Question

Predict the geometrical structure of each of the following molecules or ions: (a) \(\mathrm{NO}_{2}^{-}\) (b) \(\mathrm{PH}_{3}\) (c) PFs (d) \(\mathrm{PCl}_{4}^{+}\)

Short answer

(a) Bent, (b) Trigonal pyramidal, (c) Trigonal bipyramidal, (d) Tetrahedral.

Step-by-step solution

Determine the Central Atom and Count Valence Electrons

For each molecule, identify the central atom, typically the least electronegative. Count the total number of valence electrons from the central atom and surrounding atoms/ions. Consider any charges as well. For example, in \(\mathrm{NO}_2^-\), nitrogen is the central atom, with one extra electron for the negative charge.

Apply the VSEPR Theory

Use the valence shell electron pair repulsion (VSEPR) theory to predict the arrangement of electron pairs around the central atom, which helps determine the geometry. Each molecule might have different steric numbers. Lone pairs and bonds are treated similarly under this theory.

Predict the Molecule Geometry

Based on the electron pair arrangement, predict the geometry of each molecule. For instance:- For \(\mathrm{NO}_2^-\), with 3 electron regions (2 bonds and 1 lone pair), the shape is bent.- For \(\mathrm{PH}_3\), the geometry is trigonal pyramidal due to 3 bonds and 1 lone pair.- \(\mathrm{PF}_5\) has 5 bonds and no lone pairs, making it trigonal bipyramidal.- \(\mathrm{PCl}_4^+\) with 4 bonds, should be tetrahedral.

Key concepts

VSEPR Theory

The VSEPR Theory, which stands for Valence Shell Electron Pair Repulsion, is a simple model useful for predicting the geometry of molecular structures. It works on the principle that electron pairs surrounding a central atom will arrange themselves to be as far apart as possible. This is because electron pairs, whether they are in bonds or are lone pairs, repel each other.

• This theory helps determine the spatial arrangement of the atoms in a molecule, which defines its shape.
• By considering the number of bonding and non-bonding electron pairs, one can predict if a molecule will be linear, bent, tetrahedral, trigonal planar, or have another shape.
• A key part of VSEPR is the steric number, which is the sum of bonded atoms and lone electron pairs surrounding the central atom.

For example, in the molecule \(\mathrm{NO}_2^-\), it has a steric number of 3, with two bonds and one lone pair. Therefore, its shape is predicted to be bent, as lone pairs push the bonded atoms closer together.

Central Atom

The central atom in a molecule is typically the one with the least electronegativity, and around which other atoms are arranged. Identifying the central atom is crucial as it is the focus of the geometry prediction.

• The central atom determines the base structure around which the molecule's bonds and lone pairs will orient.
• In the process of determining molecular geometry, once the central atom is selected, the next step involves totaling its valence electrons.
• For complex ions or molecules, the central atom can sometimes be the one that is unique or appears singularly.

For example, in \(\mathrm{NO}_2^-\), nitrogen acts as the central atom.

Valence Electrons

Valence electrons are the electrons located in the outermost electron shell of an atom. They play a pivotal role in chemical bonding, as these are the electrons involved in forming bonds.

• Counting valence electrons correctly is essential in predicting molecular geometry, knowing the number of electrons available for bonding and lone pairs.
• Valence electrons for each atom are the electrons that are considered while calculating the steric number for VSEPR analysis.
• When examining charged ions, such as \(-1\) ions like \(\mathrm{NO}_2^-\), the overall charge will add or subtract one or more electrons from the total count of valence electrons. This impacts the shape and geometry of the molecule.

In the case of \(-1\) ion \(\mathrm{NO}_2^-\), there is one extra valence electron contributed due to its negative charge, resulting in a stronger push on the structure.