Problem 40 - Chemistry: An Atoms-Focused Approach

Question

Determine the electron-pair geometries around the nitrogen atoms in the following unstable nitrogen oxides: (a) \(\mathrm{N}_{2} \mathrm{O}_{2}\) (b) \(\mathrm{N}_{2} \mathrm{O}_{5} ;\) (c) \(\mathrm{N}_{2} \mathrm{O}_{3}$$\left(\mathrm{N}_{2} \mathrm{O}_{2} \text { and } \mathrm{N}_{2} \mathrm{O}_{3} \text { have } \mathrm{N}-\mathrm{N}\right.\) bonds; \(\left.\mathrm{N}_{2} \mathrm{O}_{5} \text { does not. }\right)\)

Step-by-Step Solution

Answer

Answer: The electron-pair geometries around the nitrogen atoms in the given unstable nitrogen oxides are: (a) \(\mathrm{N}_{2} \mathrm{O}_{2}\): Bent (b) \(\mathrm{N}_{2} \mathrm{O}_{5}\): Tetrahedral (c) \(\mathrm{N}_{2} \mathrm{O}_{3}\): Trigonal pyramidal

Step 1: Draw the Lewis Structure of \(\mathrm{N}_{2} \mathrm{O}_{2}\)

Create the Lewis Structure of \(\mathrm{N}_{2} \mathrm{O}_{2}\) by placing the two nitrogen atoms in the center with a single bond between them, and bond each oxygen atom to a nitrogen atom. At the end, satisfy the octet rule for each atom. The resulting Lewis Structure should look like: O = N - N = O

Step 2: Determine the electron-pair geometry of \(\mathrm{N}_{2} \mathrm{O}_{2}\) using VSEPR theory

According to the VSEPR theory, the electron-pair geometry around a central atom A with E number of lone pairs and X number of bonded atoms AXE, the electron-pair geometry is determined by the total number of X and E. In \(\mathrm{N}_{2} \mathrm{O}_{2}\), the electron-pair geometry around each nitrogen atom is determined by considering the lone pair of electrons on each nitrogen atom and the two bonded atoms (1 nitrogen and 1 oxygen). Therefore, around each nitrogen atom, there are 2 bonded atoms and 1 lone pair, resulting in an AX2E geometry which forms a bent shape.

Step 3: Draw the Lewis Structure of \(\mathrm{N}_{2} \mathrm{O}_{5}\)

Create the Lewis Structure of \(\mathrm{N}_{2} \mathrm{O}_{5}\) by placing the two nitrogen atoms in the center with the necessary number of oxygen atoms bonded to them to satisfy the octet rule. The resulting Lewis Structure should look like: O = N - O - N = O | | O O

Step 4: Determine the electron-pair geometry of \(\mathrm{N}_{2} \mathrm{O}_{5}\) using VSEPR theory

In \(\mathrm{N}_{2} \mathrm{O}_{5}\), each nitrogen atom is bonded to four other atoms (1 nitrogen and 3 oxygen), and there are no lone pairs on the nitrogen atom. Therefore, around each nitrogen atom, there are 4 bonded atoms and 0 lone pairs, resulting in an AX4 geometry which forms a tetrahedral shape.

Step 5: Draw the Lewis Structure of \(\mathrm{N}_{2} \mathrm{O}_{3}\)

Create the Lewis Structure of \(\mathrm{N}_{2} \mathrm{O}_{3}\) by placing the two nitrogen atoms in the center with a single bond between them, and bond the necessary number of oxygen atoms to satisfy the octet rule. The resulting Lewis Structure should look like: O = N - N - O | O

Step 6: Determine the electron-pair geometry of \(\mathrm{N}_{2} \mathrm{O}_{3}\) using VSEPR theory

In \(\mathrm{N}_{2} \mathrm{O}_{3}\), the electron-pair geometry around each nitrogen atom is determined by considering the lone pairs of electrons on each nitrogen atom and the bonded atoms (1 nitrogen and 2 oxygen). Therefore, around each nitrogen atom, there are 3 bonded atoms and 0 lone pairs, resulting in an AX3E geometry which forms a trigonal pyramidal shape. In conclusion, the electron-pair geometries around the nitrogen atoms in the given unstable nitrogen oxides are: (a) \(\mathrm{N}_{2} \mathrm{O}_{2}\): Bent (b) \(\mathrm{N}_{2} \mathrm{O}_{5}\): Tetrahedral (c) \(\mathrm{N}_{2} \mathrm{O}_{3}\): Trigonal pyramidal

Key Concepts

Lewis Structure

Lewis Structures are a critical tool in understanding the arrangement of electrons in a molecule. They allow us to visualize how atoms bond and share electrons to form stable compounds.
This method uses dots to represent valence electrons, showing their distribution around atoms.
In complex molecules like nitrogen oxides, Lewis Structures help us predict how atoms like nitrogen and oxygen form bonds.

• Nitrogen typically prefers to form three bonds, while oxygen normally forms two bonds.
• Each line or pair of dots represents a shared pair of electrons - a covalent bond.
• In unstable nitrogen oxides, nitrogen atoms create bonds either directly with each other or through oxygen bridges.

Drawing Lewis Structures for molecules like \(\mathrm{N}_{2} \mathrm{O}_{2}\), \(\mathrm{N}_{2} \mathrm{O}_{5}\), and \(\mathrm{N}_{2} \mathrm{O}_{3}\) helps predict molecular stability and electron arrangements. They guide us in satisfying the octet rule, ensuring every atom has a complete valence shell of eight electrons where possible.

electron-pair geometry

Electron-pair geometry refers to the spatial arrangement of electron groups around a central atom.
This concept is central to the VSEPR (Valence Shell Electron Pair Repulsion) theory, which states that electron groups repel each other and will arrange themselves as far apart as possible in three-dimensional space.
VSEPR theory helps predict the geometry of a molecule by considering the total number of electron groups, which includes both bonding pairs and lone pairs. For example:

• In \(\mathrm{N}_{2} \mathrm{O}_{2}\), each nitrogen atom has two bonded atoms and one lone pair. According to VSEPR, this results in an AX2E configuration with a bent shape.
• In \(\mathrm{N}_{2} \mathrm{O}_{5}\), each nitrogen atom is surrounded by four bonded atoms with no lone pairs, leading to an AX4 configuration with a tetrahedral shape.
• In \(\mathrm{N}_{2} \mathrm{O}_{3}\), each nitrogen has three bonded atoms and no lone pairs, giving an AX3E trigonal pyramidal configuration.

Understanding electron-pair geometry allows us to predict molecular shapes and helps in visualizing the three-dimensional structure of a molecule.

octet rule

The octet rule is an essential guideline for understanding how atoms bond in molecules. It states that atoms tend to form bonds to achieve a full set of eight electrons in their outermost (valence) shell, resembling the electron configuration of noble gases.
This rule helps explain the bonding behavior of most elements, especially nonmetals.

• Nitrogen tends to form three bonds to fulfill the octet rule, sharing three of its five valence electrons with other atoms.
• Oxygen often forms two bonds, generally accumulating six electrons by sharing, plus two lone pairs.
• In nitrogen oxides like \(\mathrm{N}_{2} \mathrm{O}_{2}\), \(\mathrm{N}_{2} \mathrm{O}_{5}\), and \(\mathrm{N}_{2} \mathrm{O}_{3}\), satisfying the octet rule ensures that each nitrogen and oxygen atom achieves relative stability through optimal sharing of electrons.

Though there are exceptions, the octet rule provides a fundamental understanding of how atoms strive to reach a stable configuration by forming covalent bonds.