How To Calculate Bond Order

The way atoms join together to form molecules (which are called compounds if the atoms are different) is a phenomenon called chemical bonding. Although individual types of atoms, called elements, are usually described in terms of their stand-alone number of protons, neutrons and electrons, most atoms in fact prefer to exist in the company of one or more other atoms.

The reason this happens is the same essential reason sentient creatures often pair off: Each has something that "completes" the other in some way. With atoms, it has to do with the way their energy changes as a result of interactions between the positively charged protons and negatively charged electrons both within and between bonding atoms.

Chemical bonds come in three basic types: Metallic bonds, which involve lots of "runaway" electrons not associated with particular parent atoms; ionic bonds, in which one atom donates an electron to another; and covalent bonds, in which the electron "orbitals" of bonding atoms overlap, resulting in sharing of electrons rather than offloading or gaining them outright.

• Electron orbitals are graphical and conceptual representations of the most probable positions of electrons around atoms.

Covalent bonds are the most versatile, as they come in three kinds, depending on how many electron pairs are shared between bonding atoms. A bond involving one electron pair (one atom shared by each atom) is called a single bond. A bond involving two electron pairs is a double bond, and a three-electron pair bond is a triple bond.

Bond order refers to the kind of bond in a molecule with two atoms. In molecules with three atoms, such as CO₂, it is determined by a simple arithmetic process described below. Bond order relates to bond energy, since bonding itself is a phenomenon of energy optimization between atomic components.

Bond energy tends to increase with decreasing bond length, and hence with increasing bond order, because single bonds are longer than double bonds, which in turn are longer than triple bonds.

A bond between two atoms stabilizes in the position it does (that is, with the nuclei of the bonding atoms spaced a precise distance apart) because this represents the optimal balance between the various positive and negative charges in play. The electrons of one atom are attracted to the proton(s) of the other, but at the same time their respective protons repel each other.

To determine the bond order of a diatomic molecule such as H₂, CO or HCl, you simply look at the kind of bond involved and that is your answer. A molecule of hydrogen gas (H₂) has single bond and a bond order of 1. A molecule of oxygen gas (O₂) has a double bond and a bond order of 2. The triple bond of CN gives it a bond order of 3.

• If you are unfamiliar with drawing Lewis structures of molecules, this would be a good time to practice these.

To calculate the bond order for a larger molecule, you need to know the number of bonds as well as the nature of those bonds (single, double or triple). You add up the total number of bonding pairs and divide by the total number of bonds. For example, for NO₃^-, you have three bonds: One double bond (2 electron pairs) and two single bonds (1 + 1= 2 electron pairs). The bond order is therefore 4/3 = 1.33.

See the Resources for a set of bond energy tables that include both length and bond energy for a variety of diatomic molecules with bond orders of 1, 2 and 3.