The number of optical isomers possible for [Cr(C\(_2\)O\(_4\))\(_3\)]\(^{3-}\) is _________.
Show Hint
For octahedral complexes, remember the key types that show optical isomerism: [M(AA)\(_3\)] (like this problem), cis-[M(AA)\(_2\)X\(_2\)], and fac-[M(A)\(_3\)B\(_3\)]. The trans-isomers of [M(AA)\(_2\)X\(_2\)] are typically achiral as they possess a plane of symmetry.
Step 1: Understanding the Question:
We need to determine the number of optical isomers for the coordination complex
tris(oxalato)chromate(III). Optical isomers are non-superimposable mirror images of each other, also known as enantiomers. Step 2: Analyzing the Complex:
- Central Metal Ion: Cr\(^{3+}\). The coordination number is typically 6.
- Ligand: Oxalate, C\(_2\)O\(_4\)\(^{2-}\) (often abbreviated as 'ox'), is a bidentate chelating ligand. Since there are three oxalate ligands, the coordination number is \(3 \times 2 = 6\).
- Geometry: A coordination number of 6 with three bidentate ligands results in an octahedral geometry. The complex type is [M(AA)\(_3\)], where AA is a symmetric bidentate ligand. Step 3: Checking for Chirality:
A molecule is chiral (and thus has optical isomers) if it is non-superimposable on its mirror image. This is typically because it lacks a plane of symmetry and a center of inversion.
The [M(AA)\(_3\)] structure, like [Cr(ox)\(_3\)]\(^{3-}\), has a shape analogous to a three-bladed propeller. It can exist in two forms: a "left-handed" propeller (\(\Lambda\)-isomer) and a "right-handed" propeller (\(\Delta\)-isomer). These two forms are mirror images of each other and cannot be superimposed. They are enantiomers.
Therefore, the complex is chiral and exists as a pair of optical isomers. Step 4: Final Answer:
The number of possible optical isomers for [Cr(C\(_2\)O\(_4\))\(_3\)]\(^{3-}\) is 2.
