Problem 25 - Chemistry The Central Science

Question

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

Step-by-Step Solution

Answer

The electron-domain and molecular geometries for the given molecules and ions are: (a) HCN: Electron-Domain Geometry - Trigonal planar, Molecular Geometry - Linear (b) \(\mathrm{SO}_{3}^{2-}\): Electron-Domain Geometry - Tetrahedral, Molecular Geometry - Trigonal pyramidal (c) \(\mathrm{SF}_{4}\): Electron-Domain Geometry - Trigonal bipyramidal, Molecular Geometry - See-saw (d) \(\mathrm{PF}_{6}\): Electron-Domain Geometry - Octahedral, Molecular Geometry - Octahedral (e) \(\mathrm{NH}_{3}\mathrm{Cl}^{+}\): Electron-Domain Geometry - Tetrahedral, Molecular Geometry - Tetrahedral (f) \(\mathrm{N}_{3}^{-}\): Electron-Domain Geometry - Trigonal planar, Molecular Geometry - Linear

Step 1: Find the Central Atom and Determine its Electron Domains

First, we identify the central atom in each molecule or ion. Then, we will count the number of bonding and non-bonding electron pairs (domains) surrounding the central atom. (a) HCN - Central atom: C C has 3 electron domains (1 single bond with H, 1 triple bond with N) (b) \(\mathrm{SO}_{3}^{2-}\) - Central atom: S S has 4 electron domains (3 double bonds with O, 1 lone pair) (c) \(\mathrm{SF}_{4}\) - Central atom: S S has 5 electron domains (4 single bonds with F, 1 lone pair) (d) \(\mathrm{PF}_{6}\) - Central atom: P P has 6 electron domains (6 single bonds with F) (e) \(\mathrm{NH}_{3}\mathrm{Cl}^{+}\) - Central atom: N N has 4 electron domains (3 single bonds with H, 1 coordinate covalent bond with Cl) (f) \(\mathrm{N}_{3}^{-}\) - Central atom: N (middle nitrogen, index 2) N has 3 electron domains (1 single bond with \(N_{1}\), 1 triple bond with \(N_{3}\))

Step 2: Determine the Electron-Domain Geometry

Using the number of electron domains found in step 1, we can determine the electron-domain geometry of each molecule or ion. (a) HCN: 3 domains - Trigonal planar (b) \(\mathrm{SO}_{3}^{2-}\): 4 domains - Tetrahedral (c) \(\mathrm{SF}_{4}\): 5 domains - Trigonal bipyramidal (d) \(\mathrm{PF}_{6}\): 6 domains - Octahedral (e) \(\mathrm{NH}_{3}\mathrm{Cl}^{+}\): 4 domains - Tetrahedral (f) \(\mathrm{N}_{3}^{-}\): 3 domains - Trigonal planar

Step 3: Determine the Molecular Geometry

Now we can determine the molecular geometries of each molecule or ion, considering the positions of bonded atoms and lone pairs: (a) HCN: 3 domains, 0 lone pairs - Linear (b) \(\mathrm{SO}_{3}^{2-}\): 4 domains, 1 lone pair - Trigonal pyramidal (c) \(\mathrm{SF}_{4}\): 5 domains, 1 lone pair - See-saw (d) \(\mathrm{PF}_{6}\): 6 domains, 0 lone pairs - Octahedral (e) \(\mathrm{NH}_{3}\mathrm{Cl}^{+}\): 4 domains, 0 lone pairs - Tetrahedral (f) \(\mathrm{N}_{3}^{-}\): 3 domains, 0 lone pairs - Linear So, the electron-domain and molecular geometries for the given molecules and ions are as follows: (a) HCN: Electron-Domain Geometry - Trigonal planar, Molecular Geometry - Linear (b) \(\mathrm{SO}_{3}^{2-}\): Electron-Domain Geometry - Tetrahedral, Molecular Geometry - Trigonal pyramidal (c) \(\mathrm{SF}_{4}\): Electron-Domain Geometry - Trigonal bipyramidal, Molecular Geometry - See-saw (d) \(\mathrm{PF}_{6}\): Electron-Domain Geometry - Octahedral, Molecular Geometry - Octahedral (e) \(\mathrm{NH}_{3}\mathrm{Cl}^{+}\): Electron-Domain Geometry - Tetrahedral, Molecular Geometry - Tetrahedral (f) \(\mathrm{N}_{3}^{-}\): Electron-Domain Geometry - Trigonal planar, Molecular Geometry - Linear

Key Concepts

Electron-Domain Geometry

Electron-domain geometry is an essential concept for understanding molecular shapes. It refers to the arrangement of electron domains (both bonding and non-bonding) around a central atom. These domains create regions of electron density that influence the overall shape of a molecule or ion. The electron-domain geometry considers all areas of electron density, including:

• Bonding pairs of electrons
• Lone pairs (non-bonding electrons)

The electron-domain geometry does not change based on whether the domains are bonds or lone pairs. For instance: - A molecule with four electron domains (like in a tetrahedral shape) can still maintain this geometry whether it has four single bonds or three bonds with one lone pair.
Understanding these geometries is crucial because they lead to the molecular geometry, which dictates the molecule's physical and chemical properties.

Central Atom

The central atom is typically the atom around which other atoms are arranged in a molecule or ion. It is a key player in determining both the electron-domain and molecular geometry. Choosing the correct central atom is essential in predicting accurate geometries.- In most cases, the central atom is the one with the lowest electronegativity. However, it can also be the atom that can form the most bonds.- For example, in the molecule \(\mathrm{HCN}\), carbon (C) is the central atom because it can form multiple bonds and is in the middle of the structure.Identifying the central atom is the first step when calculating electron domains, which subsequently helps determine the correct geometry of the molecule or ion.

Bonding Electron Pairs

Bonding electron pairs are pairs of electrons shared between atoms to form bonds. These pairs are critical in determining both electron-domain and molecular geometries, as they contribute to the electron domains around the central atom. Here's how they affect these geometries:

• Bonding pairs create electron density regions, influencing the angles between the bonds.
• The shape of the molecule can change based on the number of bonding pairs versus lone pairs.

For example, in the molecule \(\mathrm{SF}_{4}\), sulfur (S) shares electrons with four fluorine atoms, resulting in four bonding pairs and contributing to a trigonal bipyramidal electron-domain geometry.
Understanding bonding pairs helps understand how different atoms interact and combine to form the overall structure of the molecule.

Lone Pairs

Lone pairs, also known as non-bonding electron pairs, are pairs of valence electrons not shared with another atom. They are significant in shaping molecular geometry due to their influence on electron-domain geometry.- Lone pairs occupy more space around the central atom compared to bonding pairs, leading to repulsion that can alter bond angles and overall shape.- In molecular geometry determination, lone pairs can cause deviations from idealized geometries.
For example, in the \(\mathrm{SO}_{3}^{2-}\) ion, one of the four electron domains is a lone pair, creating a trigonal pyramidal molecular shape instead of a perfect tetrahedral shape that would occur if all domains were bonding.Examining lone pairs is crucial as they can distort ideal shapes, resulting in unique molecular geometries.