Problem 46 - Chemistry: The Central Science in SI Units, Global Edition

Question

Determine if each of the following metal complexes is chiral and therefore has an optical isomer: (a) square planar \(\left[\mathrm{Pd}(\mathrm{en})(\mathrm{CN})_{2}\right],(\mathbf{b})\) octahedral \(\left[\mathrm{Ni (\mathrm{en})\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+},\) (c) octahedral cis-[V(en) \(\left._{2} \mathrm{ClBr}\right]\).

Step-by-Step Solution

Answer

The square planar complex \([\mathrm{Pd}(\mathrm{en})(\mathrm{CN})_{2}]\) and the octahedral complex \([\mathrm{Ni}(\mathrm{en})(\mathrm{NH}_{3})_{4}]^{2+}\) are achiral due to the presence of planes of symmetry. In contrast, the octahedral complex cis-\([\mathrm{V}(\mathrm{en})_{2} \mathrm{ClBr}]\) is chiral and has an optical isomer, as it lacks any plane of symmetry.

Step 1: (Step 1: Analyzing Complex (a))

The first complex is a square planar complex, \([\mathrm{Pd}(\mathrm{en})(\mathrm{CN})_{2}]\). Here, the coordination geometry of the Pd metal center is square planar. The ligands are one ethylenediamine (en) molecule and two cyanide (CN) ions. To determine if it's chiral or not, we need to check if there's a plane of symmetry present in this complex.

Step 2: (Step 2: Assessing Symmetry in Complex (a))

In this complex, both cyanide ions are in trans positions, and ethylenediamine ligand spans opposite corners of the square. Therefore, there are two planes of symmetry. This means that this metal complex is achiral.

Step 3: (Step 3: Analyzing Complex (b))

The second complex is an octahedral complex, \([\mathrm{Ni}(\mathrm{en})(\mathrm{NH}_{3})_{4}]^{2+}\). The coordination geometry of the Ni metal center is octahedral. The ligands are one ethylenediamine (en) molecule and four ammonia (NH\(_3\)) molecules. To determine if it's chiral or not, we need to check if there's a plane of symmetry present in this complex.

Step 4: (Step 4: Assessing Symmetry in Complex (b))

In this complex, the four ammonia molecules occupy equatorial positions, and the ethylenediamine ligand spans the axial positions. Therefore, there is a plane of symmetry along the plane containing the four ammonia molecules. This means that this metal complex is achiral.

Step 5: (Step 5: Analyzing Complex (c))

The third complex is an octahedral complex, cis-\([\mathrm{V}(\mathrm{en})_{2} \mathrm{ClBr}]\). The coordination geometry of the V metal center is octahedral. The ligands are two ethylenediamine (en) molecules, one chloride (Cl) ion, and one bromide (Br) ion. To determine if it's chiral or not, we need to check if there's a plane of symmetry present in this complex.

Step 6: (Step 6: Assessing Symmetry in Complex (c))

In this cis complex, the ethylenediamine ligands lie next to each other, while the chloride and bromide ions occupy trans dihalide positions. There is no plane of symmetry in this complex. This means that this metal complex is chiral and has an optical isomer. In conclusion, among the given metal complexes, only complex (c) is chiral and has an optical isomer, while complexes (a) and (b) are achiral.

Key Concepts

Coordination Chemistry

Coordination chemistry is the branch of chemistry that focusses on the structures, properties, and behaviors of coordination compounds. These compounds consist of a central metal ion surrounded by molecules or ions known as ligands. This fascinating field identifies how ligands coordinate, or bind, to the metal center, thus forming complex structures.

Key to understanding coordination chemistry is the concept of coordination number, which defines the number of ligand donor atoms that are bonded to the central metal ion. The bonding between ligands and central metal typically involves coordinate covalent bonds, where ligands donate a pair of electrons to the metal.

The geometry of coordination compounds is essential. It can significantly affect their chemical properties and behavior. Various geometries like square planar and octahedral are common, significantly influencing the chirality and optical characteristics of these complexes.

Square Planar Complexes

Square planar complexes are characterized by a geometric arrangement where four ligands occupy the corners of a square plane around the central metal atom. This type of complex is typical for transition metals such as Palladium (Pd), Platinum (Pt), and Nickel (Ni).

This geometry often leads to certain symmetry elements like mirror planes, affecting whether these complexes can exhibit chirality. In a square planar arrangement, it's crucial to evaluate the positioning of the ligands. Complexes with identical ligands opposite each other can result in symmetry that prevents chirality.

• Square planar complexes often have two planes of symmetry.
• They frequently lack chirality unless the ligands are arranged in a manner disrupting symmetry.

Octahedral Complexes

Octahedral complexes are a common geometry in coordination compounds, where six ligands are symmetrically arranged around the central metal ion. This arrangement forms an octahedron, a shape with eight faces.

These complexes can be mono- or polydentate, meaning the ligands may attach through one or multiple sites. Ligand arrangement distinguishes different variations like cis and trans, influencing the complex's properties, including chirality.

• Cis isomers have similar ligands adjacent, altering symmetry and chirality.
• Trans isomers have opposite ligands, generally leading to higher symmetry and less likelihood of chirality.

The presence of planes of symmetry in octahedral complexes often determines chirality, with a lack of these planes typically resulting in chiral complexes.

Optical Isomerism

Optical isomerism arises when a molecule has non-superimposable mirror images, known as enantiomers. This form of isomerism is integral to molecules exhibiting chirality and is significant in coordination chemistry.

In coordination complexes, the spatial arrangement of ligands around a metal center can give rise to chiral centers, leading to optical isomers. These isomers exhibit different interactions with plane-polarized light, resulting in significant consequences in chemical reactions and properties.

• Chiral complexes will rotate plane-polarized light in different directions.
• The presence of optical isomers can lead to differing biological activity.

Symmetry in Molecules

Symmetry in molecules is a key concept influencing many properties, including chirality and optical activity. In coordination chemistry, the presence or absence of symmetry elements like planes and centers of symmetry impacts a complex's chirality.

Assessing symmetry involves examining features like:

• Mirror planes: Present in symmetric complexes, often preventing chirality.
• Centers of symmetry: A point equidistant from matching parts of the molecule, reducing chirality potential.

Different molecular symmetries can transform otherwise similar chemical structures, leading to differences in their chemical behavior and function, especially in chiral and achiral complexes.