# Bond Order and How to Calculate Bond Order

## Bond Order

The concept of bond order was first introduced by Linus Pauling in the early 1930s. He defined bond order as the number of shared electron pairs between two bonded atoms in a molecule. It is simply represented as a whole number.

Bond order is used to describe the strength and stability of a chemical bond between two bonded atoms. Higher bond order indicates a stronger bond between two bonded atoms. it also helps to predict the properties and reactivity of molecules.

Bond order of a molecule is directly related to the bond length and bond energy of a molecule. Shorter the bond length, higher the bond order, and stronger the bond. Similarly, higher bond energy corresponds to a higher bond order and a more stable bond because, a higher bond order signifies a greater degree of overlap between the atomic orbitals, leading to a stronger attraction between the two atoms.

Bond order is also important to understand the molecular geometry of a compound. According to the Valence Shell Electron Pair Repulsion (VSEPR) theory, the bond order between two atoms determines the shape of the molecule. For example, a bond order of 1 results in a linear shape, while a bond order of 2 results in a bent shape.

The most common applications of bond order is predicting the behavior of molecules in chemical reactions. Molecules with a higher bond order are more stable and less reactive than those with a lower bond order because, higher bond order indicates a stronger bond, which is difficult to break.

Furthermore, bond order is important to understand the strength of intermolecular forces between molecules. Molecules held together by weak intermolecular forces, such as van der Waals forces show low bond order while molecules with strong covalent bonds shows high bond order.

Calculation of bond order can also provides information about the electronic structure of molecules. Bond order is closely related to molecular orbital theory, which explain how the distribution of electrons takes place in a molecule. According to this theory, higher the bond order, greater the number of electrons occupy the bonding molecular orbitals.

The determination of bond order is not limited to simple diatomic molecules. It can also be applied to more complex molecules with multiple bonds. In such cases, the bond order is calculated by taking the average of the bond orders for each bond present in the molecule.

## How to Calculate Bond Order

For simple molecules, the bond order is calculted by a simple formula given below-

Bond Order(B.O.) = 1/2[Number of bonding electrons − Number of antibonding electrons]

### Bond Order Calculator

Examples-Bond Order in H

_{2}molecule-

Bond Order = 1/2[2 − 2] = 1

Bond order one indicates that the two hydrogen atoms are linked with each other by a single bond.

H − H

Bond Order in O

_{2}molecule-

Bond Order = 1/2[6 − 2] = 2

Bond order two indicates that the two oxygen atoms are linked with each other by a double bond.

O = O

Bond Order in N

_{2}molecule-

Bond Order = 1/2[6 − 0] = 3

Bond order three indicates that the two oxygen atoms are linked with each other by a triple bond.

N ≡ N

The method mentioned above based on Molecular orbital theory(MOT) is time consuming. A new innvative method has been introduced to calculate the bond order of molecules and ions **having total electrons 8 to 20 in a very simple way. This method is not applicable for polyatomic molecules such as BF _{3}, CH_{4}, CO_{2} etc. and is applicable for mono +2 etc. Another method has also to be introduced for atomic and diatomic molecules ans ions such as CO, NO^{+}, O_{2} determination of bond order of oxides based acid radicals in a very simple way.**

First of all one should slassify the molecules or ions into two types based on total number of electrons.

**A. Molecules and ions having total number of electrons with in the range 8 - 14.**

Examples: Be_{2}(Total Electrons = 8), B_{2}(Total Electrons = 10), C_{2}(Total Electrons = 12), C_{2}^{−}(Total Electrons = 13), C_{2}^{+}(Total Electrons = 11), N_{2}(Total Electrons = 14), N_{2}^{+}(Total Electrons = 13), O_{2}^{+2}(Total Electrons = 14), CO(Total Electrons = 14), NO^{+}(Total Electrons = 14).

**B. Molecules and ions having total number of electrons with in the range 15 - 20.**

Examples: N_{2}^{−}(Total Electrons = 15), 0_{2}(Total Electrons = 16), O_{2}^{+}(Total Electrons = 15), O_{2}^{−2}(Total Electrons = 18), F_{2}(Total Electrons = 18), Ne_{2}(Total Electrons = 20).

**Method for determination of bond order of molecules and ions having total number of electrons with in the range of 8 to 14 electrons.**

Bond Order = [N − 8] / 2

Where N = Total number of elecrons.

Examples:

Be_{2}

Total electrons = 8

So, Bond Order = [8 − 8]/2 = 0

That means He_{2} does not exist.

