Question

Which of the following can exist as a pair of enantiomers:

• A. trans-[CrCl$_2$ en$_2$]$^+$
• B. cis- [CrCl$_2$ en$_2$]$^+$
• C. trans-[CrCl$_2$(NH$_3$)$_4$]$^+$
• D. cis-[CrCl$_2$(NH$_3$)$_4$]$^+$

Answer 1

Answer: (B)

B

Answer 2

To determine which of the given complexes can exist as a pair of enantiomers, we need to identify the chiral complexes. A chiral molecule is non-superimposable on its mirror image and lacks any improper axis of rotation ($S_n$), including a plane of symmetry ($\sigma$, which is $S_1$) and a center of inversion ($i$, which is $S_2$). All the given complexes are octahedral.

Let's analyze each option:

(A) trans-[CrCl$_2$ en$_2$]$^+$

This complex is of the type trans-[M(AA)_2 X_2], where M = Cr, AA = en (ethylenediamine, a bidentate ligand), and X = Cl. In the trans isomer, the two Cl ligands are positioned 180 degrees apart. If we place the Cr atom at the origin, and the two Cl ligands along the z-axis, then the two bidentate en ligands lie in the equatorial (xy) plane. This geometry possesses several symmetry elements:

1. A plane of symmetry passing through the Cr atom and the two Cl ligands, and bisecting the C-C bonds of the two en ligands.

2. A plane of symmetry passing through the Cr atom and the four nitrogen atoms of the en ligands (the equatorial plane).

3. A center of inversion at the Cr atom.

Due to the presence of these symmetry elements, the trans-[CrCl$_2$ en$_2$]$^+$ complex is achiral and cannot exist as a pair of enantiomers.

(B) cis-[CrCl$_2$ en$_2$]$^+$

This complex is of the type cis-[M(AA)_2 X_2]. In the cis isomer, the two Cl ligands are positioned 90 degrees apart (adjacent). This cis isomer lacks a plane of symmetry and a center of inversion. It is, therefore, chiral. A molecule and its mirror image for cis-[M(AA)_2 X_2] are non-superimposable, meaning they are enantiomers. This is a classic example of optical isomerism in coordination compounds.

(C) trans-[CrCl$_2$(NH$_3$)$_4$]$^+$

This complex is of the type trans-[MA_4 X_2], where M = Cr, A = NH$_3$ (monodentate ligand), and X = Cl. In the trans isomer, the two Cl ligands are 180 degrees apart. The four NH$_3$ ligands lie in the equatorial plane. This complex has multiple planes of symmetry:

1. A plane of symmetry passing through the Cr atom and the four NH$_3$ ligands (the equatorial plane).

2. A plane of symmetry passing through the Cr atom and the two Cl ligands, and two of the NH$_3$ ligands.

3. A center of inversion at the Cr atom.

Due to these symmetry elements, trans-[CrCl$_2$(NH$_3$)$_4$]$^+$ is achiral and cannot exist as a pair of enantiomers.

(D) cis-[CrCl$_2$(NH$_3$)$_4$]$^+$

This complex is of the type cis-[MA_4 X_2]. In the cis isomer, the two Cl ligands are 90 degrees apart. The four NH$_3$ ligands occupy the remaining positions. This complex possesses a plane of symmetry. Imagine the two Cl ligands and two of the NH$_3$ ligands lying in a plane. This plane acts as a mirror plane, reflecting the other two NH$_3$ ligands onto each other. For example, if the two Cl ligands are on the y and z axes, and two NH$_3$ ligands are on the x axis, then the yz-plane (containing Cr, the two Cl, and two NH$_3$) is a plane of symmetry, reflecting the two NH$_3$ ligands on the x-axis. Therefore, cis-[CrCl$_2$(NH$_3$)$_4$]$^+$ is achiral and cannot exist as a pair of enantiomers.

Based on the analysis, only cis-[CrCl$_2$ en$_2$]$^+$ is chiral and can exist as a pair of enantiomers.

Explanation of the solution:

Chirality in coordination compounds requires the absence of a plane of symmetry and a center of inversion.

1. trans-[CrCl$_2$ en$_2$]$^+$: Possesses a plane of symmetry (equatorial plane containing Cr and four N atoms of en ligands) and a center of inversion. Achiral.

2. cis-[CrCl$_2$ en$_2$]$^+$: Lacks a plane of symmetry and a center of inversion. Chiral, exists as enantiomers.

3. trans-[CrCl$_2$(NH$_3$)$_4$]$^+$: Possesses a plane of symmetry (equatorial plane containing Cr and four NH$_3$ ligands) and a center of inversion. Achiral.

4. cis-[CrCl$_2$(NH$_3$)$_4$]$^+$: Possesses a plane of symmetry containing Cr, the two Cl ligands, and two NH$_3$ ligands. Achiral.

Thus, only cis-[CrCl$_2$ en$_2$]$^+$ can exist as a pair of enantiomers.