Which of the following compound shows optical isomerism?

\([Cr(C_2O_4)_3]^{3-}\)

The correct answer is option 3. \([Cr(C_2O_4)_3]^{3-}\).

Let us delve into the optical isomerism exhibited by the complex \([Cr(C_2O_4)_3]^{3-}\).

Complex: \([Cr(C_2O_4)_3]^{3-}\)

1. Structure:

The complex is formed by chromium (Cr) in the +3 oxidation state, coordinated with three bidentate oxalate (\(C_2O_4^{2-}\)) ligands.

The oxalate ligand (\(C_2O_4^{2-}\)) is a chelating ligand with two oxygen atoms capable of coordinating to the metal center.

2. Coordination Geometry:

The complex is octahedral, as chromium can form six-coordinate bonds. Each oxalate ligand forms two bonds with the chromium center, resulting in a total of six coordination bonds.

3. Chirality:

Chirality arises due to the presence of three identical bidentate ligands arranged in an octahedral coordination sphere. The arrangement of the ligands can lead to optical isomerism, where the complex and its mirror image are non-superimposable.

4. Optical Isomerism:

Each oxalate ligand can bind to the chromium center in two different ways, resulting in enantiomeric forms. The two possible arrangements of the ligands are mirror images that cannot be superimposed, making the complex optically active.

5. Representation:

The optical isomers can be represented as "right-handed" (D-enantiomer) and "left-handed" (L-enantiomer) configurations.

6. Center of Symmetry:

In the absence of a center of symmetry within the complex, optical isomerism is observed.

In summary, the complex \([Cr(C_2O_4)_3]^{3-}\) exhibits optical isomerism due to the chiral arrangement of three bidentate oxalate ligands in an octahedral coordination environment around the chromium center. Each enantiomer represents a different spatial arrangement of the ligands, and they are non-superimposable mirror images.