Barium azide is 62.04\(\%\) Ba and 37.96\(\%\) 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.

We are given the percentage of Barium and Nitrogen in Barium azide. Barium azide: 62.04% Ba, 37.96% N Let's assume that there is 100 g of Barium azide. Then we have: 62.04 g of Ba and 37.96 g of N. Now, we will convert the grams into moles. - Molar mass of Ba is 137.33 g/mole - Molar mass of N is 14.01 g/mole Moles of Ba = 62.04 g / 137.33 g/mole = 0.4517 moles Moles of N = 37.96 g / 14.01 g/mole = 2.711 moles For the chemical formula, we need to find the simplest whole number ratio between Ba and N. To do that, we will divide the moles by the smallest moles among them, which is the moles of Ba: Moles of Ba / moles of Ba = 0.4517 / 0.4517 = 1 Moles of N / moles of Ba = 2.711 / 0.4517 ≈ 6 The simplest whole number ratio is: Ba: 1 and N: 6 Thus, the molecular formula of Barium azide is Ba(N_3)_2. Since the net charge of azide ion is 1-, the azide ion is N_3^-.

Azide ion (N_3^-) is a linear ion with a Nitrogen-Nitrogen-Nitrogen (N-N-N) bonding arrangement. There are three possible resonance structures: Resonance structure 1: N=N=N^- Resonance structure 2: N^-=N=N Resonance structure 3: -N=N+=N

Resonance structures are a way of representing different electron arrangements in a molecule. The most important structure is the one with the lowest energy, which usually has the least formal charge separation and the least number of formal charges. In our case, the most important structure among the three resonance structures is Resonance structure 1: N=N=N^- This structure has a more evenly distributed charge and less formal charge separation than the other two structures.

As the most important resonance structure is N=N=N^-, the bond in the azide ion is a combination of a double bond and a single bond. The bond lengths in the azide ion can be predicted by considering the average bond lengths of single and double N-N bonds. N-N single bond length ≈ 1.45 Å (Angstroms) N-N double bond length ≈ 1.25 Å (Angstroms) As azide ion has one and a half bond (between a single and a double bond) between each pair of adjacent nitrogen atoms, the average bond length can be calculated as: Average N-N bond length ≈ (1.45 Å + 1.25 Å) / 2 ≈ 1.35 Å (Angstroms) Hence, the predicted bond lengths in the azide ion (N_3^-) are approximately 1.35 Å each.