What is the bond order of CN−?

The bond order of CN^− (cyanide ion) can be determined by examining its molecular orbital diagram. The CN^− ion consists of a carbon atom (C) bonded to a nitrogen atom (N) with a triple bond and an additional lone pair of electrons on the nitrogen atom.

In the molecular orbital diagram, the nitrogen atom contributes three valence electrons, while the carbon atom contributes four. These electrons are distributed among the molecular orbitals formed by the overlapping atomic orbitals of the carbon and nitrogen atoms.

The molecular orbital diagram for CN^− would show the following arrangement:

σ(2p) ──── σ*(2p)
↑
π(2p) ──── π*(2p)
↑
σ(2s) ──── σ*(2s)

In this diagram, the σ(2p) bonding orbital is lower in energy and occupied by two electrons, representing the triple bond. The π(2p) bonding orbital is also lower in energy and occupied by two electrons, representing the pi bond. The lone pair of electrons on the nitrogen atom occupies the σ(2s) orbital.

The bond order is calculated by subtracting the number of electrons in the antibonding orbitals from the number of electrons in the bonding orbitals and then dividing by 2. In the case of CN^−, there are 4 electrons in the bonding orbitals (2 in σ(2p) and 2 in π(2p)) and 2 electrons in the antibonding orbitals (1 in σ*(2p) and 1 in π*(2p)). Therefore, the bond order is:

(4 - 2) / 2 = 2 / 2 = 1

The bond order of CN^− is 1, indicating a single bond character.