Problem 92 - Chemistry: The Central Science

Question

The following three Lewis structures can be drawn for \(\mathrm{N}_{2} \mathrm{O}\) : \(: \mathrm{N} \equiv \mathrm{N}-\ddot{\mathrm{O}}: \longleftrightarrow: \ddot{\mathrm{N}}-\mathrm{N} \equiv \mathrm{O}: \longleftrightarrow: \ddot{\mathrm{N}}=\mathrm{N}=\ddot{\mathrm{O}}:\) (a) Using formal charges, which of these three resonance forms is likely to be the most important? (b) The \(\mathrm{N}-\mathrm{N}\) bond length in \(\mathrm{N}_{2} \mathrm{O}\) is \(1.12 \AA\), slightly longer than a typical \(\mathrm{N} \equiv \mathrm{N}\) bond; and the \(\mathrm{N}-\mathrm{O}\) bond length is \(1.19 \AA\) Ä, slightly shorter than a typical bond (see Table 8.5). Based on these data, which resonance structure best represents \(\mathrm{N}_{2} \mathrm{O}\) ?

Step-by-Step Solution

Answer

Based on the formal charges, Resonance Form I with charges (+1, 0, 0) is the most important resonance form. However, considering the given bond lengths, Resonance Form II, \(\ddot{\mathrm{N}}-\mathrm{N} \equiv \mathrm{O}\), best represents \(\mathrm{N}_{2} \mathrm{O}\) as it has a double bond between \(\mathrm{N}\) and \(\mathrm{O}\) and a single bond between \(\mathrm{N}\) atoms, which correlates with the observed bond lengths.

Step 1: Calculate the Formal Charges

To determine which of the given resonance forms is likely to be the most important, we need to calculate the formal charge of each atom in each resonance form. The formula to calculate formal charge is: Formal charge = (Valence electrons) - (Nonbonding electrons) - (Bonding electrons/2)

Step 1.1: Determine Formal Charges for Resonance Form I

In this resonance form, we have \(\mathrm{N} \equiv \mathrm{N}-\ddot{\mathrm{O}}\). Let's find the formal charge for each atom: 1. Left N atom: formal charge = 5 - 0 - (8/2) = +1 2. Right N atom: formal charge = 5 - 2 - (6/2) = 0 3. O atom: formal charge = 6 - 4 - (4/2) = 0

Step 1.2: Determine Formal Charges for Resonance Form II

In this resonance form, we have \(\ddot{\mathrm{N}}-\mathrm{N} \equiv \mathrm{O}\). Let's find the formal charge for each atom: 1. Left N atom: formal charge = 5 - 4 - (4/2) = 0 2. Right N atom: formal charge = 5 - 2 - (6/2) = 0 3. O atom: formal charge = 6 - 2 - (8/2) = -1

Step 1.3: Determine Formal Charges for Resonance Form III

In this resonance form, we have \(\ddot{\mathrm{N}}=\mathrm{N}=\ddot{\mathrm{O}}\). Let's find the formal charge for each atom: 1. Left N atom: formal charge = 5 - 4 - (4/2) = 0 2. Right N atom: formal charge = 5 - 2 - (8/2) = -1 3. O atom: formal charge = 6 - 4 - (4/2) = 0 Answer (a): Based on the formal charges, Resonance Form I has the lowest formal charges (+1, 0, 0) and is thus the most important resonance form.

Step 2: Determine Which Resonance Structure Best Represents N2O

Given the bond lengths of the \(\mathrm{N}-\mathrm{N}\) and \(\mathrm{N}-\mathrm{O}\) bonds, we can best guess which resonance form best represents \(\mathrm{N}_{2} \mathrm{O}\): Answer (b): Since the \(\mathrm{N}-\mathrm{N}\) bond is slightly longer than a typical \(\mathrm{N} \equiv \mathrm{N}\) bond, it suggests that this bond is weaker as expected from a single bond or double bond. The \(\mathrm{N}-\mathrm{O}\) bond is slightly shorter than a typical bond, indicating that it is stronger as expected from a double bond. Thus, Resonance Form II, \(\ddot{\mathrm{N}}-\mathrm{N} \equiv \mathrm{O}\), which has a double bond between \(\mathrm{N}\) and \(\mathrm{O}\) and a single bond between \(\mathrm{N}\) atoms, best represents \(\mathrm{N}_{2} \mathrm{O}\).

Key Concepts

Formal Charge

Formal charge is a concept used in chemistry to determine the distribution of electric charge within a molecule. It helps us understand which resonance structure is more stable or predominant. You can calculate the formal charge using a simple formula:

• Formal charge = (Valence electrons) - (Nonbonding electrons) - (Bonding electrons/2).

To apply this, each atom in a molecule is evaluated to see how it shares its electrons in bonds or holds its own electrons. A lower formal charge generally indicates a more stable or likely structure.

For instance, in nitrogen monoxide (\(\mathrm{N}_2\mathrm{O}\), three resonance structures are identified. In the given examples,

• Resonance Form I has formal charges of +1, 0, and 0,
• Resonance Form II has formal charges of 0, 0, and -1,
• Resonance Form III has formal charges of 0, -1, and 0.

Given these values, Resonance Form I is considered the most stable due to its minimal formal charges.

This understanding helps chemists choose between potential structures based on minimizing the separation of charge within a molecule.

Resonance

Resonance is an important concept in concert to Lewis structures, where more than one valid arrangement of electrons exists for molecules. It portrays how electrons are delocalized or spread over multiple atoms rather than stuck between two specific atoms.

In the given example of \(\mathrm{N}_{2}\mathrm{O}\), three resonance forms are possible. These structures differ in the placement of electrons and bonds. Importantly, resonance structures do not exist in isolation but rather represent a hybrid of all possibilities. This hybrid provides a more complete view of the electron distribution in the actual molecule.

Each resonance structure can weigh differently depending on factors like:

• Formal charges,
• Bond polarity,
• Energy stability.

In the exercise, although Resonance Form I has suitable formal charges, the bond lengths align better with Resonance Form II, as it shows stronger and weaker bonds akin to the observed physical data. This emphasizes the fact that resonance structures provide insight into the nature of bonding and molecular geometry.

Bond Length

Bond length refers to the average distance between the nuclei of two bonded atoms. It is influenced by factors such as the type of bond (single, double, triple) and the atoms involved. For example, a single bond is generally longer than a double bond, which in turn is longer than a triple bond.

In the context of \(\mathrm{N}_{2}\mathrm{O}\), bond lengths provide clues to the correct resonance structure. The given bond lengths are slightly atypical:

• The nitrogen-nitrogen bond is longer than that typically seen in a triple bond.
• The nitrogen-oxygen bond is shorter than usual, suggesting increased bond strength.

These observations suggest that in \(\mathrm{N}_{2}\mathrm{O}\), the nitrogen-nitrogen bond might not be a triple bond as long characteristic of \((\mathrm{N}\equiv\mathrm{N})\) but closer to a double or single bond. Meanwhile, the nitrogen-oxygen bond, being shorter, acts more like a typical double bond. This supports considering Resonance Form II, which includes this bond arrangement, as the most representation of the actual molecular structure.