Q.Out of the following two coordination entities which is chiral (optically active)?

Concept: Geometrical isomerism and chirality in octahedral complexes — a complex is chiral if it lacks any improper axis of rotation ($S_n$), i.e., it is non-superimposable on its mirror image.

Reasoning:

1. Both complexes are octahedral with two identical monodentate ligands (Cl) and two identical bidentate ligands (oxalate, ox). The key difference is the relative positions of the Cl ligands: cis (adjacent, 90°) or trans (opposite, 180°). …

Why Chirality Matters in Coordination Chemistry

A molecule is chiral (optically active) if it is non-superimposable on its mirror image. In coordination chemistry, this usually happens when the complex lacks an improper axis of rotation — most commonly, a plane of symmetry or a centre of inversion. For octahedral complexes with bidentate ligands, chirality often appears when the arrangement of ligands creates a "handedness," like a left-handed vs. right-handed screw.

The key question here: does the cis or trans isomer of $[CrCl_2(ox)_2]^{3-}$ have a plane of symmetry? The oxalate ion ($ox^{2-}$) is a bidentate ligand — it binds through two oxygen atoms, forming a five-membered chelate ring. Chromium(III) is in the +3 oxidation state, and the complex is octahedral.

Step-by-Step Analysis

1. Draw the cis isomer.

   In the cis arrangement, the two chloride ligands are adjacent (90° apart). The two oxalate ligands occupy the remaining four positions. Each oxalate spans two adjacent sites, forming a chelate ring.

   Visualise the structure: imagine the two Cl atoms at, say, positions 1 and 2 of an octahedron. One oxalate can occupy positions 3 and 4, the other oxalate positions 5 and 6.

   Now check for symmetry: is there any plane that cuts through the molecule and reflects one half onto the other?

   • A plane containing the two Cl atoms and the metal centre? That plane would cut through the oxalate rings — but the rings are not symmetric about that plane because each oxalate is a flat, planar unit that lies at an angle.
   • A plane perpendicular to the Cl–Cr–Cl axis? The two oxalates are oriented differently; one is "above" and one "below" relative to any such plane. In fact, the cis isomer has no plane of symmetry and no centre of inversion. Its mirror image cannot be superimposed on the original — it is chiral. This is analogous to the classic case of $cis-[Co(en)_2Cl_2]^+$, which is optically active.

2. Draw the trans isomer.

   In the trans arrangement, the two chloride ligands are opposite each other (180° apart). The two oxalate ligands then occupy the four equatorial positions in a plane.

   Now look for symmetry:

   • There is a plane of symmetry that contains the two Cl atoms and the metal centre, and bisects the angle between the two oxalate ligands. This plane cuts through the centre of each oxalate ring, reflecting one half of the molecule onto the other.
   • Additionally, there is a centre of inversion at the chromium atom. …

Method: Symmetry & Mirror Image Test for Optical Activity

Concept: A coordination compound is chiral (optically active) if it lacks any plane of symmetry, centre of symmetry, or improper rotation axis — i.e., it is non-superimposable on its mirror image.

Step 1 — Draw the structures

Both complexes have:

• Central metal: $Cr^{3+}$
• Ligands: two $Cl^-$ (monodentate) and two $ox^{2-}$ (bidentate, oxalate)
• Coordination number = 6 → octahedral geometry

(a) cis-$[CrCl_2(ox)_2]^{3-}$

• Two $Cl$ are adjacent (90° apart)
• Two oxalate rings occupy the remaining four positions

(b) trans-$[CrCl_2(ox)_2]^{3-}$

• Two $Cl$ are opposite (180° apart)
• Two oxalate rings lie in the equatorial plane

Step 2 — Check for plane of symmetry

Step 3 — Mirror image test …

Common Mistakes & How to Avoid Them

Mistake 1: Assuming all cis-isomers are chiral

The error: Students often memorise "cis = chiral, trans = achiral" as a blanket rule. This is not always true — it depends on the symmetry of the complex.

Why it fails here:

In $[CrCl_2(ox)_2]^{3-}$, the oxalate ligand ($ox$) is a bidentate ligand. In the cis-isomer, the two oxalate rings lie in different planes, and the complex has no plane of symmetry — so it is chiral.

But if the bidentate ligand were symmetrical and planar (like oxalate), the trans-isomer can still have a plane of symmetry.

How to avoid:

• Never rely on "cis = chiral" blindly.
• Always draw the structure and check for:
  • A plane of symmetry
  • A centre of inversion
  • An improper axis of rotation ($S_n$)

Mistake 2: Forgetting that bidentate ligands create rings

The error: Students treat $[CrCl_2(ox)_2]^{3-}$ as if it were $[CrCl_2(A-A)_2]$ where $A-A$ is just two donor atoms — ignoring that the oxalate backbone locks the geometry.

Why it matters:

Oxalate ($\ce{C2O4^{2-}}$) is a rigid, planar bidentate ligand. In the cis isomer, the two oxalate rings are not coplanar — they are oriented at an angle, breaking symmetry.

In the trans isomer, the two oxalate rings lie in the same plane, giving a plane of symmetry.

How to avoid:

• Always sketch the chelate rings — don't just draw dots for donor atoms.
• Remember: bidentate ligands restrict rotation and create ring planes that affect symmetry.

Mistake 3: Confusing optical activity with geometric isomerism

The error: Students think "cis and trans are geometric isomers, so optical activity is separate" — and then forget to check chirality within each geometric isomer.

The truth:

• Geometric isomerism (cis/trans) is about different spatial arrangements of identical ligands.
• Optical activity is about non-superimposable mirror images (chirality).
• A complex can be cis but achiral (if it has a plane of symmetry) or trans but chiral (rare, but possible with asymmetric ligands).

How to avoid:

• Treat chirality as a separate check after identifying cis/trans.
• For each geometric isomer, ask: Does this structure have any symmetry element that makes it superimposable on its mirror image?

Mistake 4: Not drawing the mirror image and checking superimposability

The error: Students try to decide chirality by "looking" at the formula or by vague memory.

The fix:

• Draw the complex in 3D (use wedge-dash or Fischer-type projection).
• Draw its mirror image.
• Try to rotate the mirror image to see if it matches the original.
• If no rotation makes them identical → chiral.

For this question: …