Problem 14 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) Boron trichloride \(\left(\mathrm{BCl}_{3}\right)\) and the carbonate ion \(\left(\mathrm{CO}_{3}^{2-}\right)\) are both described as trigonal. What does this indicate about their bond angles? (b) The \(\mathrm{PCl}_{3}\) molecule is trigonal pyramidal, while \(\mathrm{ICl}_{3}\) is T-shaped. Which of these molecules is flat?

Step-by-Step Solution

Answer

In BCl3 and CO₃²⁻, both have trigonal planar molecular geometries, which indicates that their bond angles are equal to 120°. PCl3 has a trigonal pyramidal geometry, while ICl3 has a T-shaped geometry. Among these, ICl3 is the flat molecule as all atoms lie in the same plane.

Step 1: Determining Molecular Geometries of BCl3 and CO₃²⁻

The central atom in BCl3 is B (boron) and in CO₃²⁻ is C (carbon). Using the VSEPR (Valence Shell Electron Pair Repulsion) theory and considering the number of bonding pairs (BP) and lone pairs (LP) on the central atom, we can determine the molecular geometries. BCl3 has 3 bonding pairs (BP) and 0 lone pairs (LP) on the central atom (B). So, the VSEPR notation is AX₃, which indicates a trigonal planar geometry. CO₃²⁻ also has 3 bonding pairs (BP) and 0 lone pairs (LP) on the central atom (C). So, the VSEPR notation is AX₃, which again indicates a trigonal planar geometry.

Step 2: Determining Bond Angles in BCl3 and CO₃²⁻

In both BCl3 and CO₃²⁻, the molecular geometries are trigonal planar, which implies that the bond angles will be equal to 120°.

Step 3: Determining Molecular Geometries of PCl₃ and ICl₃

The central atom in PCl3 is P (phosphorus) and in ICl3 is I (iodine). Using the VSEPR theory, we can determine their molecular geometries based on their electron domains. PCl3 has 3 bonding pairs (BP) and 1 lone pair (LP) on the central atom (P), making it an AX₃E system. This gives the molecule a trigonal pyramidal geometry. ICl3 has 3 bonding pairs (BP) and 2 lone pairs (LP) on the central atom (I), making it an AX₃E₂ system. The geometry of this molecule is T-shaped.

Step 4: Identifying the Flat Molecule

Now that we know the molecular geometries of PCl3 (trigonal pyramidal) and ICl3 (T-shaped), we can identify which of these molecules is flat. A flat molecule is one where all the atoms lie in the same plane. The trigonal pyramidal geometry of PCl₃ is not flat, as the phosphorus atom isn't in the same plane as the chlorine atoms. However, the T-shaped geometry of ICl₃ is flat, as the iodine atom, the central atom, lies in the same plane with all the chlorine atoms.

Key Concepts

Molecular Geometry

Molecular geometry describes the three-dimensional arrangement of atoms in a molecule. This arrangement is crucial for understanding the molecule's properties and behavior.
For instance, the molecular geometry affects the reactivity, polarity, phase of matter, color, magnetism, biological activity, and more.
One of the methods to determine molecular geometry is the VSEPR (Valence Shell Electron Pair Repulsion) theory.

• VSEPR theory predicts the shape of molecules based on electron pairs surrounding a central atom.
• The electron pairs repel each other and place themselves as far apart as possible, resulting in a specific geometric arrangement.
• The notation AXE is used to describe the geometry, where A is the central atom, X is the number of bonding pairs, and E is the number of lone pairs.

In the case of \(\mathrm{BCl}_3\) and \(\mathrm{CO}_3^{2-}\), both have a trigonal planar molecular geometry.
For \(\mathrm{PCl}_3\) and \(\mathrm{ICl}_3\), applying VSEPR gives a trigonal pyramidal and T-shaped geometry, respectively.

Bond Angles

Bond angles refer to the angle formed between three atoms across at least two bonds in a molecule.
These angles are influenced heavily by the molecule's geometry and the repulsion between electron pairs.
A common theme in VSEPR theory is that molecules will adjust to have bond angles that minimize electron-electron repulsion.

• In a trigonal planar geometry, like in \(\mathrm{BCl}_3\) and \(\mathrm{CO}_3^{2-}\), the bond angles are typically 120°.
• Other molecular geometries will have different bond angles based on their shape. For example, a tetrahedral shape has bond angles of about 109.5°.

Understanding bond angles allows chemists to predict how molecules will interact with each other and behave in different environments.
They are also a vital component in computational chemistry and molecular modelling.

Trigonal Planar

A trigonal planar shape is a type of molecular geometry where a central atom is bonded to three other atoms, placed equidistantly in a flat, triangular shape.
This geometry is characterized by bond angles of 120° due to the equal repulsion between the bonding pairs.
The AX₃ VSEPR notation indicates a trigonal planar geometry.

• No lone pairs are on the central atom, which is crucial for maintaining the flat, planar shape.
• In \(\mathrm{BCl}_3\) and \(\mathrm{CO}_3^{2-}\), the trigonal planar shape plays a significant role in their reactivity and interaction with other molecules.

Trigonal planar molecules are often seen in compounds involving elements that typically form three bonds, such as boron in \(\mathrm{BCl}_3\).
This geometry allows the atoms to be as far apart as possible, minimizing repulsion and stabilizing the molecule.

Trigonal Pyramidal

Trigonal pyramidal molecular geometry is formed when a central atom is bonded to three other atoms and has one lone pair, making it different from a trigonal planar geometry.
The presence of the lone pair affects the angle and spatial arrangement of the bonded atoms.
For the \(\mathrm{PCl}_3\) molecule:

• The AX₃E VSEPR notation describes the arrangement, where E represents the lone pair.
• The bond angles are typically less than 109.5° due to the lone pair-bond pair repulsion being greater than bond pair-bond pair repulsion.

In trigonal pyramidal geometry, the molecule is not flat as the lone pair pushes the bonded atoms closer, creating a pyramid-like shape.
This affects the molecule's overall polarity and reactivity since the lone pair is often involved in interactions with other molecules.
Understanding why a molecule like \(\mathrm{PCl}_3\) is not flat can explain its distinct chemical properties compared to molecules with a similar layer of bonding but different numbers of lone pairs.