Question

Use electron-repulsion arguments to explain the following: a. The \(\mathrm{H}-\mathrm{N}-\mathrm{H}\) bond angle in \(\mathrm{NH}_{4}^{+}\) is larger than in \(\mathrm{NH}_{3}\). b. The \(\mathrm{H}-\mathrm{N}-\mathrm{H}\) bond angle in \(\mathrm{NH}_{3}\left(107.3^{\circ}\right)\) is larger than the \(\mathrm{F}-\mathrm{N}-\mathrm{F}\) bond angles in \(\mathrm{NF}_{3}\left(102.1^{\circ}\right)\). c. The \(\mathrm{Cl}-\mathrm{C}-\mathrm{Cl}\) angle in \(\mathrm{Cl}_{2} \mathrm{C}=\mathrm{O}\) (phosgene, \(111.3^{\circ}\) ) is less than the \(\mathrm{H}-\mathrm{C}-\mathrm{H}\) angle in \(\mathrm{H}_{2} \mathrm{C}=\mathrm{O}\) (methanal, \(118^{\circ}\) ). d. The \(\mathrm{H}-\mathrm{C}-\mathrm{H}\) angle in methanal \(\left(118^{\circ}\right)\) is greater than the \(\mathrm{H}-\mathrm{C}-\mathrm{H}\) angle in ethene \(\left(116.7^{\circ}\right)\).

Short answer

a. Lone pair repulsion in NH3 reduces angle; no lone pairs in NH4+. b. Electronegativity of F reduces bond angle in NF3. c. Larger Cl atoms cause smaller angle in Cl2C=O. d. More electron density in ethene compresses angle.

Step-by-step solution

Comparing Bond Angles in NH4+ and NH3

In the ammonium ion (\(\text{NH}_4^+\)), the central nitrogen atom is surrounded by four hydrogen atoms that are symmetrically arranged. The repulsion between these bonded pairs results in a tetrahedral geometry with bond angles of \(109.5^\circ\). In ammonia (\(\text{NH}_3\)), there is a lone pair of electrons on nitrogen. Lone pairs exhibit more repulsion compared to bond pairs, causing the bond angle to decrease to \(107.3^\circ\). Hence, the \(\text{H-N-H}\) bond angle in \(\text{NH}_4^+\) is larger than in \(\text{NH}_3\) because there is no lone pair to decrease the bond angle.

Explaining Differences in Bond Angles between NH3 and NF3

Both \(\text{NH}_3\) and \(\text{NF}_3\) have a similar trigonal pyramidal shape due to one lone pair on nitrogen. However, in \(\text{NF}_3\), the electronegativity of fluorine pulls the electrons closer to it, enhancing lone pair repulsion effect and thus reducing the \(\text{F-N-F}\) bond angle compared to the \(\text{H-N-H}\) bond angle in \(\text{NH}_3\). As a result, the bond angle in \(\text{NH}_3\) is larger.

Variance in Angles between Cl2C=O and H2C=O

Phosgene (\(\text{Cl}_2\text{C} = \text{O}\)) and methanal (\(\text{H}_2\text{C} = \text{O}\)) both involve a carbon double bonded to oxygen. In \(\text{Cl}_2\text{C} = \text{O}\), chlorine's larger size and significant electron-withdrawing effect create greater electron repulsion in the plane, leading to a smaller \(\text{Cl-C-Cl}\) bond angle. In \(\text{H}_2\text{C} = \text{O}\), the hydrogen atoms induce less repulsion, allowing a larger \(\text{H-C-H}\) bond angle.

Contrasting Bond Angles in Methanal and Ethene

In methanal (\(\text{H}_2\text{C} = \text{O}\)), with a carbon-oxygen double bond and less electron dense regions, the \(\text{H-C-H}\) bond angle is slightly larger. For ethene (\(\text{C}_2\text{H}_4\)), the bonding involves \(sp^2\) hybridized carbon atoms forming a planar molecule with pairs of electrons between carbons resulting in slightly more compression due to additional electron density, setting the \(\text{H-C-H}\) angle to \(116.7^\circ\).

