitals from the number of electrons in bonding orbitals and then divide by two. The formula looks like this:

$\text{Bond order =}\frac{(\text{Number of bonding electrons}-\text{Number of antibonding electrons})}{2}$

This calculation can help predict the stability of molecules and the lengths of the bonds between atoms. A bond order of zero implies that the bond is not stable and is unlikely to exist under normal conditions.