How to Calculate Bond Order

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Understanding the concept of bond order is essential to perceive how chemistry deals in which subatomic particles bond together to make atoms. In molecular orbital theory, bond order plays a significant role in finding bond strength and is also utilized in valence bond theory. Bond order may be a measurement of the number of electrons involved in bonds between two atoms during a molecule. The Bond order can be defined as half the difference between the number of bonding and anti-bonding electrons. Stable bonds have a positive bond order. The amount of covalent bonds in a molecule is also known as bond order.

 The bond order concept is defined because of the difference between the number of bonds and anti-bonds. The quantity of electron pairs between two atoms is itself the bond number. In most cases, the higher the bond order, the stronger the bond. Bond order is usually sufficient for the number of bonds between two atoms. Exceptions occur when the molecule contains anti-bonding orbitals. It’s an indicator of the stability of a bond. Bond order is an indication of bond strength and is used extensively in valence bond theory.

 This article will elaborate on the bond order, explain the bond order formula, calculate the bond order step by step, and give examples of its applications.

Bond Order Formula

Between two atoms, the number of chemical bonds is the bond order. Furthermore, the Bond Order Formula is frequently defined as half of the difference in the number of electrons in bonding and anti-bonding orbitals. Bond order is an indication of bond strength, and it’s used extensively in valence bond theory.

Bond Order = [(Number of bonding electrons) – (Number of anti-bonding electrons)] / 2

What is Bond Order

There are a lot of other bond order definitions. According to valence bond theory (VBT), bond order is the number of chemical bonds between a pair of atoms. In molecular orbital theory (MOT), bond order is the difference between the number of bonded electrons and the number of anti-bonded electrons divided by 2. Both VBT and MOT refer to the position of electrons. While the first one is relatively simple, the second one comes from quantum mechanics.

How to find the bond order can be illustrated by both theories. The Bond order is the quantity of bonding electron pairs between a pair of atoms. In a covalent bond between a pair of atoms, an individual bond has a bond order of 1, similarly, a double bond has a bond order of 2 and a triple bond has a bond order of 3, and so on. For instance, in diatomic nitrogen molecule (N≡N), the bond order is three, while in acetylene molecule (H−C≡C−H), the bond order between the two carbon atoms is three, and therefore the C−H bond order is 1.

Electrons fill the orbitals from s block to f block, so from the most to least energy efficient. The s block elements have one anti-bonding and one bonding orbital available for bonding, each with two electrons. Those in the p block have three bonding orbitals, those in the d block have five, and those in the f block have seven. Thus, each orbital comprises a bonding and an anti-bonding orbital, with all of the bonding orbitals of an energy level being filled first.

Significance of Calculating Bond Order

The following factors show that calculating bond order is very important.

●      It tells us about the number of bonds between the atoms. For instance, the bond order of O2 is 2, which clearly shows that there are two bonds between two oxygen atoms.

●      It helps us to know about the stability of the bond between the atoms. The higher the bond order, higher the stability.

●      It also describes the bond strength. Higher the bond order, more will be the required energy to break the bond.

●      It also gives a partial idea about the hybridization of the molecule.

●      It helps us in predicting if a bond can exist or not. For Ex: if the bond order is fractional, then there are low or no chances that the molecule can exist.

How to Calculate Bond Order

Calculations Step by Step

To determine the bond order between a pair of covalently bonded atoms by valence bond theory (VBT):

  1. Draw the Lewis structure.
  2. Determine the type of bonds between the atom pair.

●      0: No bond

●      1: Single bond

●      2: double bond

●      3: triple bond

A molecule is not formed if the bond order is zero.

 Tips for calculating Bond Order:

In order to determine the bond order between two covalently bonded atoms by molecular orbital theory:

  1. Write the electronic configuration of the atoms. Consult a diagram of electron orbital shells.
  2. Bonding electrons are, essentially, the electrons that stick together and fall into the lowest states. Note the number of bonding electrons.
  3. Anti-bonding electrons are the “free” or unbonded electrons that are pushed to higher orbital states. Note the number of anti-bonding electrons.
  4. Apply the formula,

Bond Order = (Number of bonding electrons – Number of antibonding electrons) / 2

Example 1

The bond order of N2 (nitrogen) – nitrogen molecule has a triple bond, so the bond order is three.

Step 1. Write the electron configuration of a N2 molecule.

Electronic configuration of N2 = (σ2s)2 (σ*2s)2 n(2px)2 n(2py)2 n(2pz)2

Step 2. From the above electron configuration, put the values in the formula

Bond order = (Nb – Na) / 2

            = (10 – 4 )/ 2

= 3 

Calculation of Bond Order using Excel

Example 2

To determine the bond order of an oxygen molecule, write its configuration and show the electrons in orbitals.

Write the total number of bonding electrons in cell H4 using the following formula:

= C4 + E4 + G4

Similarly, write the total number of ant bonding electrons in cell I4 using the following formula:

= D4 + F4

Calculate the Bond Order applying the formula in cell J4:

= (H4 – I4) / 2

Example 3 

Determine Bond order for hydrogen gas (H2). Also, draw its molecular Orbital Diagram by using Molecular Orbital theory.

No of Bonding electron = C4+D4

There is no anti-bonding electron as shown in cell F4 because hydrogen has only one electron which contributes to bonding.

Bond Order = (E4-F4)/2

Hence, the bond order of Hydrogen gas is 1. the molecular orbital diagram of hydrogen gas is given below;

Molecular Orbital diagram for Helium gas He2

Let’s draw the Molecular orbital diagram of Helium gas (He2 ) and find out the bond order.

Number of Bonding electron = 2

Number of antibonding electrons = 2

Bond order = (Nb – Na) / 2

            = (2– 2)/ 2

= 0

From the above Molecular orbital diagram of Helium gas, it can be concluded, there are two bonding and anti-bonding electrons in Helium gas.  Hence, the bond order of Helium gas is 0.


1Is a bond order of 1.5 stable?The higher the bond order, the higher will be the stability, indicating that a bond order of 1.5 is more stable than a bond order of 1 but less stable than the bond order of 2.
2Which one is the strongest bond?The strongest bond is the Ionic Bond.
3What is the major difference between bonding and anti-bonding?The prime difference between anti-bonding and bonding molecular orbitals is that the shape of the molecules is represented by the bonding molecular orbitals, whereas anti-bonding molecular orbitals do not contribute to the determination of the shape of a molecule.
4Which one is the weakest bond?The weakest bond is the Covalent Bond.

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