Question

Give the electron-domain and molecular geometries for the following molecules and ions: (a) \(\mathrm{HCN}\), (b) \(\mathrm{SO}_{3}{ }^{2-}\), (c) \(S F_{4}\) (d) \(\mathrm{PF}_{6}\), (e) \(\mathrm{NH}_{3} \mathrm{Cl}^{+}\), (f) \(\mathrm{N}_{3}^{-}\).

Short answer

(a) HCN: Electron-domain geometry is linear, molecular geometry is linear. (b) \(\mathrm{SO}_{3}{ }^{2-}\): Electron-domain geometry is tetrahedral, molecular geometry is trigonal planar. (c) \(SF_{4}\): Electron-domain geometry is trigonal bipyramidal, molecular geometry is seesaw. (d) \(\mathrm{PF}_{6}\): Electron-domain geometry is octahedral, molecular geometry is octahedral. (e) \(\mathrm{NH}_{3} \mathrm{Cl}^{+}\): Electron-domain geometry is trigonal planar, molecular geometry is trigonal planar. (f) \(\mathrm{N}_{3}^{-}\): Electron-domain geometry is linear, molecular geometry is linear.

Step-by-step solution

(a) Electron-domain and molecular geometries for HCN

1. Identify the central atom: In HCN, the central atom is Carbon (C). 2. Determine the number of electron domains: Carbon has 4 valence electrons, 1 forms a single bond with Hydrogen (H), and 3 form a triple bond with Nitrogen (N). Thus, there are 2 electron domains around carbon. 3. Determine the electron-domain geometry: With 2 electron domains, the electron-domain geometry is linear. 4. Determine the molecular geometry: Since there are no lone pairs on the central atom, the molecular geometry is also linear.

(b) Electron-domain and molecular geometries for \(\mathrm{SO}_{3}{ }^{2-}\)

1. Identify the central atom: In \(\mathrm{SO}_{3}{ }^{2-}\), the central atom is Sulfur (S). 2. Determine the number of electron domains: Sulfur has 6 valence electrons, 3 form single bonds with Oxygen (O) atoms, and there are 2 additional electrons due to the 2- charge. Thus, there are 4 electron domains around sulfur. 3. Determine the electron-domain geometry: With 4 electron domains, the electron-domain geometry is tetrahedral. 4. Determine the molecular geometry: Since there are no lone pairs on the central atom, the molecular geometry is trigonal planar.

(c) Electron-domain and molecular geometries for \(SF_{4}\)

1. Identify the central atom: In \(SF_{4}\), the central atom is Sulfur (S). 2. Determine the number of electron domains: Sulfur has 6 valence electrons, and 4 form single bonds with Fluorine (F) atoms. Thus, there are 5 electron domains around sulfur. 3. Determine the electron-domain geometry: With 5 electron domains, the electron-domain geometry is trigonal bipyramidal. 4. Determine the molecular geometry: Since there is only 1 lone pair on the central atom, the molecular geometry is seesaw.

(d) Electron-domain and molecular geometries for \(\mathrm{PF}_{6}\)

1. Identify the central atom: In \(\mathrm{PF}_{6}\), the central atom is Phosphorus (P). 2. Determine the number of electron domains: Phosphorus has 5 valence electrons, and 6 form single bonds with Fluorine (F) atoms, which means an expanded octet. Thus, there are 6 electron domains around phosphorus. 3. Determine the electron-domain geometry: With 6 electron domains, the electron-domain geometry is octahedral. 4. Determine the molecular geometry: Since there are no lone pairs on the central atom, the molecular geometry is also octahedral.

(e) Electron-domain and molecular geometries for \(\mathrm{NH}_{3} \mathrm{Cl}^{+}\)

1. Identify the central atom: In \(\mathrm{NH}_{3} \mathrm{Cl}^{+}\), the central atom is Nitrogen (N). 2. Determine the number of electron domains: Nitrogen has 5 valence electrons, 3 form single bonds with Hydrogen (H) atoms, and there are 1 fewer electrons due to the 1+ charge. Thus, there are 3 electron domains around nitrogen. 3. Determine the electron-domain geometry: With 3 electron domains, the electron-domain geometry is trigonal planar. 4. Determine the molecular geometry: Since there are no lone pairs on the central atom, the molecular geometry is trigonal planar.

(f) Electron-domain and molecular geometries for \(\mathrm{N}_{3}^{-}\)

1. Identify the central atom: In \(\mathrm{N}_{3}^{-}\), the central atom is the middle Nitrogen (N) atom. 2. Determine the number of electron domains: The central Nitrogen atom has 5 valence electrons, 2 form a single bond with the first Nitrogen (N) atom, and the remaining 3 form a double bond with the last Nitrogen (N) atom. Thus, there are 2 electron domains around the central nitrogen. 3. Determine the electron-domain geometry: With 2 electron domains, the electron-domain geometry is linear. 4. Determine the molecular geometry: Since there are no lone pairs on the central atom, the molecular geometry is also linear.

Key concepts

Electron-Domain Geometry

Electron-domain geometry is a way to visualize how different pairs of electrons are arranged around a central atom in a molecule. The number of electron domains determines the geometry. These domains include both bonding pairs (shared between two atoms) and lone pairs (not shared).

• If there are 2 electron domains, the geometry is linear.
• With 3 domains, it becomes trigonal planar.
• 4 domains lead to a tetrahedral shape.
• 5 domains create a trigonal bipyramidal structure.
• 6 domains result in an octahedral geometry.

Understanding electron-domain geometry helps predict molecular geometry, which describes the actual shape of the molecule based on the location of the atoms.

Valence Electrons

Valence electrons are the outermost electrons of an atom. They play a crucial role in forming chemical bonds. Knowing how many valence electrons an atom has helps in predicting how it will bond with other atoms.
For example:

• Carbon has 4 valence electrons, allowing it to form 4 bonds.
• Oxygen has 6 valence electrons, typically forming 2 bonds.
• Phosphorus has 5 valence electrons, forming multiple bonds depending on the molecule.

Valence electrons are used to determine the number of electron domains around a central atom, which, in turn, influences the molecule's shape.

Central Atom

In a molecule, the central atom is usually the one with the highest bonding capacity or the least electronegative element that can form multiple bonds. It's the atom around which other atoms are arranged.
Here are some examples:

• In \(\text{HCN}\), Carbon is the central atom because it can form the most bonds.
• In \(\text{SO}_3^{2-}\), Sulfur is central, having multiple bonding options.
• In complex ions like \(\text{PF}_6^-\), Phosphorus acts as the central atom due to its ability to expand its valence shell.

Identifying the central atom is a key step in determining the overall structure and geometry of the molecule.

Lone Pairs

Lone pairs are non-bonding pairs of electrons that belong to a single atom. They can influence the shape and geometry of a molecule significantly.

• Lone pairs occupy space and can repel bonding pairs, affecting angles between atoms.
• In \(\text{SF}_4\), the lone pair causes a seesaw shape instead of a trigonal bipyramidal geometry.
• In molecules without lone pairs like \(\text{PF}_6^-\), the electron-domain and molecular geometries are identical.

Understanding lone pairs is vital in predicting not just the shape but also the reactivity and properties of the molecule.