We will calculate the bond length, bond energy of CN and CN – species with the help of molecular orbital theory.
Hence we first need the electronic configuration of the given species.
For CN:
CN has 13 electrons and its electronic configuration will be:
CN: KK σ (2s)2 σ*(2s)2π (2py)2σ (2pz)1
As, Bond order = [number of bonding electrons – number of anti-bonding electrons]/ 2
Hence, Bond order = 1/2(7–2) =2.5
For CN–, the one electron is added to the σ(2pz) 1
Molecular orbital so its electronic configuration will be:
CN–: KKσ(2s)2σ*(2s)2π(2py)2σ (2pz)2
Hence, Bond order = 1/2 (8–2) = 3
From above it is concluded that CN– has higher bond order. We know that higher bond order larger will be the bond energy and smaller will be the bond length. Hence CN– has higher bond order larger will be the bond energy and smaller will be the bond length than CN.