Question

Draw all possible diastereoisomers of \(\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]^{-}\). Which can exist as a pair of enantiomers?

Short answer

Two diastereoisomers exist: cis (which is chiral and has enantiomers) and trans (achiral).

Step-by-step solution

Determine Structure and Ligands

The complex \([\mathrm{Cr}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{2}\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\right]^{-}\) consists of two oxalate ligands and two water molecules bound to a chromium center.

Understand Ligand Orientation

Oxalate (\(\mathrm{C}_{2}\mathrm{O}_{4}^{2-}\)) is a bidentate ligand, meaning it can attach at two points to the metal. The water molecules are monodentate coordinating through oxygen.

Sketch Possible Configurations

Consider the octahedral geometry. The oxalate ligands can be in the cis (adjacent) or trans (opposite) positions, while water molecules can also be placed cis or trans accordingly.

Identify Diastereoisomers

For the complex, possible configurations include cis (where both oxalate ligands are adjacent) and trans (where they are opposite each other) arrangements.

Determine Enantiomerism

Only the cis configuration can have chiral centers and exist as enantiomers, because the trans configuration results in a plane of symmetry, making it achiral.

Key concepts

Coordination Chemistry

Coordination chemistry deals with the study of coordination compounds, which are substances consisting of a central metal atom or ion bonded to surrounding molecules or ions, known as ligands. In our complex,

• the chromium (Cr) acts as the central metal ion.
• Oxalate (\(\mathrm{C}_{2}\mathrm{O}_{4}^{2-}\)) ligands are bidentate, meaning they bind through two donor atoms.
• Water molecules are monodentate ligands, coordinating through a single oxygen atom.

This study is crucial for understanding how different arrangements and types of ligands can influence the properties and reactivity of the metal complex.

Chiral Complexes

Chirality in complexes refers to the property where a molecule cannot be superimposed on its mirror image, much like your left and right hands are non-superimposable. In coordination chemistry, certain geometries and arrangements of ligands around the metal center can result in chiral complexes. For example, the cis-arrangement of oxalate ligands in our hexacoordinate complex can form chiral centers. This means:

• It can exist in left-handed and right-handed forms, known as enantiomers.
• The trans configuration does not achieve chirality due to its symmetry.

In general, only the cis-formation can potentially form chiral complexes because it has the necessary asymmetry.

Octahedral Geometry

Octahedral geometry is a common shape for coordination complexes where six ligand atoms are symmetrically arranged around a central atom, usually at the corners of an octahedron.For the complex \([\mathrm{Cr}(\mathrm{C}_{2}\mathrm{O}_{4})_{2}(\mathrm{H}_{2}\mathrm{O})_{2}]^{-}\), this shape facilitates different configurations:

• In the cis configuration, both bidentate ligands are adjacent, and two monodentate water molecules are also next to each other.
• In the trans configuration, each bidentate ligand is opposite its pair, creating a perfect symmetry in the horizontal plane.

This geometric arrangement allows for the formation of certain isomers, particularly diastereoisomers, which are not mirror images but have different spatial arrangements.