Problem 102 - Chemistry The Molecular Science

Question

The azide ion, \(\mathrm{N}_{3}^{-}\), has three resonance hybrid structures. (a) Write the Lewis structure of each. (b) Use formal charges to determine which is the most favorable resonance structure.

Step-by-Step Solution

Answer

Structure 2 with all nitrogen atoms having zero formal charge is most favorable.

Step 1: Understanding Resonance in the Azide Ion

The azide ion, \(\mathrm{N}_{3}^{-}\), is composed of three nitrogen atoms. Resonance structures occur when there can be more than one valid Lewis structure for a molecule or ion. To find these structures, we must distribute the electrons between the atoms, keeping the overall charge in mind, and ensure each nitrogen can reach a stable electron configuration. We need three resonance structures for the azide ion.

Step 2: Drawing the Lewis Structures

To draw the Lewis structures, allocate the total of 16 valence electrons (5 from each nitrogen and 1 additional electron for the negative charge) across the three nitrogen atoms. Start by forming a triple bond between the first and second nitrogen atoms and a single bond between the second and third nitrogen atoms, using lone pairs to satisfy the octet rule as much as possible:1. Structure 1: \( [N\equiv N - N]^{-} \)2. Structure 2: \( [N=N=N]^{-} \)3. Structure 3: \( [N - N\equiv N]^{-} \).

Step 3: Calculating Formal Charges

The formal charge of an atom in a molecule is calculated using the formula:\[ \text{Formal charge} = \text{Valence electrons} - (\text{Non-bonding electrons} + 0.5 \times \text{Bonding electrons}) \]This helps determine the most stable structure:1. Structure 1 - Left N: \(5 - (2 + 0.5\times6) = +1\) - Middle N: \(5 - (0 + 0.5\times8) = 0\) - Right N: \(5 - (6 + 0.5\times2) = -2\)2. Structure 2 - All N: \(5 - (2 + 0.5\times6) = 0\)3. Structure 3 - Left N: \(5 - (6 + 0.5\times2) = -2\) - Middle N: \(5 - (0 + 0.5\times8) = 0\) - Right N: \(5 - (2 + 0.5\times6) = +1\).

Step 4: Analyzing Formal Charges to Determine Stability

The best resonance structure minimizes formal charges, especially avoiding charges greater than +1 or -1. Structure 2, where all formal charges equal zero, is the most favorable because it has the lowest energy and is therefore the most stable configuration.

Key Concepts

Lewis Structures

Lewis structures are visual representations of molecules that show the arrangement of atoms, bonds, and electron pairs. For the azide ion, \(\mathrm{N}_3^-\), these structures help us understand how electrons are shared between the nitrogen atoms and their connectivity.

To create a Lewis structure, we first calculate the total number of valence electrons. Each nitrogen has 5 valence electrons, and we include one additional electron because of the -1 charge, giving us a total of 16 valence electrons.

• Start with single bonds between the nitrogen atoms.
• Adjust to double or triple bonds if needed to fulfill the octet rule.
• Place extra electrons as lone pairs to complete the octets.

For the azide ion, the three resonance structures vary in how electrons are distributed to stabilize each nitrogen:

• Structure 1: A triple bond between the first and second nitrogen atoms, and a single bond between the second and third.
• Structure 2: Three double bonds linking each pair of nitrogen atoms.
• Structure 3: A single bond between the first and second nitrogen atoms, and a triple bond between the second and third.

These structures represent possible ways for electrons to be arranged and indicate that the actual configuration is a hybrid of these scenarios.

Formal Charge

Formal charge is a concept used to determine which Lewis structure is most stable by calculating the charge of each atom. It helps in predicting the most likely arrangement of electrons.

To find the formal charge, use the formula:\[\text{Formal charge} = \text{Valence electrons} - (\text{Non-bonding electrons} + 0.5 \times \text{Bonding electrons})\]This calculation helps verify that the electrons are distributed for maximum stability.

• A neutral molecule or ion aims to have formal charges close to zero.
• Lewis structures aim to minimize formal charges, especially those higher than +1 or less than -1.

In the azide ion:

• Structure 1 results in a +1 charge on the left nitrogen, a 0 charge on the middle, and -2 on the right.
• Structure 2 shows all nitrogen atoms with 0 charge, which is ideal.
• Structure 3, like Structure 1, features negative and positive charges that could lead to higher energy.

Structure 2 is the most favorable due to its zero formal charges, indicating a lower-energy, more stable configuration for the azide ion.

Azide Ion Chemistry

The azide ion, \(\mathrm{N}_3^-\), is a fascinating example in chemistry due to its resonance and energetic properties. Resonance in the azide ion shows how electrons can be delocalized across different atoms, leading to stability.

The azide ion is linear due to the nature of the nitrogen-nitrogen bonding and hybridization. Each atom seeks to achieve a full octet, resulting in different resonance structures.

• All structures share similar bond angles, giving the ion linear geometry.
• The distribution of charges and arrangement of electrons contribute to the azide ion’s reactivity.

Azide compounds are found in both organic and inorganic chemistry due to their ability to serve as precursors for the production of foam and explosives or as intermediates in organic synthesis.
The stability and chemical behavior of azide compounds rely heavily on their resonance structure and the associated formal charge distribution. Therefore, understanding both concepts is vital to manipulating azide ions in laboratory and industry practices.