Question

Use VSEPR theory to predict the geometric shapes of the following molecules and ions: (a) \(\mathrm{PCl}_{3} ;\) (b) \(\mathrm{SO}_{4}^{2-}\); (c) \(\mathrm{SOCl}_{2} ;\) (d) \(\mathrm{SO}_{3} ;\) (e) \(\mathrm{BrF}_{4}^{+}\).

Short answer

The geometric shapes are (a) PCl3 - trigonal pyramidal; (b) SO42- - tetrahedral; (c) SOCl2 - trigonal planar; (d) SO3 - trigonal planar; (e) BrF4+ - square planar.

Step-by-step solution

Determine the Electron Domains (PCl3)

First, identify the central atom (P) and its bonding (3 from Cl) and non-bonding electron pairs. Phosphorus (P), in the 5th group of the Periodic Table, has 5 valence electrons. There are 3 Chlorines (Cl), each contributes an electron for bonding. So there are 3 bonding pairs and one lone pair in PCl3.

Predict the Shape (PCl3)

Four domains in total (3 bonding, 1 non-bonding) suggest a tetrahedral arrangement. However, due to the lone pair, the actual shape realized is 'trigonal pyramidal'.

Determine the Electron Domains (SO42-)

Sulfur (S) is the central atom. It has 6 valence electrons. Oxygen atoms contribute 4 electrons for bonding. Taking into consideration 2 additional electrons due to the negative charge (2-), there are 6 pairs in total: 4 bonding and 2 non-bonding.

Predict the Shape (SO42-)

Six domains in total suggest an octahedral arrangement. However, considering 2 non-bonding pairs, the actual shape is tetrahedral.

Repeat for Rest of the Molecules/Ions

Repeat steps 1 and 2 for each remaining molecule/ion. This should lead to the following shapes: SOCl2 - 'trigonal planar', SO3 - 'trigonal planar', and BrF4+ - 'square planar'.

Key concepts

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. Understanding this geometry is crucial for predicting physical and chemical properties of substances.
The VSEPR (Valence Shell Electron Pair Repulsion) theory helps us determine molecular shapes by considering electron domains—regions where electrons are likely to be found around the central atom.
These domains include both bonding pairs of electrons (shared between atoms) and lone pairs (not shared with another atom).

• Bonding pairs influence the geometry by pulling atoms into specific arrangements.
• Lone pairs also affect geometry, often altering ideal shapes due to their stronger repulsion compared to bonding pairs.

This understanding allows chemists to predict not only the shape but also reactivity and polar characteristics of molecules.

Electron Domains

Electron domains are the regions around a central atom occupied by electrons. They can be divided into:

• Bonding domains: These involve electrons shared between atoms, forming bonds.
• Non-bonding domains: Also known as lone pairs, these are not involved in bonding.

The number and types of electron domains determine the molecular geometry. For example, in determining the shape of \( \text{PCl}_3 \), phosphorus has one lone pair and three bonding pairs.
Counting all electron domains helps in predicting the ideal arrangement, such as tetrahedral or octahedral, using VSEPR theory.
However, if lone pairs are present, the actual geometric shape may differ from the idealized model due to the lone pair's tendency to push bonding pairs closer together.

Trigonal Pyramidal

The trigonal pyramidal shape is a result of having four electron domains where one is a lone pair. This geometry can be seen in molecules like \( \text{PCl}_3 \).
In this shape, the central atom forms a base with three other atoms in a triangular plane, and a lone electron pair sits above this plane, like a pyramid.

• The presence of the lone pair affects angles between the atoms, usually making them slightly less than the ideal 109.5° found in a perfect tetrahedral arrangement.
• The asymmetry caused by the lone pair can result in a molecule being polar, affecting how it interacts with other substances.

This characteristic shape alters chemical properties, making trigonal pyramidal molecules distinct in reactions and interactions.

Tetrahedral

The tetrahedral geometry occurs when there are four electron domains equally spaced around the central atom. This shape features in molecules like \( \text{CH}_4 \) and \( \text{SO}_4^{2-} \), though in the latter, it results after considering adjustments due to lone pairs.

• In its ideal form, a tetrahedral shape has bond angles of 109.5°.
• The symmetry ensures that if all substituents are the same, the molecule is nonpolar.

The tetrahedral arrangement is very stable and minimizes electron-pair repulsions, explaining why it is common in nature.

Octahedral

An octahedral geometry features six electron domains around a central atom. This shape is named for resembling two square pyramids base-to-base.
In its pure form, it has an impressive symmetry, with bond angles of 90° and 180°.
Molecules like \( \text{SF}_6 \) demonstrate this structure, but sometimes, fewer bonding and more lone pairs adjust the shape.

• For example, in \( \text{SO}_4^{2-} \) analysis, an octahedral arrangement is just a starting point before understanding real geometries based on non-bonding pairs.
• Changes in actual arrangement due to lone pairs lead to different resultant shapes, influencing molecular interactions and reactivity.

The octahedral form is seen in many transition metal complexes, contributing to their diversity in reactions.