Problem 103 - 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⁻. There are three resonance structures for the azide ion: [N=N=N]⁻, [N-N≡N]⁻, and [N≡N-N]⁻, with structures 1 and 3 being the most important as they have the lowest formal charges. The nitrogen-nitrogen bond lengths in the azide ion are intermediate between single and double (or double and triple) bonds due to the resonance structures.

Step 1: Part (a): Determine the chemical formula of the azide ion

We know that barium azide is \(62.04 \%\) Ba and \(37.96 \%\) N. Since barium is present as a divalent cation (Ba²⁺), let's determine the moles of barium and nitrogen in the compound. Let's assume we have 100 g of the compound. Moles of Ba = \(\frac{62.04 \text{g Ba}}{137.33 \text{g/mol (Ba)}} = 0.452 \text{mol}\) Moles of N = \(\frac{37.96 \text{g N}}{14.01 \text{g/mol (N)}} = 2.710 \text{mol}\) Now, we will determine the ratio of moles of nitrogen to moles of barium in the compound: \(\frac{2.710 \text{mol N}}{0.452 \text{mol Ba}} \approx 6\) The azide ion has a net charge of 1-, therefore the chemical formula of barium azide is Ba(N₃)₂. Consequently, the chemical formula of the azide ion is N₃⁻.

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

Azide ion (N₃⁻) consists of three nitrogen atoms with one extra electron. To draw resonance structures, let's begin by determining the Lewis structure of the azide ion. The central nitrogen atom is double-bonded to one of the terminal nitrogen atoms and single bonded to the other. The extra electron is located on the singly-bonded nitrogen atom. This creates three possible resonance structures as shown below: 1. [N=N=N]⁻ 2. [N-N≡N]⁻ 3. [N≡N-N]⁻

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

To determine the most important resonance structure, we need to consider the formal charge of each nitrogen atom in the resonance structures. The desired structure should have the lowest formal charge. The formal charges for each resonance structure are as follows: 1. [N=N=N]⁻ : N(0), N(+1), N(-1) 2. [N-N≡N]⁻ : N(-1), N(+1), N(0) 3. [N≡N-N]⁻ : N(0), N(+1), N(-1) The most important resonance structure is the one with the lowest formal charges on the atoms, which are structures 1 and 3.

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

In the azide ion, the resonance structures show that the three nitrogen atoms are connected by a combination of single, double, and triple bonds. The actual structure is an average of these resonance structures, resulting in intermediate bond lengths between single and double or double and triple bonds. Therefore, both nitrogen-nitrogen bonds in the azide ion will have similar bond lengths, which are between the bond lengths of a typical single bond and double bond (or double bond and triple bond) in nitrogen.

Key Concepts

Barium Azide

Barium azide is a compound that combines barium, a metal, with the azide ion, which consists of nitrogen atoms. This compound has a specific composition by mass: it is about 62.04% barium and 37.96% nitrogen. This information helps us determine the chemical makeup of the compound.
Since barium forms a divalent cation (Ba²⁺), the azide ion must compensate for this charge by forming two azide ions for each barium ion. This results in the chemical formula for barium azide as Ba(N₃)₂. This signifies two azide ions N₃⁻ counterbalancing one Ba²⁺ ion, rendering the compound neutra.l. Understanding this proportion is crucial for recognizing the charge balance and molecule formation in barium azide.

Resonance Structures

Resonance structures are various ways to represent molecules with delocalized electrons. The azide ion (N₃⁻) is a perfect example, as it can be drawn in different configurations. In general, resonance structures help depict the spread-out nature of electrons.
In the case of the azide ion, three resonance structures are possible:

• Structure 1: [N=N=N]⁻
• Structure 2: [N-N≡N]⁻
• Structure 3: [N≡N-N]⁻

These variations arise because electrons can be redistributed among the nitrogen atoms, altering bond types (single, double, or triple) in the process. Resonance structures do not imply that the molecule flips between forms, but rather that the true nature of the molecule is a blend of these forms.

Formal Charge

Formal charge is a useful concept in determining the most important resonance structure of a molecule. It indicates the charge distribution in a molecule by assigning charges based on the ideal number of electrons surrounding each atom.
Calculating the formal charge involves comparing the electrons each atom "owns" in a particular structure to its standard number of valence electrons:

• Formal Charge = (Valence electrons) - (Non-bonding electrons) - (Bonding electrons / 2)

For the azide ion, examining the formal charges helps identify which resonance structure is most significant. The most stable resonance structure generally has the smallest number of atoms carrying a formal charge and furthers the neutrality of charges. Structures 1 and 3 of the azide ion are the most favorable due to their formal charge values.

Bond Lengths

Bond lengths are vital in understanding molecular structure. In molecules, the length of the bond reflects the strength and type of bond between atoms. For azide ion (N₃⁻), bond lengths dominate its molecular structure analysis.
Resonance structures suggest different bond types that might seem perplexing. However, in reality, these bonds exist in a hybrid form. This means the bond lengths are averages based on the contributing resonance structures.
Thus, the N=N and N-N bonds in azide are neither entirely double bonds nor entirely single bonds. Instead, they represent a median between the two extremes. This intermediate nature gives azide a distinct set of bond lengths, commonly shorter than a single bond but longer than a typical triple bond, offering balanced stability.