Question: 75: Which amongst the following is incorrect statement?
(1) \mathrm{H}_{2}^{+} ion has one electron
(2) \mathrm{O}_{2}^{+} ion is diamagnetic
(3) The bond orders of \mathrm{O}_{2}^{+}, \mathrm{O}_{2}, \mathrm{O}_{2}^{-} and \mathrm{O}_{2}^{2-} are 2.5, 2, 1.5 and 1, respectively
(4) \mathrm{C}_{2} molecule has four electrons in its two degenerate \pi molecular orbitals
Answer: Option (2)
Explanation:
The ion \mathrm{H}_{2}^{+} is formed by removing one electron from \mathrm{H}_{2}, so it contains only one electron.
Hence, statement (1) is correct.
The molecular orbital configuration of \mathrm{O}_{2}^{+} has one unpaired electron
because it is formed by removing one electron from the antibonding
\pi^{*} orbital of \mathrm{O}_{2}.
Since the presence of an unpaired electron makes a species paramagnetic,
\mathrm{O}_{2}^{+} is paramagnetic, not diamagnetic.
Therefore, statement (2) is incorrect.
The bond order is given by \frac{N_b-N_a}{2},
where N_b is the number of bonding electrons and N_a is the number of antibonding electrons.
Using molecular orbital theory, the bond orders of \mathrm{O}_{2}^{+}, \mathrm{O}_{2}, \mathrm{O}_{2}^{-} and \mathrm{O}_{2}^{2-} are correctly given as 2.5, 2, 1.5 and 1, respectively.
Hence, statement (3) is correct.
In the \mathrm{C}_{2} molecule, four electrons occupy the two degenerate bonding \pi molecular orbitals according to Hund’s rule.
Therefore, statement (4) is correct.
Thus, the incorrect statement is option (2).