Problem 87 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following complex ions will not show optical activity? (a) \(\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right]^{+}\) (b) \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+}\) (c) \(\left[\mathrm{Pt}(\mathrm{Br})(\mathrm{Cl})\right.\) (I) \(\left(\mathrm{NO}_{2}\right)\) (Py) \(\left.\mathrm{NH}_{3}\right]\) (d) \(\operatorname{cis}=\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\)

Step-by-Step Solution

Answer

Option (b) is not optically active.

Step 1: Understand Optical Activity

Optical activity occurs when a compound has the ability to rotate the plane of polarized light. For a complex ion to exhibit optical activity, it must have a non-superimposable mirror image, meaning it is chiral.

Step 2: Analyze Option (a)

The compound \[\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right]^{+}\]contains ethylenediamine (en), which is a bidentate ligand that can create a chiral center. However, due to the ligands' arrangement, this complex can form non-superimposable mirror images; thus, it can show optical activity.

Step 3: Analyze Option (b)

The compound \[\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+}\]has two chloride ions and four ammonia ligands, which create an octahedral geometry. This geometry with two identical pairs of ligands is symmetrical and cannot form non-superimposable mirror images. Therefore, it will not show optical activity.

Step 4: Analyze Option (c)

The compound \[\left[\mathrm{Pt}(\mathrm{Br})(\mathrm{Cl})\right. (\mathrm{I}) \left(\mathrm{NO}_{2}\right)\right.\left.\mathrm{Py}\left.\mathrm{NH}_{3}\right]\right]\]contains various monodentate ligands around a central Pt atom, creating potential asymmetry that can lead to optical activity. Each ligand is different, which allows for non-superimposable mirror images.

Step 5: Analyze Option (d)

The compound \[cis=\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\]has ethylenediamine ligands in a cis configuration. This orientation creates a chiral center as the bidentate chelation and arrangement cannot be superimposed on its mirror image, leading to optical activity.

Step 6: Conclusion: Identify the Complex

Only the complex from option (b) \[\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+}\]is not able to form non-superimposable mirror images, and thus does not show optical activity.

Key Concepts

Chirality in Coordination Compounds

In chemistry, chirality refers to a property where a molecule cannot be superimposed on its mirror image, much like left and right hands. This property is crucial when studying coordination compounds, as it often determines whether these substances will exhibit optical activity. In coordination chemistry, chirality is usually observed in complex ions, which consist of a central metal ion bonded to surrounding molecules or ions called ligands. These complexes become chiral when their structures allow for non-superimposable mirror images. For instance, when a compound utilizes bidentate ligands—ligands that attach to the metal atom at two points—chirality can occur if these bonds create an arrangement similar to twisting, forming a specific kind of isomer called an optical isomer. Compounds that display chirality usually exhibit optical activity. Such molecules can rotate the plane of polarized light, which can be measured to confirm the presence of chiral structures. It's like having doors that swing open in only one direction; the arrangement is distinct and can't be changed without altering the entire complex.

Symmetry in Chemical Structures

Symmetry plays a significant role in understanding whether a chemical structure can be optically active. Most symmetrical molecules do not show optical activity, as their mirrored counterparts can be perfectly superimposed, meaning they are achiral.Consider an octahedral complex where symmetry is prevalent. For instance, in the complex \[\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+}\] the geometry consists of four ammonia ligands and two chloride ligands. The arrangement offers a high degree of symmetry. In such cases, the complex appears the same from multiple perspectives. Even if the ligands were varied, if the arrangement retained symmetry, the molecules would still not be optically active.Symmetry is like a balancing act; take away the balance, and chirality comes into play. Breaking this symmetry, for example by using at least one unique ligand or through asymmetrical attachment, can result in chiral—and therefore optically active—compounds. It's much like decorating a mirror image—without distinct differences, the symmetry keeps them indistinguishable.

Bidentate Ligands and Optical Isomerism

Bidentate ligands play a fascinating role in creating complex ions that can exhibit optical isomerism. By definition, a bidentate ligand bonds to the central metal atom through two atoms, which allows for a chelating effect, wrapping the metal and forming potential chiral centers.Consider the ethylenediamine (en) ligand, a classic example of a bidentate ligand. This ligand forms a ring with the metal center, like wrapping an arm around to grab hold. The number and type of these ligands can cause significant changes in the geometry of the complex ion. In the complex \[\text{cis-}\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\], the bidentate ethylenediamine ligands create an arrangement that cannot be mirrored exactly. This leads to the ability to form two enantiomers, non-superimposable mirror images of each other. Optical isomerism arises when such structures allow for a twist or a turn in the arrangement, which makes one form distinct from its mirror twin. It is like twisting a cable—doing so creates a directionality that can't simply be flipped to match its twin exactly, marking the presence of chirality in what seems like a simple bonding action.