(a) Draw the best Lewis structure(s) for the nitrite ion, \(\mathrm{NO}_{2}^{-}\). (b) With what allotrope of oxygen is it isoelectronic? (c) What would you predict for the lengths of the bonds in \(\mathrm{NO}_{2}^{-}\) relative to \(\mathrm{N}-\mathrm{O}\) single bonds and double bonds?

To determine the best Lewis structure(s) for \(\mathrm{NO}_{2}^{-}\), we will first count the total number of valence electrons. Nitrogen has 5 valence electrons, each oxygen atom has 6, and there is an additional electron due to the negative charge. Therefore, the total number of valence electrons is 5 + 6(2) + 1 = 18. Now, we will construct different resonance structures for \(\mathrm{NO}_{2}^{-}\) and verify if they fulfill the octet rule. Two possible structures are: (i) N atom connected to one O atom with a double bond, and to another O atom with a single bond, which has an extra lone pair of electrons. (ii) N atom connected to one O atom with a single bond with an extra lone pair of electrons, and another O atom with a double bond. Both of these structures satisfy the octet rule.

Isoelectronic species have the same number of electrons. In this case, we have \(5 + 6(2) + 1 = 18\) electrons in the nitrite ion. Now, we need to check which allotrope of oxygen has the same number of electrons. Oxygen exists in various allotropic forms such as O\(_2\) (16 electrons) and O\(_3\) (ozone, 24 electrons). None of these molecules have 18 electrons. However, if we consider a superoxide ion (O\(_2^{-}\)), it has 16 + 1 = 17 electrons, and a peroxide ion (O\(_2^{2-}\)) has 16 + 2 = 18 electrons. Therefore, the peroxide ion (O\(_2^{2-}\)) is isoelectronic with the nitrite ion.

We have two possible Lewis resonance structures for \(\mathrm{NO}_{2}^{-}\), and the actual molecule is a hybrid of these two structures. In resonance hybrid structure, bond lengths are intermediate between single and double bonds. For the nitrite ion, the N-O bond lengths will be intermediate between the single bond length found in \(\mathrm{N}-\mathrm{O}\) single bond compounds and the double bond length found in \(\mathrm{N}=\mathrm{O}\) double bond compounds.