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According to MO theory which of the following lists ranks the nitrogen species in terms of increasing bond order?
A
$N_2^- < N_2^{2-} < N_2$
B
$N_2^- < N_2 < N_2^{2-}$
C
$N_2^{2-} < N_2^- < N_2$
D
$N_2 < N_2^{2-} < N_2^-$
Detailed Solution
$N_2$ (14 electrons): $\sigma1s^2\ \sigma^*1s^2\ \sigma2s^2\ \sigma^*2s^2\ \pi2p_x^2 = \pi2p_y^2\ \sigma2p_z^2$; bond order = $\frac{10 - 4}{2} = 3$
$N_2^-$ (15 electrons): the extra electron enters an antibonding $\pi^*2p$ orbital; bond order = $\frac{10 - 5}{2} = 2.5$
$N_2^{2-}$ (16 electrons): two extra electrons in antibonding $\pi^*2p$ orbitals; bond order = $\frac{10 - 6}{2} = 2$
Increasing bond order: $N_2^{2-}$ (2) < $N_2^-$ (2.5) < $N_2$ (3)
$N_2^-$ (15 electrons): the extra electron enters an antibonding $\pi^*2p$ orbital; bond order = $\frac{10 - 5}{2} = 2.5$
$N_2^{2-}$ (16 electrons): two extra electrons in antibonding $\pi^*2p$ orbitals; bond order = $\frac{10 - 6}{2} = 2$
Increasing bond order: $N_2^{2-}$ (2) < $N_2^-$ (2.5) < $N_2$ (3)