Question

Predict the geometries of the following species: (a) ${\mathrm{AlCl}}_3$ (b) ${\mathrm{ZnCl}}_2$ (c) ${\mathrm{HgBr}}_2$ (d) ${\mathrm{N}}_2\mathrm{O}$ (arrangement of atoms is NNO).

Short answer

(a) Trigonal planar, (b) Linear, (c) Linear, (d) Linear (NNO arrangement).

Step-by-step solution

Identify the central atom

For each molecule, identify the central atom, which is usually the least electronegative or the atom with the highest valency. In ${\mathrm{AlCl}}_3$, $\mathrm{Al}$ is the central atom; in ${\mathrm{ZnCl}}_2$ and ${\mathrm{HgBr}}_2$, $\mathrm{Zn}$ and $\mathrm{Hg}$ are the central atoms, respectively; and in ${\mathrm{N}}_2\mathrm{O}$, both nitrogen atoms are involved, but the arrangement is NNO.

Determine the steric number

Calculate the steric number, which is the sum of bonded atoms and lone pairs on the central atom. For ${\mathrm{AlCl}}_3$, the central atom has three bonded atoms (steric number = 3). For ${\mathrm{ZnCl}}_2$ and ${\mathrm{HgBr}}_2$, the central atoms have two bonded atoms and no lone pairs (steric number = 2). For ${\mathrm{N}}_2\mathrm{O}$, consider the arrangement as linear with respect to the nitrogen atoms.

Apply VSEPR theory

Use the Valence Shell Electron Pair Repulsion (VSEPR) theory to predict the shapes based on the steric number. With a steric number of 3, ${\mathrm{AlCl}}_3$ has a trigonal planar shape. With steric numbers of 2, both ${\mathrm{ZnCl}}_2$ and ${\mathrm{HgBr}}_2$ are linear. For ${\mathrm{N}}_2\mathrm{O}$, given the NNO arrangement, the molecule is linear.

Confirm molecule structure using knowledge of exceptions

Check if there are any known exceptions or structural peculiarities that affect the geometries. ${\mathrm{AlCl}}_3$ is typically planar due to potential dimerization under some conditions, but monomer ${\mathrm{AlCl}}_3$ is still categorically trigonal planar. ${\mathrm{ZnCl}}_2$ and ${\mathrm{HgBr}}_2$ do not have common exceptions and are linear. The linearity of ${\mathrm{N}}_2\mathrm{O}$ is consistent with non-equivalent nitrogen involvement.

Key concepts

VSEPR theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is critical for determining molecular geometry. It is based on the idea that electron pairs around a central atom will try to position themselves as far apart as possible to minimize the repulsion between them. This theory enables us to predict the shape of a molecule. The shape depends on the number of bonding pairs and lone pairs of electrons surrounding the central atom.
For example:

• If there are two regions of electron density (like in the case of ${\mathrm{ZnCl}}_2$ and ${\mathrm{HgBr}}_2$), the geometry is linear.
• With three regions, like in ${\mathrm{AlCl}}_3$, the shape is trigonal planar.
• The linear form is also applicable to linear molecules such as ${\mathrm{N}}_2\mathrm{O}$, despite its more complex central atom situation.

Understanding VSEPR theory is essential for predicting and explaining molecular shapes based on electron pair interactions.

Steric Number

The steric number is a fundamental concept in molecular geometry. It helps us determine the shape of a molecule by summarizing how many atoms are bonded to a central atom and how many lone pairs are present. The steric number is simply the sum of:

• The number of atoms bonded to the central atom.
• Plus the number of lone pairs on the central atom.

For practical application, consider ${\mathrm{AlCl}}_3$ with a steric number of 3 (three bonded atoms and no lone pairs), leading to a trigonal planar shape. Similarly, both ${\mathrm{ZnCl}}_2$ and ${\mathrm{HgBr}}_2$ have a steric number of 2, resulting in a linear molecular shape.
By calculating the steric number, we get crucial insight into the molecular geometry and can predict the molecular shape according to VSEPR theory.

Central Atom

A central atom acts as the anchor point in a molecule. It is typically the least electronegative atom or the atom with the highest valency. The choice of a central atom significantly influences the structure of the molecule. For molecules given in the exercise:

• ${\mathrm{AlCl}}_3$ features aluminum $\mathrm{Al}$ as the central atom because of its capability to bond with three chlorine atoms, forming a stable structure.
• In ${\mathrm{ZnCl}}_2$ and ${\mathrm{HgBr}}_2$, $\mathrm{Zn}$ and $\mathrm{Hg}$ serve as central atoms, respectively, each linking with two surrounding atoms to stabilize the molecular form.
• For ${\mathrm{N}}_2\mathrm{O}$, the arrangement 'NNO' shows nitrogen's role, allowing this linear molecule to maintain its atomic sequence amidst the presence of multiple bonds.

The identification of the central atom is the first step in determining a molecule's geometry. It influences how other atoms bond to it, affecting the overall molecular shape.