Barium azide is \(62.04 \% \mathrm{Ba}\) and \(37.96 \% \mathrm{~N}\). Each azide ion has a net charge of \(1-\) (a) Determine the chemical formula of the azide ion. (b) Write three resonance structures for the azide ion. (c) Which structure is most important? (d) Predict the bond lengths in the ion.

Since barium azide is 62.04% Ba and 37.96% N, we can assume that the azide ion contains only nitrogen atoms. The molar mass of nitrogen is approximately 14.01 g/mol, so we can calculate the number of nitrogen atoms in the azide ion as follows. 37.96 g N * (1 mol N / 14.01 g N) ≈ 2.7 mol N The ratio of nitrogen to barium in the azide ion is approximately 2.7:1, which means that the azide ion contains three nitrogen atoms. Therefore, the chemical formula of the azide ion is N3-.

To draw the resonance structures, we will first determine the number of valence electrons the azide ion has. Nitrogen atoms have 5 valence electrons each, and since there are three nitrogen atoms in the ion, we have a total of 15 valence electrons. Since the azide ion has a net charge of 1-, there is one additional electron, bringing the total valence electrons to 16. The resonance structures can be drawn by distributing the valence electrons among the atoms and bonds following the octet rule: 1. Structure 1: The left nitrogen atom has a triple bond to the middle nitrogen atom, and the middle nitrogen atom has a single bond to the right nitrogen atom. This leaves 6 valence electrons to be distributed between the nitrogen atoms as lone pairs. Both left and right nitrogen atoms have 2 lone pairs each, while the middle nitrogen atom has no lone pairs. 2. Structure 2: The middle nitrogen atom has a triple bond to the left nitrogen atom, and a single bond to the right nitrogen atom. This leaves 6 valence electrons to be distributed as lone pairs. The right nitrogen atom has 2 lone pairs, while the middle and left nitrogen atoms each have none. 3. Structure 3: The left nitrogen atom has a single bond to the middle nitrogen atom, and the middle nitrogen atom has a triple bond to the right nitrogen atom. This leaves 6 valence electrons to be distributed as lone pairs. Both left and right nitrogen atoms have no lone pairs, whereas the middle nitrogen atom has 2 lone pairs.

The most important resonance structure is the one that best satisfies the octet rule and has the lowest formal charges. In this case, Structure 1 is the most important, as it has the lowest formal charges for each nitrogen atom, and each atom has a full octet.

The most important resonance structure contains one triple bond and one single bond. A single bond between nitrogen atoms has a bond length of approximately 1.47 Å, and a triple bond between nitrogen atoms has a bond length of approximately 1.09 Å. However, due to the contribution from other resonance structures, the actual bond lengths in the azide ion will be somewhere in between these values, with the central nitrogen-nitrogen bond slightly shorter than the outer nitrogen-nitrogen bond.