C_{2}

Total electrons = 12

So, Bond Order = [12 − 8]/2 = 2

C_{2}^{−}

Total electrons = 13

So, Bond Order = [13 − 8]/2 = 2.5

C_{2}^{+}

Total electrons = 11

So, Bond Order = [11 − 8]/2 = 1.5

N_{2}

Total electrons = 14

So, Bond Order = [14 − 8]/2 = 3

N_{2}^{+}

Total electrons = 13

So, Bond Order = [13 − 8]/2 = 2.5

CO

Total electrons = 14

So, Bond Order = [14 − 8]/2 = 3

NO^{+}

Total electrons = 14

So, Bond Order = [14 − 8]/2 = 3

CN^{+}

Total electrons = 12

So, Bond Order = [12 − 8]/2 = 2

CN^{−}

Total electrons = 14

So, Bond Order = [14 − 8]/2 = 3

**Method for determination of bond order of molecules and ions having total number of electrons with in the range of 15 to 20 electrons.**

Bond Order = [20 − N] / 2

Where N = Total number of elecrons.

Examples:

N_{2}^{−}

Total electrons = 15

So, Bond Order = [20 − 15]/2 = 2.5

O_{2}

Total electrons = 16

So, Bond Order = [20 − 16]/2 = 2

O_{2}^{−}

Total electrons = 17

So, Bond Order = [20 − 17]/2 = 1.5

O_{2}^{−2}

Total electrons = 18

So, Bond Order = [20 − 18]/2 = 1

NO

Total electrons = 15

So, Bond Order = [20 − 15]/2 = 2.5

F_{2}

Total electrons = 18

So, Bond Order = [20 − 18]/2 = 1

Ne_{2}

Total electrons = 20

So, Bond Order = [20 − 20]/2 = 0

That means Ne_{2} does not exist.

**Method for determination of Bond Order of Oxide based Acid Radials**

In case of Acid Radicals-

Bond Order = Valency of Peripheral Atom + (Charge on Acid Radical ÷ Number of Peripheral Atoms)

__ This formula is very very important for NEET, IIT-JEE, GATE, IIT-JAM, CSIR, SLET, DRDO, TIFR, ICT, IISc, and other entrance exams.__

### Acid Radical Bond Order Calculator

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Bond Order:

SO_{4}^{−2}:

Valency of peripheral atom (i.e. oxygen) = 2

Charge on acid radical = −2

Number of peripheral atoms = 4

So, the Bond Order = 2 + (−2 ÷ 4) = 1.5

SO_{3}^{−2}:

Valency of peripheral atom (i.e. oxygen) = 2

Charge on acid radical = −2

Number of peripheral atoms = 3

So, the Bond Order = 2 + (−2 ÷ 3) = 1.33

PO_{4}^{−3}:

Valency of peripheral atom (i.e. oxygen) = 2

Charge on acid radical = −3

Number of peripheral atoms = 4

So, the Bond Order = 2 + (−3 ÷ 4) = 1.25

MnO_{4}^{−}:

Valency of peripheral atom (i.e. oxygen) = 2

Charge on acid radical = −1

Number of peripheral atoms = 4

So, the Bond Order = 2 + (−1 ÷ 4) = 1.75

NO_{3}^{−}:

Valency of peripheral atom (i.e. oxygen) = 2

Charge on acid radical = −1

Number of peripheral atoms = 3

So, the Bond Order = 2 + (−1 ÷ 3) = 1.66

NO_{2}^{−}:

Valency of peripheral atom (i.e. oxygen) = 2

Charge on acid radical = −1

Number of peripheral atoms = 2

So, the Bond Order = 2 + (−1 ÷ 2) = 1.5

BO_{3}^{−3}:

Valency of peripheral atom (i.e. oxygen) = 2

Charge on acid radical = −3

Number of peripheral atoms = 3

So, the Bond Order = 2 + (−3 ÷ 3) = 1

CO_{3}^{−2}:

Valency of peripheral atom (i.e. oxygen) = 2

Charge on acid radical = −2

Number of peripheral atoms = 3

So, the Bond Order = 2 + (−2 ÷ 3) = 1.33

ClO_{4}^{−}:

Valency of peripheral atom (i.e. oxygen) = 2

Charge on acid radical = −1

Number of peripheral atoms = 4

So, the Bond Order = 2 + (−1 ÷ 4) = 1.75

SiO_{4}^{−4}:

Valency of peripheral atom (i.e. oxygen) = 2

Charge on acid radical = −4

Number of peripheral atoms = 4

So, the Bond Order = 2 + (−4 ÷ 4) = 1

### Relation of Bond Order with Bond Length, Bond Strength, Bond Dissociation Energy, Thermal Stability and Reactivity

✍︎ Bond order is inversely proportional to Bond Length✍︎ Bond order is directly proportional to Bond Strength

✍︎ Bond order is directly proportional to Bond Dissociation Energy

✍︎ Bond order is directly proportional to Thermal Stability

✍︎ Bond order is inversely proportional to Reactivity