To determine the increasing order of the bond order for the given oxygen species: O\(_2^-\), O\(_2\), O\(_2^+\), O\(_2^{2-}\), we need to understand the concept of molecular orbital theory and how it affects bond order. Bond order can be calculated using the formula:
\(\text{Bond order} = \frac{1}{2} (n_b - n_a)\)
Where \(n_b\)is the number of electrons in bonding molecular orbitals and \(n_a\)is the number of electrons in antibonding molecular orbitals.
Let us calculate the bond order for each species:
- For O\(_2\):
- Oxygen molecule, O\(_2\), has 16 electrons.
- Electronic configuration: \(\sigma(1s)^2\sigma^*(1s)^2\sigma(2s)^2\sigma^*(2s)^2\pi(2p_x)^2 = \pi(2p_y)^2\sigma(2p_z)^2\pi^*(2p_x)^1 = \pi^*(2p_y)^1\)
- Bond order: \(\frac{1}{2} (10 - 6) = 2\)
- For O\(_2^-\):
- O\(_2^-\) has 17 electrons (one additional electron in the antibonding orbital compared to O\(_2\)).
- Electronic configuration: \(\sigma(1s)^2\sigma^*(1s)^2\sigma(2s)^2\sigma^*(2s)^2\pi(2p_x)^2 = \pi(2p_y)^2\sigma(2p_z)^2\pi^*(2p_x)^2 = \pi^*(2p_y)^1\)
- Bond order: \(\frac{1}{2} (10 - 7) = 1.5\)
- For O\(_2^+\):
- O\(_2^+\) has 15 electrons (one less electron in the antibonding orbital compared to O\(_2\)).
- Electronic configuration: \(\sigma(1s)^2\sigma^*(1s)^2\sigma(2s)^2\sigma^*(2s)^2\pi(2p_x)^2 = \pi(2p_y)^2\sigma(2p_z)^2\pi^*(2p_x)^1\)
- Bond order: \(\frac{1}{2} (10 - 5) = 2.5\)
- For O\(_2^{2-}\):
- O\(_2^{2-}\) has 18 electrons (two additional electrons in the antibonding orbitals compared to O\(_2\)).
- Electronic configuration: \(\sigma(1s)^2\sigma^*(1s)^2\sigma(2s)^2\sigma^*(2s)^2\pi(2p_x)^2 = \pi(2p_y)^2\sigma(2p_z)^2\pi^*(2p_x)^2 = \pi^*(2p_y)^2\)
- Bond order: \(\frac{1}{2} (10 - 8) = 1\)
Based on the bond orders calculated, the increasing order is:
O\(_2^{2-}\), O\(_2^-\), O\(_2\), O\(_2^+\)
Therefore, the correct answer is the first option: O\(_2^{2-}\), O\(_2^-\), O\(_2\), O\(_2^+\)