Question

Determine if each of the following metal complexes is chiral and therefore has an optical isomer: (a) tetrahedral \(\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Cl}_{2}\right],(\mathbf{b})\) octahedral trans-[Ru(bipy) \()_{2} \mathrm{Cl}_{2} ],(\mathbf{c})\) octahedral cis-[Ru(bipy) \(_{2} \mathrm{Cl}_{2} ] .\)

Short answer

In summary, the metal complexes have the following chirality: a) Tetrahedral \(\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Cl}_{2}\right]\) is achiral (no optical isomer). b) Octahedral trans-\([\mathrm{Ru}(\mathrm{bipy})_{2} \mathrm{Cl}_{2}]\) is achiral (no optical isomer). c) Octahedral cis-\([\mathrm{Ru}(\mathrm{bipy})_{2} \mathrm{Cl}_{2}]\) is chiral (has an optical isomer).

Step-by-step solution

Understanding chirality

Chirality refers to the property of a molecule where it cannot be superimposed onto its mirror image. A chiral molecule has a non-superimposable mirror image, called an enantiomer. If a molecule has a center of symmetry or any point of symmetry, it is considered achiral.

Analyzing the first complex (a) Tetrahedral [Zn(H2O)2Cl2]

This complex has a tetrahedral geometry due to the coordination of 4 ligands to the central Zn atom. To determine its chirality, let's check for any symmetry elements. In this complex, there are 2 water ligands and 2 chloride ligands. The symmetry elements can be found by imagining a line (axis) connecting the Zn atom to the mid-point of the line connecting the two identical ligands. There are two symmetry elements in this complex, one passing through the two water ligands and the other passing through the two chloride ligands. Since the complex has symmetry elements, it is achiral and does not have an optical isomer.

Analyzing the second complex (b) Octahedral trans-[Ru(bipy)2Cl2]

In this complex, the Ru atom is coordinated to 2 bipy and 2 Cl ligands with an octahedral geometry. The trans-[Ru(bipy)2Cl2] complex has the two Cl ligands positioned opposite (trans) to each other. This conformation leads to the presence of a center of symmetry. Because of this symmetry, the complex is achiral and does not have an optical isomer.

Analyzing the third complex (c) Octahedral cis-[Ru(bipy)2Cl2]

Similar to the second complex, the Ru atom coordinates to 2 bipy and 2 Cl ligands with an octahedral geometry. The only difference is that the Cl ligands are now positioned adjacent (cis) to each other. In this conformation, there is no center of symmetry nor any other symmetry element in the cis-[Ru(bipy)2Cl2] complex. Therefore, this molecule is chiral and has an optical isomer. In summary: a) Tetrahedral [Zn(H2O)2Cl2] is achiral (no optical isomer) b) Octahedral trans-[Ru(bipy)2Cl2] is achiral (no optical isomer) c) Octahedral cis-[Ru(bipy)2Cl2] is chiral (has an optical isomer)

Key concepts

Optical Isomers

Optical isomers, also known as enantiomers, are molecules that are mirror images of each other but cannot be superimposed onto one another. A common analogy to understand optical isomers is comparing them to left and right hands; they are similar yet not identical, as they cannot easily overlap each other perfectly. For a molecule to exhibit optical isomerism and thus be chiral, it must lack a plane of symmetry or any other symmetry element that would make it identical to its mirror image. In the context of the provided exercise, this means assessing whether the complexes have any internal symmetry. For example, in tetrahedral or octahedral complexes, if the arrangement of atoms is such that it prevents superimposability, optical isomers can occur. It's essential to recognize that despite having the same chemical composition, optical isomers can have highly different properties, especially in how they interact with light and biological systems.

Tetrahedral Complex

A tetrahedral complex involves a central metal atom bonded to four ligands arranged at the corners of a tetrahedron. This geometry is particularly common in complexes where the metal center has a coordination number of four. In the exercise example, \([\mathrm{Zn}(\mathrm{H}_{2}\mathrm{O})_{2}\mathrm{Cl}_{2}]\), the zinc ion serves as the central metal atom. Tetrahedral complexes are interesting due to their potential for chirality. Even though many tetrahedral complexes with identical ligands tend to be achiral due to symmetrical distribution, if the ligands are different, the complex can become chiral. However, if there are identical pairs of ligands arranged opposite each other, resulting in the presence of symmetry elements, the complex is likely achiral, as seen in the Zn complex with symmetry elements through water and chloride ligands leading to superimposable images.

Octahedral Complex

An octahedral complex features a central metal atom surrounded by six ligands arranged symmetrically at the vertices of an octahedron. This geometry is common for metals with a coordination number of six. In the context of the exercise, the complexes \([\mathrm{Ru}(\mathrm{bipy})_{2}\mathrm{Cl}_{2}]\) exhibit octahedral geometry. Depending on the arrangement of ligands, these complexes can display different forms. For instance, in the trans form, symmetry can lead to achirality, as seen in trans-[Ru(bipy)2Cl2] where chloride ions are opposite, providing a center of symmetry. Conversely, in the cis form, where similar ligands are adjacent, there is typically no center of symmetry, allowing for chirality and the existence of optical isomers. Understanding these configurations aids in predicting the properties and potential isomerism of octahedral complexes.

Symmetry Elements

Symmetry elements are crucial in determining the chirality of a molecule. These elements include points, lines, or planes that describe the symmetric features of a molecule. Some key symmetry elements to consider include:

• Center of symmetry: A point within a molecule through which identical components are inverted equidistantly.
• Plane of symmetry: A plane dividing the molecule into two mirror-image halves.
• Axis of symmetry: An imaginary line where a molecule can rotate to appear unchanged.

A molecule possessing any of these elements is usually achiral since superimposable mirror images can be found. Evaluating these symmetry elements in the metal complexes discussed, such as trans-[Ru(bipy)2Cl2], can lead to identifying achiral complexes. Conversely, the absence of identifying symmetry elements, as in the case of cis-[Ru(bipy)2Cl2], can indicate potential chirality due to the irregular arrangement of ligands influencing spatial orientation and molecular behavior.