Problem 45 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Statement-1 : The geometrical isomers of the complex \(\left[M\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]\) are optically inactive. Statement-2 : Both geometrical isomers of the complex \(\left[M\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]\) possess axis of symmetry.

Step-by-Step Solution

Answer

Both statements are true; the geometrical isomers are optically inactive due to being symmetrical.

Step 1: Identify the Complex Type

The complex \( \left[M\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \) typically represents an octahedral coordination complex, where two chloride ions and four ammonia molecules coordinate with the central metal atom M.

Step 2: Determine the Possible Isomers

For an octahedral complex like \( \left[M\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \), there are two possible geometrical isomers: cis and trans. In the cis isomer, the two chloride ions are adjacent to each other, whereas in the trans isomer, the two chloride ions are opposite each other.

Step 3: Assess Optical Activity

Optical activity occurs in chiral compounds, which possess non-superimposable mirror images and lack an axis of symmetry. Since both cis and trans geometrical isomers of \( \left[M\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \) have an axis of symmetry, they are not chiral and therefore are optically inactive.

Step 4: Validate Statement-2

For both the cis and trans isomers, the presence of an axis of symmetry implies that the two forms are not optically active as they can be superimposed with their mirror images. This confirms that both geometrical isomers possess axes of symmetry, making Statement-2 true.

Step 5: Verify Statement-1 Conclusion

Since both isomers of the complex are optically inactive due to the presence of symmetry, Statement-1 is correct. The lack of optical activity is a result of them not being chiral, due to having an axis of symmetry.

Key Concepts

Geometrical Isomerism

Coordination complexes, specifically the octahedral type, can exhibit a phenomenon called geometrical isomerism. This occurs when the spatial arrangement of ligands around the central metal atom can form distinct structures resulting in different chemical properties. For the complex \(\left[M\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]\), two geometrical isomers exist: the cis and trans isomers.

• **Cis Isomer:** In this configuration, the two chloride ions are adjacent to each other, like neighboring seats in a theater. This proximity can influence the compound's properties, including its reactivity.
• **Trans Isomer:** Here, the chloride ions are positioned opposite each other, similar to sitting across someone at a table. This opposing positioning can drastically change how the compound interacts in concert with others.

Understanding these spatial differences is crucial because each isomer can have significantly different chemical behaviors, affecting their use and function.

Optical Activity

Optical activity is a property of some chiral substances that can rotate the plane of polarized light. For a compound to show optical activity, it must be chiral, meaning its mirror image cannot be superimposed onto the original molecule, like left and right hands. However, for coordination complexes like \(\left[M\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]\), both the cis and trans isomers do not exhibit optical activity.

• Neither the cis nor the trans isomer is chiral due to the presence of symmetry axes, which allows them to be superimposed on their mirror images.
• The presence of an axis of symmetry means these isomers do not have the unique handedness necessary for optical activity.

This lack of optical activity is an important concept in chemistry because it determines how these molecules will behave in biological systems and chemical reactions.

Octahedral Complexes

Octahedral complexes are a common and vital coordination complex where six ligands symmetrically surround a central metal atom. This arrangement is analogous to the six faces of an octahedron.

• The complex \(\left[M\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]\) is an example of an octahedral complex, featuring four ammonia ions and two chloride ions as ligands.
• The symmetrical distribution of ligands allows such complexes to adopt multiple geometrical forms, leading to phenomena like geometrical isomerism.

Understanding these complexes is critical in chemistry due to their prevalence in various applications, including catalysis, material science, and bioinorganic chemistry.