Question

Given below are two statements:
Statement-I : $[\text{Fe}(\text{ox})_3]^{3-}$ is chiral.
Statement-II : trans-$[\text{Cr}(\text{H}_2\text{O})_2(\text{ox})_2]^-$ is chiral.
(Given : \(\text{oxH}_2 = \text{HOOC}-\text{COOH}\))
In light of the above statements, choose the most appropriate answer from the options given below:

• A. Statement-I is incorrect but Statement-II is correct
• B. Both Statement-I and Statement-II are correct
• C. Both Statement-I and Statement-II are incorrect
• D. Statement-I is correct but Statement-II is incorrect

Hint:

For octahedral complexes with bidentate ligands: - All tris-chelated complexes like $[\text{M}(\text{AA})_3]$ are always chiral. - For bis-chelated complexes like $[\text{M}(\text{AA})_2\text{B}_2]$: the cis-isomer is always chiral, while the trans-isomer contains planes of symmetry and is always achiral.

Answer 1

The Correct Option is D

Concept: A coordination complex molecule is defined as chiral (and therefore optically active) if its structural geometry lacks an improper axis of rotation ($S_n$), which practically means it contains neither a plane of symmetry ($\sigma$) nor a center of inversion ($i$). Such a complex forms two non-superimposable mirror images called enantiomers ($\Delta$ and $\Lambda$ forms).

• Symmetric bidentate chelating ligands like oxalate ($\text{ox}^{2-} = \text{C}_2\text{O}_4^{2-}$) form five-membered rings with the central metal ion, introducing rigid spatial constraints.

• Tris-chelated octahedral complexes with the general formula $[\text{M}(\text{AA})_3]$ take on a propeller-like geometry that inherently lacks a plane of symmetry.

Step 1: Evaluating Statement-I (\([\text{Fe}(\text{ox})_3]^{3-}\)).
The complex ion $[\text{Fe}(\text{ox})_3]^{3-}$ features an iron central metal ion coordinated by three symmetric bidentate oxalate ligands, matching the general coordination form $[\text{M}(\text{AA})_3]$. Its structural configuration is octahedral with a coordination number of 6. Let us examine its symmetry elements: - The three chelate rings are locked in mutually perpendicular planes, wrapping around the central iron core like a propeller or a three-bladed fan. - Because of this helical twist, it is impossible to pass any plane through the molecule that splits it into two symmetrical mirror halves. - It also lacks a center of inversion. Since the molecule has no internal symmetry elements, its mirror image is completely non-superimposable. It exists as a pair of stable enantiomers (d and l forms). Therefore, $[\text{Fe}(\text{ox})_3]^{3-}$ is chiral, making Statement-I correct.

Step 2: Evaluating Statement-II (trans-\([\text{Cr}(\text{H}_2\text{O})_2(\text{ox})_2]^-\)).
The complex trans-$[\text{Cr}(\text{H}_2\text{O})_2(\text{ox})_2]^-$ belongs to the general stereochemical category trans-$[\text{MA}_2(\text{BB})_2]$. Let us examine its octahedral geometry: - The prefix trans- specifies that the two monodentate aqua ($\text{H}_2\text{O}$) ligands are located directly opposite one another ($180^\circ$ apart) at the two axial positions (top and bottom vertices). - The two bidentate oxalate ($\text{ox}^{2-}$) ligands lie entirely within the flat equatorial plane, occupying the four remaining planar coordination sites. Let us check for symmetry elements in this arrangement: 1) Plane of Symmetry (\(\sigma_h\)): If we pass a horizontal cutting plane directly through the equatorial position containing the chromium atom and the two oxalate rings, it splits the molecule in half. The top axial $\text{H}_2\text{O}$ ligand is reflected across this plane into the identical bottom axial $\text{H}_2\text{O}$ ligand. 2) Center of Inversion ($i$): Moving from any atom through the central chromium atom leads directly to an identical atom on the opposite side. Because the molecule possesses a clear plane of symmetry and a center of inversion, it is completely achiral (optically inactive). Statement-II claims that this trans complex is chiral, which is false. Thus, Statement-II is incorrect.

Step 3: Conclusion.
Since Statement-I is correct and Statement-II is incorrect, the corresponding selection is Option (4).