Problem 27 - Chemistry The Science in Context

Question

Determine the bond angles in the following ions: (a) \(\mathrm{NH}_{4}^{+}\) (b) \(\mathrm{SO}_{3}^{2-} ;\) (c) \(\mathrm{NO}_{2}^{-} ;\) (d) \(\mathrm{XeF}_{5}^{+}\)

Step-by-Step Solution

Answer

Answer: (a) \(\mathrm{NH}_4^+\): bond angles are 109.5°. (b) \(\mathrm{SO}_3^{2-}\): bond angles are 120°. (c) \(\mathrm{NO}_2^-\): bond angle is slightly less than 120° (closer to 118°). (d) \(\mathrm{XeF}_5^+\): bond angles are 90° between axial and equatorial fluorine atoms, and 180° between the equatorial fluorine atoms.

Step 1: Determine Electron Domains

For each ion, calculate the number of electron domains (ED) which include bonding pairs and lone pairs. This can be determined through the Lewis structure. (a) \(\mathrm{NH}_{4}^{+}\) There are 4 single bonds (covalent electron regions) in \(\mathrm{NH}_{4}^{+}\). Therefore, its ED = 4. (b) \(\mathrm{SO}_{3}^{2-}\) There are 3 double bonds (covalent electron regions) in \(\mathrm{SO}_{3}^{2-}\). Therefore, its ED = 3. (c) \(\mathrm{NO}_{2}^{-}\) There are 1 double bond, 1 single bond, and 1 unshared electron pair. Therefore, its ED = 3. (d) \(\mathrm{XeF}_{5}^{+}\) There are 5 single bonds and 1 unshared electron pair in \(\mathrm{XeF}_{5}^{+}\). Therefore, its ED = 6.

Step 2: Determine the Molecular Geometries

Using the number of electron domains from Step 1, we can determine the molecular geometries. (a) \(\mathrm{NH}_{4}^{+}\): 4 ED corresponds to a tetrahedral geometry. (b) \(\mathrm{SO}_{3}^{2-}\): 3 ED corresponds to a trigonal planar geometry. (c) \(\mathrm{NO}_{2}^{-}\): 3 ED corresponds to a bent geometry (due to the presence of a lone pair). (d) \(\mathrm{XeF}_{5}^{+}\): 6 ED corresponds to a square pyramidal geometry (due to the presence of a lone pair).

Step 3: Determine the Bond Angles

Now that we have the molecular geometries, we can determine the bond angles associated with each geometry. (a) \(\mathrm{NH}_{4}^{+}\): In a tetrahedral geometry, bond angles are 109.5°. (b) \(\mathrm{SO}_{3}^{2-}\): In a trigonal planar geometry, bond angles are 120°. (c) \(\mathrm{NO}_{2}^{-}\): In bent geometry with 3 electron regions (trigonal planar-based), bond angles are about 120°. However, due to the presence of a lone pair, the bond angle will be slightly less than 120° (closer to 118°). (d) \(\mathrm{XeF}_{5}^{+}\): In a square pyramidal geometry (with 6 electron regions - octahedral-based), bond angles are 90° between axial and equatorial fluorine atoms, and 180° between the equatorial fluorine atoms.

Key Concepts

Molecular Geometry

Understanding molecular geometry is essential for predicting the shape of molecules. It determines how atoms are spatially arranged which affects physical and chemical properties. Molecular geometry uses the concept of electron domains to predict shapes.
For example, in the ammonium ion (\(\mathrm{NH}_{4}^{+}\)), four electron domains lead to a tetrahedral shape with bond angles of 109.5°. The sulfate ion (\(\mathrm{SO}_{3}^{2-}\)) has a trigonal planar shape due to its three electron domains, resulting in 120° bond angles.

• These geometries are predicted using the VSEPR (Valence Shell Electron Pair Repulsion) theory, which suggests that electron pairs will arrange themselves to minimize repulsion.

Knowing the geometry helps you understand reactions and interactions between molecules.

Electron Domains

Electron domains are regions where electrons are likely found around a central atom. This includes bonding pairs (shared between atoms) and lone pairs (not shared).
For instance, the \(\mathrm{NH}_{4}^{+}\) ion has four bonding pairs, giving it four electron domains.

• The ion \(\mathrm{NO}_{2}^{-}\) has three electron domains: one lone pair and two bonding pairs.
• Electron domains help determine molecular geometry by considering not just bonds but all electron-containing regions.

Counting the total electron domains gives insights into the molecular structure and potential angles between atoms.

Lewis Structure

Lewis structures are diagrams that show the bonds between atoms in a molecule and any unpaired electrons. They are instrumental in figuring out the arrangement of valence electrons.
Take \(\mathrm{SO}_{3}^{2-}\) as an example; it has double bonds between sulfur and oxygen, reflected in its Lewis structure with no lone pairs on sulfur. For \(\mathrm{XeF}_{5}^{+}\), there’s a lone pair on xenon alongside five bonds.

• Lewis structures lay the foundation for predicting molecular geometry by showing possible arrangements of electron domains.
• These structures also help identify the regions of electron density that determine bond angles.

Mastering Lewis structures improves understanding of both complex and simple molecular shapes.

Covalent Bonding

Covalent bonding involves the sharing of electron pairs between atoms, forming a stable balance of attractive and repulsive forces. This is key to the formation of molecules like \(\mathrm{NO}_{2}^{-}\) and \(\mathrm{NH}_{4}^{+}\).
In \(\mathrm{NH}_{4}^{+}\), each nitrogen-hydrogen bond is a covalent bond where electrons are shared between the atoms.

• These types of bonds contribute to the molecule's overall stability and geometry.
• The sharing of electrons in covalent bonds allows atoms to fulfill the desired electron configuration, often achieving a noble gas electron arrangement.

Covalent bonding's impact is fundamental on molecular geometry and bond angles, influencing how compounds interact and react.