Question

Which has the greater \(\mathrm{O}-\mathrm{N}-\mathrm{O}\) bond angle, \(\mathrm{NO}_{2}\) or \(\mathrm{NO}_{2}^{+} ?\) Explain your answer.

Short answer

\(\mathrm{NO}_2^{+}\) has the greater \(\mathrm{O}-\mathrm{N}-\mathrm{O}\) bond angle.

Step-by-step solution

Understanding the Molecules

First, recognize the structures of \(\mathrm{NO}_2\) and \(\mathrm{NO}_2^+\). \(\mathrm{NO}_2\) is a neutral molecule with 17 valence electrons, while \(\mathrm{NO}_2^+\) is a cation with 16 valence electrons.

Analyze Lone Pairs and Bond Pairs

In \(\mathrm{NO}_2\), there is one unpaired electron, which creates a repulsion that affects the bond angle. In \(\mathrm{NO}_2^+\), the positive charge results in the removal of an electron and leads to a clean bond structure with no lone pairs or unpaired electrons.

Apply the VSEPR Theory

The VSEPR (Valence Shell Electron Pair Repulsion) theory suggests that bond angles are determined by the repulsions between electron pairs. In \(\mathrm{NO}_2\), the angle is reduced due to lone pair repulsion. In \(\mathrm{NO}_2^+\), there are no lone pairs to repel, suggesting a larger bond angle.

Conclude the Comparison of Bond Angles

Since \(\mathrm{NO}_2^+\) has no lone pairs or unpaired electrons affecting the structure, it has a greater \(\mathrm{O}-\mathrm{N}-\mathrm{O}\) bond angle compared to \(\mathrm{NO}_2\), where lone pair repulsion is present.

Key concepts

VSEPR Theory

When it comes to understanding the shape and angle of bonds in molecules, the VSEPR Theory is a crucial tool. VSEPR stands for Valence Shell Electron Pair Repulsion. This theory predicts the geometry of individual molecules based on the idea that electron pairs around a central atom will repel each other.

• This repulsion forces the electron pairs to position themselves as far apart as possible, minimizing repulsion and thereby determining the shape of the molecule.
• The types of electron pairs considered in this theory are bonding pairs, which form the chemical bonds, and lone pairs, which do not participate directly in bonding.
• Due to this repulsion, lone pairs tend to take up more space than bonding pairs, affecting the bond angles within the molecule.

In the case of \(\mathrm{NO}_{2}\), having an unpaired electron affects the bond angle due to repulsion, making it smaller. Conversely, \(\mathrm{NO}_{2}^{+}\) lacks any unpaired electrons or lone pairs, resulting in larger bond angles according to VSEPR theory.

Valence Electrons

Valence electrons play a key role in determining the chemical properties and reactivity of an element. These are the electrons located in the outermost shell of an atom, directly involved in forming bonds with other atoms.

• In molecular compounds like \(\mathrm{NO}_{2}\) and \(\mathrm{NO}_{2}^{+}\), the total count of valence electrons affects molecular stability and shape.
• \(\mathrm{NO}_{2}\) has 17 valence electrons, which includes one unpaired electron. This setup influences its molecular geometry and bond angles.
• On the other hand, \(\mathrm{NO}_{2}^{+}\) has 16 valence electrons because it has lost an electron compared to \(\mathrm{NO}_{2}\). This "cleaner" configuration, void of lone pairs or unpaired electrons, leads to less electron repulsion and contributes to a wider bond angle.

Understanding the distribution and count of valence electrons in a molecule is essential for predicting how it will bond and what shapes it can form, as these factors dictate much of its chemical behavior.

Molecular Geometry

The three-dimensional shape of a molecule—a concept known as molecular geometry—impacts not only its physical appearance but also its reactivity and interaction with other molecules.

• The shape is defined by the spatial arrangement of atoms and can be predicted using VSEPR theory.
• For example, in linear, bent, or trigonal planar geometries, the angles between the atoms vary according to the presence of lone pairs and the number of bonded atoms.
• In the specific case of \(\mathrm{NO}_{2}\), it is predicted to be a bent molecule with one unpaired electron leading to smaller bond angles due to additional repulsive forces.
• In contrast, \(\mathrm{NO}_2^+\) is also bent but more symmetrical without lone pair interference, which results in a larger bond angle.

Recognizing molecular geometry helps us understand how molecules behave and interact in various chemical environments, impacting properties such as boiling points, solubility, and reactivity.