Problem 105 - Chemistry Principles and Practice

Question

A Draw the Lewis structures of \(\mathrm{N}_{2} \mathrm{O}\) and \(\mathrm{NO}_{2}\). Based on these structures, predict which has the shorter \(\mathrm{N}-\mathrm{O}\) bond. Does either of these molecules contain unpaired electrons?

Step-by-Step Solution

Answer

The N-O bond in \(\mathrm{NO}_2\) is shorter. \(\mathrm{NO}_2\) has unpaired electrons.

Step 1: Count Valence Electrons for N2O

Nitrogen (N) has 5 valence electrons, and Oxygen (O) has 6 valence electrons. In the molecule \(\mathrm{N}_2\mathrm{O}\), there are two nitrogen atoms and one oxygen atom. Therefore, the total count is \(2 \times 5 + 6 = 16\) valence electrons.

Step 2: Draw the Lewis Structure for N2O

1. Start by arranging the atoms: \(\mathrm{N} - \mathrm{N} - \mathrm{O}\).2. Connect the atoms with single bonds: \(\mathrm{N} - \mathrm{N} - \mathrm{O}\).3. Distribute the remaining electrons to satisfy the octets, starting from the outer atom.4. Adjust bonds to minimize formal charges, resulting in a triple bond between the first N and the second N (\(\mathrm{N}\equiv\mathrm{N}\)) and a single bond between the second N and O (\(\mathrm{N} - \mathrm{O}\)).

Step 3: Count Valence Electrons for NO2

Nitrogen (N) has 5 valence electrons, and each Oxygen (O) has 6 valence electrons. Additionally, \(\mathrm{NO}_2\) is a radical with one unpaired electron. The total count is \(5 + 2 \times 6 + 1 = 18\) valence electrons.

Step 4: Draw the Lewis Structure for NO2

1. Arrange the atoms with nitrogen in the center: \(\mathrm{O} - \mathrm{N} - \mathrm{O}\).2. Connect each oxygen atom to nitrogen with a single bond.3. Distribute remaining electrons to complete the octets, resulting in a lone pair on the nitrogen and one unpaired electron.4. Form one double bond between \(\mathrm{N}\) and one \(\mathrm{O}\) to minimize formal charges and complete octets.

Step 5: Compare N-O Bond Lengths in N2O and NO2

The multiple bond character (triple vs double) suggests that the N-O bond in \(\mathrm{N}_2\mathrm{O}\) is primarily single-bonded while in \(\mathrm{NO}_2\), one bond is double-bonded, which results in a shorter bond length for the double bond in \(\mathrm{NO}_2\).

Step 6: Check for Unpaired Electrons

\(\mathrm{NO}_2\) contains an unpaired electron on the nitrogen atom, making it a radical. Therefore, \(\mathrm{NO}_2\) has unpaired electrons, while \(\mathrm{N}_2\mathrm{O}\) does not.

Key Concepts

Valence Electrons

Valence electrons are the outermost electrons of an atom and play a crucial role in chemical bonding. They determine how atoms interact and form molecules. To understand Lewis structures, you must first know how to count valence electrons. In the case of nitrogen (N), it has 5 valence electrons, while oxygen (O) has 6. Therefore, when determining the total number of valence electrons for a molecule like \(N_2O\), it's necessary to sum up the valence electrons of each atom involved:

• You have 2 nitrogen atoms and 1 oxygen atom.
• The calculation is: \(2 \times 5 + 6 = 16\) valence electrons for \(N_2O\).

For \(NO_2\), which is a radical, an unpaired electron adds to the count:

• One nitrogen and two oxygens, plus the unpaired electron.
• That means \(5 + 2 \times 6 + 1 = 18\) valence electrons for \(NO_2\).

This knowledge forms the basis for drawing Lewis structures accurately, which then guides us in understanding the molecule's bonding and properties.

N-O Bond Length

In chemistry, bond length is the average distance between the nuclei of two bonded atoms. It provides valuable information about the strength and type of bonding. In the specific case of \(N-O\) bonds, the comparison between \(N_2O\) and \(NO_2\) reveals different bonding characteristics:

• In \(N_2O\), the structure forms a triple bond between two nitrogens followed by a single bond to oxygen. This arrangement results in a single bond character for the N-O bond.
• In \(NO_2\), nitrogen forms one double bond with oxygen, leading to a shorter bond length for this pair due to the increased electron sharing in a double bond.

The presence of a double bond in \(NO_2\) makes its \(N-O\) bond shorter compared to the primarily single-bonded \(N-O\) in \(N_2O\). Double bonds increase electron density between atoms, reducing the interatomic space, and thus the bond length. Understanding these differences is critical for predicting molecular behavior and reactivity.

Unpaired Electrons

Unpaired electrons are electrons in an atom or molecule that are not paired with another electron in an orbital. These unpaired electrons have significant effects on the chemical properties and reactivity of compounds. Consider the molecules \(N_2O\) and \(NO_2\):

• \(N_2O\) has a stable configuration without any unpaired electrons, which means it is not a radical.
• \(NO_2\), on the other hand, possesses an unpaired electron on the nitrogen atom. This makes \(NO_2\) a radical and explains why it's more reactive.

Unpaired electrons often lead to radical behavior, which is associated with high reactivity and the ability to participate in further chemical reactions. Being aware of the presence of unpaired electrons helps in predicting the chemical fate and transformations of molecules in various processes.