Key concepts

Bond Angles

Bond angles are an important feature in molecular chemistry that determine the shape and stability of molecules. Essentially, bond angles refer to the angle formed between three atoms across at least two bonds. These angles are influenced by the electron pairs surrounding a central atom.

The key factor that influences bond angles is the repulsion between electron pairs, according to the Electron Repulsion Theory. This theory posits that electron pairs will arrange themselves as far apart as possible to minimize repulsion. Therefore, the geometry of molecule and its bond angles are greatly affected by the type and presence of electron pairs, whether they are bonded pairs (shared between atoms) or lone pairs (not shared).

For example, in the ammonium ion (\(\mathrm{NH}_{4}^{+}\)), the four bonding pairs of electrons create an ideal tetrahedral shape, leading to bond angles of approximately \(109.5^{\circ}\). Conversely, in \(\mathrm{NH}_3\), the presence of a lone pair distorts this angle to \(107.3^{\circ}\) due to increased electron repulsion.

Lone Pair Repulsion

Lone pair repulsion is a critical factor affecting molecular geometry and bond angles. A lone pair consists of two electrons on a central atom that are not shared with another atom. These pairs are more repulsive than bonding pairs because they occupy more space around the central atom.

The increased repulsion from lone pairs can cause significant reductions in bond angles. For instance, in ammonia (\(\mathrm{NH}_3\)), the \(\mathrm{H}-\mathrm{N}-\mathrm{H}\) bond angle is smaller than that in ammonium ion due to the presence of a lone pair on nitrogen. This lone pair pushes the bonded hydrogen atoms closer together, reducing the angle.

This behavior is evident in the comparison between \(\mathrm{NH}_3\) and \(\mathrm{NF}_3\). Both molecules feature a lone pair on nitrogen, but the electronegativity of fluorine in \(\mathrm{NF}_3\) enhances the lone pair repulsion effect more than in ammonia, resulting in even smaller \(\mathrm{F}-\mathrm{N}-\mathrm{F}\) bond angles. This example clearly demonstrates how lone pairs can alter the geometry of molecules and underscores their role in electron repulsion theory.

Molecular Geometry

Molecular geometry is the three-dimensional arrangement of atoms in a molecule. This geometry is determined primarily by the electron pairs around a central atom, which arrange themselves to minimize repulsion and achieve a state of lower energy.

Various molecular shapes include linear, bent, trigonal planar, trigonal pyramidal, and tetrahedral, each defined by specific bond angles. For instance, methane (\(\mathrm{CH}_4\)) displays a tetrahedral geometry due to four bonding pairs of electrons. This configuration results in bond angles of \(109.5^{\circ}\), typical for a tetrahedral arrangement.

In contrast, molecules featuring lone pairs, such as ammonia and water, deviate from their ideal geometries. Ammonia (\(\mathrm{NH}_3\)), with its trigonal pyramidal shape, has a bond angle of \(107.3^{\circ}\), indicating the effect of lone pair repulsion. Understanding these effects is crucial for predicting the structure and reactivity of molecules.

Tetrahedral Geometry

Tetrahedral geometry is a prevalent molecular shape in chemistry characterized by four groups of electrons or atoms around a central atom. Each corner of the tetrahedron represents a bond or group.This shape arises when no lone pairs are present and all electron pairs are bonding pairs.

The ideal bond angle in a tetrahedral geometry is \(109.5^{\circ}\). This can be seen in molecules like methane (\(\mathrm{CH}_4\)), where four hydrogen atoms are symmetrically arranged around carbon. Similarly, the ammonium ion (\(\mathrm{NH}_{4}^{+}\)) also exhibits this geometry due to its four identical bonding pairs.

Variations in bond angles, such as those in ammonia (\(\mathrm{NH}_3\)), result from the presence of lone pairs. While tetrahedral geometry is ideal for solely bonded pairs, molecules with lone pairs will experience deviations due to the increased repulsion lone pairs exert compared to bonded pairs.