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.

Short answer

The azide ion has the chemical formula N3-. Its most important resonance structures are N≡N=N^(-) and N^(-)=N≡N. The actual bond lengths in the azide ion are a blend of the single and double bond lengths, with a bond order of 1.5, resulting in intermediate bond lengths between single and double bonds.

Step-by-step solution

Determine the chemical formula of the azide ion

Given that Barium azide is 62.04% Ba and 37.96% N, let's first determine the ratio of Ba and N atoms in the compound. The molar mass of Ba is 137.33 g/mol and the molar mass of N is 14.01 g/mol. We need to calculate the moles of each element in 100 g of Barium azide: Moles of Ba = (62.04 g) / (137.33 g/mol) = 0.4516 mol Moles of N = (37.96 g) / (14.01 g/mol) = 2.7109 mol Now we need to find the simplest ratio between the moles of Ba and N by dividing both by the smallest value (0.4516): Ba ratio = 0.4516 / 0.4516 = 1 N ratio = 2.7109 / 0.4516 ≈ 6 Thus, the simplest ratio is Ba:N = 1:6. Since the azide ion has a net charge of 1-, we can assign Ba a charge of 2+ which means there must be 2 azide ions per Ba to balance the charges. Therefore, the chemical formula of the azide ion is N3-.

Write three resonance structures for the azide ion

Now, let's use Lewis structures to represent three possible resonance structures for the azide ion: 1. First resonance structure: N≡N=N^(-) 2. Second resonance structure: N^(-)=N≡N 3. Third resonance structure: N≡N^(-)-N

Identify the most important resonance structure

To determine which resonance structure is most important, we need to consider the following: 1. All atoms have a complete octet (8 electrons). 2. The formal charge on each atom is close to zero. 3. Opposite charges should be close together. Comparing the three resonance structures: 1. In the first resonance structure, the first nitrogen has a formal charge of 0, the second nitrogen has a formal charge of +1, and the third nitrogen has a formal charge of -1. All nitrogens have complete octets. 2. In the second resonance structure, the first nitrogen has a formal charge of -1, the second nitrogen has a formal charge of +1, and the third nitrogen has a formal charge of 0. All nitrogens have complete octets. 3. In the third resonance structure, the first nitrogen has a formal charge of 0, the second nitrogen has a formal charge of -1, and the third nitrogen has a formal charge of +1. The second nitrogen does not have a complete octet. The most important resonance structure is the one that best satisfies these criteria. Resonance structures 1 and 2 satisfy the first two criteria, while the third resonance structure does not satisfy the first criterion. Thus, the most important resonance structures are 1 and 2, which are equivalent.

Predict the bond lengths in the ion

In the most important resonance structures, there is a single bond and a double bond between the nitrogen atoms. In reality, the bonds in the azide ion are a resonance hybrid (an average) of these two possibilities. The actual bond lengths in the azide ion are a blend of the single and double bond lengths. The bond order is 1.5 (the average of a single and double bond). The bond lengths are expected to be intermediate between those typical for a single and double bond.

Key concepts

Resonance Structures

In chemistry, resonance structures are used to represent the different ways electrons can be arranged within molecules that have delocalized electrons. For the azide ion, the resonance structures depict alternate forms of bonding between the nitrogen atoms. By determining these structures, we see how the electron distribution can vary while the atomic positions remain the same. This concept is essential for understanding the behavior and stability of certain molecules.

Visualizing the Azide Ion

For the azide ion (N3-), we consider three different Lewis structures that exhibit electron sharing between the nitrogens in diverse ways, keeping the total number of electrons consistent. We represent the resonance structures using double-headed arrows to indicate their equivalence in contributing to the overall hybrid structure, which represents the real, observed distribution of electrons.

Percent Composition by Mass

Understanding the percent composition by mass of a compound is essential when trying to deduce its chemical formula. The percent by mass indicates how much of each element is present in a compound, relative to the total mass of the compound. With barium azide, you'll find that barium accounts for 62.04%, while nitrogen makes up the remaining 37.96%.

Calculating Moles and Ratios

By converting these percentages to moles, based on the atomic weights of barium and nitrogen, students can reveal the mole-to-mole ratio and thus, the number of atoms of each element in the simplest form of the compound's formula. It's crucial to recognize that the percentage of an element in a compound directly affects the stoichiometry, which in turn determines the compound's empirical formula.

Lewis Structure

The Lewis structure is a graphical representation that illustrates the bonding between atoms of a molecule and the lone pairs of electrons that may exist. It's vital for predicting the molecular geometry and reactivity of a molecule.

Building the Azide Ion's Lewis Structure

For the azide ion, each Lewis structure shows different placements of bonds and lone pairs while always satisfying the octet rule for each nitrogen. This approach helps students visualize how the compound might behave during chemical reactions and contributes to their understanding of the azide ion’s overall electron structure.

Formal Charge

The concept of formal charge helps us to determine how electrons are distributed in a molecule and is calculated based on the assumption that electrons in bonds are equally shared between atoms. Through formal charge calculations, we can evaluate the likely charge distribution in a given resonance structure.

Formal Charge in Azide Ion Structures

For the azide ion, the formal charge calculation helps identify which resonance structures are more favorable energetically. Structures where formal charges are minimized and are near zero are favored. The formal charge also assists in predicting molecular shape because structures with lower formal charges are more stable and thus more common.