What is the bond order for O2^-2
The Correct Answer and Explanation is:
The bond order for O22−\text{O}_2^{2-}O22− (the peroxide ion) is 1.
Explanation:
To determine the bond order of a molecule or ion, we use molecular orbital (MO) theory. According to MO theory, atomic orbitals combine to form molecular orbitals that are spread over the entire molecule. Electrons are placed into these molecular orbitals in order of increasing energy.
The bond order is calculated using the formula:Bond Order=12(Nb−Na)\text{Bond Order} = \frac{1}{2} \left( N_b – N_a \right)Bond Order=21(Nb−Na)
Where:
- NbN_bNb = number of electrons in bonding molecular orbitals
- NaN_aNa = number of electrons in antibonding molecular orbitals
Step-by-step:
Oxygen has an atomic number of 8, so a neutral O2\text{O}_2O2 molecule has 16 electrons. The O22−\text{O}_2^{2-}O22− ion has 2 extra electrons, giving a total of 18 electrons.
For diatomic molecules formed from elements with atomic number > 7 (like oxygen), the MO filling order is:σ1s,σ1s∗,σ2s,σ2s∗,σ2pz,π2px=π2py,π2px∗=π2py∗,σ2pz∗\sigma_{1s}, \sigma^*_{1s}, \sigma_{2s}, \sigma^*_{2s}, \sigma_{2p_z}, \pi_{2p_x} = \pi_{2p_y}, \pi^*_{2p_x} = \pi^*_{2p_y}, \sigma^*_{2p_z}σ1s,σ1s∗,σ2s,σ2s∗,σ2pz,π2px=π2py,π2px∗=π2py∗,σ2pz∗
Now distribute the 18 electrons into these orbitals:
- σ1s\sigma_{1s}σ1s: 2 electrons (bonding)
- σ1s∗\sigma^*_{1s}σ1s∗: 2 electrons (antibonding)
- σ2s\sigma_{2s}σ2s: 2 electrons (bonding)
- σ2s∗\sigma^*_{2s}σ2s∗: 2 electrons (antibonding)
- σ2pz\sigma_{2p_z}σ2pz: 2 electrons (bonding)
- π2px\pi_{2p_x}π2px, π2py\pi_{2p_y}π2py: 4 electrons (2 each in bonding)
- π2px∗\pi^*_{2p_x}π2px∗, π2py∗\pi^*_{2p_y}π2py∗: 4 electrons (2 each in antibonding)
Tallying:
- Bonding electrons = 2 (σ1s) + 2 (σ2s) + 2 (σ2p_z) + 4 (π2p_x and π2p_y) = 10
- Antibonding electrons = 2 (σ1s) + 2 (σ2s) + 4 (π2p_x and π2p_y) = 8
Bond Order=12(10−8)=1\text{Bond Order} = \frac{1}{2} (10 – 8) = 1Bond Order=21(10−8)=1
Thus, the bond order of O22−\text{O}_2^{2-}O22− is 1, indicating a single bond between the oxygen atoms.
