Question

Sketch the chiral isomers of \(\left[\mathrm{CrCl}_{2}(\mathrm{en})_{2}\right]^{+}\). Is there a non-chiral isomer of this complex?

Short answer

Two chiral isomers can be sketched, by placing the Cl ligands trans to each other and arranging the ethylenediamine ligands in a propeller shape; one isomer is the mirror image of the other. There is no non-chiral (meso) isomer for this complex.

Step-by-step solution

Understand the molecular composition

Determine the structure of \(\left[\mathrm{CrCl}_{2}(\mathrm{en})_{2}\right]^{+}\). The complex consists of a chromium center (Cr) with two ethylenediamine (en) ligands, which are bidentate, and two chlorine (Cl) ligands.

Draw the first isomer

Sketch the first chiral isomer with the ethylenediamine ligands creating a propeller shape. Both chlorine ligands should be positioned to either the front or the back of the propeller but on opposite sides of the central metal atom.

Draw the second isomer

Draw the enantiomer of the first isomer. This is done by creating a mirror image of the first isomer, which cannot be superimposed onto the original. The chlorines should be trans to each other, just as in the first one.

Consider the possibility of a non-chiral isomer

To determine if there is a non-chiral (meso) isomer, explore the spatial arrangement where both ethylenediamine ligands are in the same plane. However, because the complex has only two bidentate ligands and two monodentate ligands, there is no plane of symmetry. Thus, there are no non-chiral isomers for this complex.

Key concepts

Enantiomers

Enantiomers are a pair of molecules that are mirror images of each other, much like left and right hands. These molecules contain at least one chiral center—an atom, typically a carbon, bonded to four different groups. In coordination chemistry, this chiral center is usually the central metal atom surrounded by ligands in a specific manner. The importance of enantiomers in a chemical context is significant because they can exhibit markedly different behaviors in biological systems, despite having the same molecular formula. Their different spatial arrangements can lead to different interactions with enzymes, receptors, or other chiral molecules.

In the given exercise involving the coordination complex \(\left[\mathrm{CrCl}_{2}(\mathrm{en})_{2}\right]^{+}\), enantiomers would be the two forms of the complex that are non-superimposable mirror images. The presence of the bidentate ethylenediamine ligands (en) adds to the complexity as they introduce multiple points of attachment, further enabling the formation of chiral structures. It's crucial for students to visualize the three-dimensional arrangement of the ligands around the chromium center to correctly identify the enantiomers.

Coordination Complex

A coordination complex consists of a central atom or ion, which is usually metallic and is called the coordination center, surrounded by a set of molecules or ions known as ligands. These ligands can be neutral or negatively charged and are bonded to the central atom via coordinate covalent bonds. The ligands donate a pair of electrons to the metal center.

In our example, the coordination complex \(\left[\mathrm{CrCl}_{2}(\mathrm{en})_{2}\right]^{+}\) involves a chromium metal as the central ion, which forms bonds with two chloride ions and two molecules of ethylenediamine. Such coordination compounds are ubiquitous in biochemistry, geology, and technology. In teaching these concepts, it's highly beneficial to emphasize the critical roles these complexes play in various processes, from the oxygen-transporting function of hemoglobin to catalysts in industrial syntheses.

Bidentate Ligands

Bidentate ligands are a type of chelating ligands that have two atoms capable of binding to a central metal atom or ion. These atoms are typically nitrogen, oxygen, or sulfur. 'Bi-', meaning two, and '-dentate', meaning teeth, suggest that these ligands grab onto the metal like two teeth. The 'bite' of such ligands can bridge two coordination sites on a single metal, creating rings in the molecular structure known as chelate rings. This 'biting' action stabilizes the complex significantly, a fact known as the chelate effect.

In the instance of \(\left[\mathrm{CrCl}_{2}(\mathrm{en})_{2}\right]^{+}\), ethylenediamine acts as the bidentate ligand. Each ethylenediamine molecule forms two bonds with chromium thereby creating a five-membered ring, which is a favored size in coordination chemistry. The use of bidentate ligands can introduce chirality into a complex due to the fixed spatial arrangement that they impose on the metal center.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. It is defined by the distances and angles between the nuclei of the atoms. The geometry is influenced by the electronic repulsions between regions of electron density, such as bonds and lone pairs of electrons. In coordination chemistry, molecular geometry plays a pivotal role in dictating the properties and reactivity of complexes.

For the complex \(\left[\mathrm{CrCl}_{2}(\mathrm{en})_{2}\right]^{+}\), visualizing the molecular geometry helps to predict the potential isomers. Because each ethylenediamine is bidentate, the most probable arrangement is an octahedral geometry where the chromium ion is at the center of an octahedron. The geometry is crucial in facilitating the understanding of how the ligands can be arranged spatially to produce different isomers of the same molecular formula.

Optical Isomerism

Optical isomerism is a form of stereoisomerism where isomers, known as optical isomers, have the same molecular formula and bond structure but differ in the orientation of atoms in space. This difference results in the isomers' ability to rotate plane-polarized light in different directions—one isomer rotates the light clockwise and the other counterclockwise, which is referred to as dextrorotatory and levorotatory, respectively.

In the case of \(\left[\mathrm{CrCl}_{2}(\mathrm{en})_{2}\right]^{+}\), this optical isomerism arises from the chiral nature of the complex. This chiral complex will have two non-superimposable isomers, which are mirror images of each other. No meso form exists for this complex because a meso isomer requires the presence of a symmetry element, like a plane of symmetry, which this complex lacks due to the arrangement of its ligands. Optical isomerism is particularly important in the pharmaceutical industry as the different isomers can lead to different biological activities.