Question

Alternative strategies to the one used in this chapter have been proposed for applying the VSEPR theory to molecules or ions with a single central atom. In general, these strategies do not require writing Lewis structures. In one strategy, we write (1) the total number of electron pairs \(=[\) (number of valence electrons) \(\pm\) (electrons required for ionic charge) \(] / 2\) (2) the number of bonding electron pairs \(=\) (number of atoms) -1 (3) the number of electron pairs around central atom \(=\) total number of electron pairs \(-3 \times[\) number of terminal atoms (excluding \(\mathrm{H}\) )] (4) the number of lone-pair electrons = number of central atom pairs - number of bonding pairs After evaluating items \(2,3,\) and \(4,\) establish the VSEPR notation and determine the molecular shape. Use this method to predict the geometrical shapes of the following: (a) \(\mathrm{PCl}_{5} ;\) (b) \(\mathrm{NH}_{3} ;\) (c) \(\mathrm{ClF}_{3} ;\) (d) \(\mathrm{SO}_{2} ;\) (e) \(\mathrm{ClF}_{4}^{-}\); (f) \(\mathrm{PCl}_{4}^{+}\). Justify each of the steps in the strategy, and explain why it yields the same results as the VSEPR method based on Lewis structures. How does the strategy deal with multiple bonds?

Short answer

The predicted geometrical shapes are: \( \mathrm{PCl}_{5} \) - Trigonal Bipyramidal; \( \mathrm{NH}_{3} \) - Trigonal Pyramidal; \( \mathrm{ClF}_{3} \) - T-shaped; \( \mathrm{SO}_{2} \) - Bent (V-shaped); \( \mathrm{ClF}_{4}^{-} \) - Square Planar; \( \mathrm{PCl}_{4}^{+}\) - Tetrahedral. The strategy works because it counts regions of electron density similar to the VSEPR theory. Multiple bonds are treated as a single electron pair, retaining a simplified perspective of electron density.

Step-by-step solution

Calculation for PCl5

Use the given formulas to calculate the number of total electron pairs, bonding electron pairs, electron pairs around the central atom, and lone-pair electrons. For \(PCl_5\), the number of valence electrons on P is 5 and Cl contributes 5 electrons, so total electron pairs = (5 + (5*7))/2 = 20. The number of atoms is 6, so bonding pairs = 6-1 = 5. Therefore, there are no lone pair electrons. The shape is determined by 5 regions of electron density which implies in a trigonal bipyramidal shape.

Calculation for NH3

Repeat the process with \(NH_3\). Total pairs = (5 + (3*1))/2 = 4, bonding pairs = 4 - 1 = 3. Thus, there is one lone pair electron. This molecule has 4 electron density regions, yielding a tetrahedral electronic geometry, however due to the presence of lone pair electrons, molecular geometry is trigonal pyramidal.

Calculation for the Remaining Molecules/Ions

Repeat the process for the remaining molecules/ions \(\mathrm{ClF}_{3}\), \(\mathrm{SO}_{2}\), \(\mathrm{ClF}_{4}^{-}\), and \(\mathrm{PCl}_{4}^{+}\) by substituting the appropriate number of valence electrons and atoms into the formulas.

Comparison with Lewis structures

Compare the result obtained through this method with that obtained from Lewis Structure to confirm its validity. For example, both NH3 and SO2, with calculated lone pair electrons, will have trigonal pyramidal and V-shape (or bent) geometry, respectively, which corresponds to the Lewis structures.

Dealing with multiple bonds

In a molecule with a multiple bond, both the actual bond and implied bond pairs are considered to be a single region by both this strategy and VSEPR. Hence, the molecular geometry of a molecule such as SO2 with multiple bonds (double bonds in this case), is correctly predicted to be V-shaped.

Key concepts

Lewis Structures

Lewis structures play a key role in the prediction of molecular geometry using VSEPR theory. These diagrams serve as visual representations of molecules, illustrating how atoms are bonded and where the lone pair electrons reside.
The Lewis structure consists of atomic symbols, dots representing electrons, and lines for the bonds between atoms. These structures are crucial because they help us determine the arrangement of electron pairs around the central atom. This is essential for predicting the molecular geometry according to VSEPR.
Alternate methods that do not require Lewis structures still derive their calculations from concepts developed through Lewis structures. Understanding them can help students visualize bonding and lone pair placement, providing a foundation for more complex geometric analysis.

Electron Pairs

Electron pairs are at the heart of VSEPR theory. These pairs include both bonding pairs, which are shared between atoms in a bond, and lone pairs, which are unshared electrons located on a single atom.
In VSEPR theory, it’s important to recognize how these electron pairs are positioned around a central atom, as they dictate the three-dimensional shape of the molecule. Electron pairs repel each other and tend to arrange themselves as far apart as possible. This minimizes repulsion and leads to the molecule adopting a particular shape.
Calculating the total number of electron pairs involves dividing the sum of valence electrons and adjusted electrons for ionic charges by 2. This number helps predict the overall arrangement of the molecule, offering insights into its geometry.

Molecular Geometry

Molecular geometry refers to the specific three-dimensional arrangement of atoms around a central atom. In VSEPR theory, it is deduced from the number and type of electron pairs surrounding the central atom.
This geometry is important because it influences the properties and reactions of the molecule. For instance, a molecule like water ( H_2O) is bent due to the presence of lone pair electrons, which differ from the linear structure found in a molecule like carbon dioxide ( CO_2).
By understanding molecular geometry, chemists can predict molecular behavior and interactions. VSEPR theory provides a clear and systematic approach by using the electron pair count to define geometric shapes such as linear, trigonal planar, tetrahedral, and more.

Bonding Pairs

Bonding pairs of electrons are shared between atoms and form covalent bonds. They contribute significantly to determining the molecular geometry in VSEPR theory.
In a molecule, each bond, whether single, double, or triple, is treated as a single region of electron density. The arrangement of these regions determines the 3D structure of the molecule.
When predicting the molecular geometry, it’s important to account for both the number of bonding pairs and the presence of lone pairs, as these can alter the shape. Recognizing the balance between bonding and non-bonding pairs is crucial for understanding the resulting geometry. VSEPR provides the means to predict how these pairs spatially organize to form the overall shape of a molecule.