Question

Consider the following species
1. $[O_2]^{2-}$ 2. $[CO]^+$ 3. $[O_2]^+$
Among these sigma bond alone is present in

• A. 1 alone
• B. 2 alone
• C. 3 alone
• D. 1 and 2
• E. 1, 2 and 3

Hint:

Species with a bond order of 1 in the second period usually have a single sigma bond if the pi-bonding and pi-antibonding orbitals are both completely filled or completely empty.

Answer 1

The Correct Option is A

Concept: According to Molecular Orbital Theory (MOT), the bond order and the types of bonds (sigma or pi) present in a diatomic species are determined by the distribution of electrons in its molecular orbitals. A "sigma bond alone" implies a bond order of 1 consisting only of a \(\sigma\)-bond.

Step 1: Analyze \([O_2]^{2-}\) (Peroxide ion).
Total electrons = \(8 + 8 + 2 = 18\). The MO configuration is: \[ \sigma_{1s}^2 \sigma_{1s}^{*2} \sigma_{2s}^2 \sigma_{2s}^{*2} \sigma_{2p_z}^2 (\pi_{2p_x}^2 = \pi_{2p_y}^2) (\pi_{2p_x}^{*2} = \pi_{2p_y}^{*2}) \]
• Bond Order = \(\frac{1}{2}(10 - 8) = 1\).
• Since the \(\pi\) and \(\pi^*\) orbitals are both fully filled, the net \(\pi\) bonding effect is zero.
• Only the \(\sigma_{2p_z}\) bond remains.

Step 2: Analyze \([CO]^+\) and \([O_2]^+\).

• \([O_2]^+\): Total electrons = 15. Bond order is 2.5, which includes \(\pi\) bonds.
• \([CO]^+\): Total electrons = 13. Bond order is 2.5, which also includes \(\pi\) bonds.