Problem 104 - Chemistry The Central Science

Question

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.

Step-by-Step Solution

Answer

The chemical formula of the azide ion is N₃⁻. The three resonance structures are: 1) N=N=N⁻, 2) N⁻=N=N, and 3) -N=N+=N. The most important structure is N=N=N⁻ due to its more evenly distributed charge. The predicted bond lengths in the azide ion are approximately 1.35 Å each.

Step 1: (a) Determine the chemical formula of the azide 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^-.

Step 2: (b) Write three resonance structures for the azide ion

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

Step 3: (c) Which structure is most important?

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.

Step 4: (d) Predict the bond lengths in the ion

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.

Key Concepts

Chemical Formula

The chemical formula of a compound reveals the ratio of elements within it. For Barium azide, identifying its chemical formula requires understanding the composition of both Barium (Ba) and Nitrogen (N). Given that the azide ion (N_3^-) features a 1- charge, we need to balance the elements and charge. Calculating based on the percentages, in 100 g of Barium azide:

• 62.04 g is Barium, and
• 37.96 g is Nitrogen.

To convert these masses to moles:

• The molar mass of Ba is 137.33 g/mol, which gives us 0.4517 moles of Barium.
• The molar mass of N is 14.01 g/mol, leading to 2.711 moles of Nitrogen.

By dividing by the smaller mole value (0.4517), we determine the ratio of Barium to Nitrogen is approximately 1:6. Thus, the chemical formula for Barium azide is Ba(N_3)_2, indicating two azide ions per Barium due to the ionic charge balance.

Resonance Structures

Resonance structures offer a snapshot of the possible electron distributions in a molecule or ion. For the azide ion ( _3^-), which is linear, there are three primary resonance structures to consider that illustrate its electron configuration.

• Structure 1: N=N=N^-
• Structure 2: N^-=N=N
• Structure 3: -N=N+=N

Each shows a different arrangement of the nitrogen-oxygen bonds and electron charges. Resonance is significant because it reflects the delocalization of electrons, contributing to overall ion stability. By comparing these structures, chemists evaluate which has the preferable electron distribution.

Bond Lengths

Bond length is the average distance between the nuclei of two bonded atoms. In the azide ion ( _3^-), the resonance structures indicate alternating single and double bonds between the nitrogen atoms. This suggests a distinctive combination of bond types. The typical bond lengths are:

• N-N single bond: approximately 1.45 Å.
• N-N double bond: approximately 1.25 Å.

Given the hybrid nature of the bonds from resonance, the azide ion exhibits bond lengths that average between these two. Thus, experimentally, the bond length for each nitrogen-nitrogen bond in the azide ion comes out to about 1.35 Å. This approximated length reflects the mix between a single and double N-N bond, enhancing stability through resonance.

Formal Charge

Formal charge is essential for understanding the most stable resonance structure of a molecule. It helps predict the electron distribution by assigning theoretical charges to atoms, assuming equal sharing of electrons in bonds. Calculating formal charge involves:

• Counting valence electrons in the free atom.
• Subtracting non-bonding electrons (those not shared in bonds).
• Subtracting half the electrons involved in bonding, as they are shared.

For the azide ion, resonance structure 1 (N=N=N^-) maintains the minimal separation of formal charges and is thus considered the most important. Choosing the resonance form with the smallest formal charges across the atoms typically results in the most stable configuration, as electrons are more evenly shared, avoiding excessive charge on any one atom.