Question

Just as \(\mathrm{AlCl}_{3}\) forms dimers (Section 2.11), in the \(\left[\mathrm{Bi}_{2} \mathrm{Cl}_{4}\right]^{2-}\) ion two of the \(\mathrm{Cl}\) atoms form "bridges" between the two \(\mathrm{Bi}\) atoms. Propose a structure for the \(\left[\mathrm{Bi}_{2} \mathrm{Cl}_{4}\right]^{2-}\) ion.

Short answer

The \(\left[\mathrm{Bi}_{2} \mathrm{Cl}_{4}\right]^{2-}\) ion has a structure with a central \(\mathrm{Bi}_2\) core. Two \(\mathrm{Cl}\) atoms serve as bridges between \(\mathrm{Bi}\) atoms, and each \(\mathrm{Bi}\) atom also binds to a single terminal \(\mathrm{Cl}\) atom, giving the ion a \(2-\) charge.

Step-by-step solution

Understand the concept of dimerization

Dimerization occurs when two identical units (monomers) combine to form a dimer. In the case of \(\mathrm{AlCl}_{3}\), it forms a dimer \(\mathrm{Al}_2\mathrm{Cl}_6\) in which two aluminum atoms are bridged by two chloride ions. The same principle can be applied to the \(\left[\mathrm{Bi}_{2} \mathrm{Cl}_{4}\right]^{2-}\) ion.

Determine the covalency of \(\mathrm{Bi}\) atoms

Bi has a valency of 3, meaning it can form three covalent bonds. Since we have a \(2-\) ion, overall, there would be two extra electrons beyond what is needed for neutral bonding.

Arrange the \(\mathrm{Cl}\) atoms to satisfy the valency rules

In the \(\left[\mathrm{Bi}_{2} \mathrm{Cl}_{4}\right]^{2-}\) ion, two \(\mathrm{Cl}\) atoms will act as bridging ligands between the \(\mathrm{Bi}\) atoms, and the other two will be terminal ligands, one for each \(\mathrm{Bi}\) atom, to fulfill the valency of bismuth.

Complete the structure

The proposed structure will have a central \(\mathrm{Bi}_2\) core with two bridging \(\mathrm{Cl}\) atoms and one terminal \(\mathrm{Cl}\) atom on each \(\mathrm{Bi}\). This arrangement satisfies all the valencies, with two extra electrons contributing to a \(2-\) charge on the ion.

Key concepts

Chemical Bonding

Chemical bonding is the force that holds atoms together in molecules and compounds. It involves the attraction between the positive nucleus of one atom and the negative electrons of another. This attraction can create different types of bonds, such as ionic, covalent, and metallic bonds.

In the context of the \(\left[\mathrm{Bi}_{2} \mathrm{Cl}_{4}\right]^{2-}\) ion, we are particularly interested in covalent bonding. Covalent bonds form when two atoms share one or more pairs of electrons to achieve stability. These bonds are strong and directional, meaning they align specific atoms in particular orientations.

When it comes to dimerization, such as in the formation of the \(\left[\mathrm{Bi}_{2} \mathrm{Cl}_{4}\right]^{2-}\) ion, two molecules (often called monomers) link together, usually via covalent bonds. In our example, bridging \(\mathrm{Cl}\) atoms create a link between the two \(\mathrm{Bi}\) atoms, leading to a unique structural arrangement called a 'dimer'.

Valency and Covalent Bonds

Valency is a measure of an atom's ability to bond with other atoms. It is determined by the number of electrons an atom needs to lose, gain, or share to fill its outer electron shell and achieve a noble gas configuration.

In covalent bonding, atoms share electrons to fulfill their valency requirements. Each pair of shared electrons constitutes one bond, and the number of covalent bonds an atom can form is equal to its valency. For instance, bismuth (\(\mathrm{Bi}\)) has a valency of 3, meaning it can share three pairs of electrons, forming three covalent bonds.

Dimerization can be better understood by looking at the valencies involved. In the \(\left[\mathrm{Bi}_{2} \mathrm{Cl}_{4}\right]^{2-}\) ion, the two extra electrons contribute to a \(2-\) charge by adding more valence electrons that need to be accounted for in bonding. Thus, the \(\mathrm{Bi}\) atoms exceed their usual valency to accommodate the additional electrons, resulting in a stable dimer structure.

Inorganic Chemistry

Inorganic chemistry is the study of the properties and behavior of inorganic compounds, which generally do not contain carbon. This branch of chemistry covers a broad range of substances, including metals, minerals, and organometallics, and encompasses various reactions and processes used to form these compounds.

The dimerization process we explore with the \(\left[\mathrm{Bi}_{2} \mathrm{Cl}_{4}\right]^{2-}\) ion is a key example of inorganic chemistry because it deals with metal ions and their interactions with halogen atoms. Understanding the principles of inorganic chemistry, such as the periodic table, electronegativity, and coordination chemistry, allows students to predict and rationalize the structure of complex ions and compounds.

In our case, recognizing the role of metal ion valency, the behavior of chloride ions (\(\mathrm{Cl}\)) as both bridging and terminal ligands, and the general rules of charge balance are crucial for constructing the correct geometry of the dimer. These fundamentals are not just important for solving textbook exercises, but they are also foundational for real-world applications, such as designing new materials or understanding biological processes involving metal ions.