Problem 108 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the following spatial arrangements of the octahedral complex ion \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+} .\) Which of the following statements is incorrect regarding these structures? (a) 2 and 3 are cis and trans isomers respectively (b) 1 and 3 are enantiomers (c) 3 and 4 have identical structures (d) 2 and 4 are trans and cis isomers respectively

Step-by-Step Solution

Answer

Statement (b) is incorrect as isomers can't have enantiomeric arrangement due to identical ligands.

Step 1: Understanding the Complex Ion Structure

The given complex ion is \([\text{Co(NH}_3)_4 \text{Cl}_2]^+\). It is an octahedral complex, meaning it has six positions around the cobalt ion. Four positions are occupied by \(\text{NH}_3\) ligands, and two positions are occupied by \(\text{Cl}\) ligands. These ligands can arrange themselves differently, creating geometric isomers.

Step 2: Identifying Cis and Trans Isomers

Cis and trans isomers differ in the arrangement of ligands around the central metal ion. In cis isomers, the like ligands occupy adjacent positions, while in trans isomers, they occupy opposite positions. In \([\text{Co(NH}_3)_4 \text{Cl}_2]^+\), two \(\text{Cl}\) ligands can either be adjacent (cis) or opposite (trans) to each other.

Step 3: Analyzing Statement (a)

Statement (a) says 2 and 3 are cis and trans isomers respectively. This suggests structure 2 has \(\text{Cl}\) ligands adjacent, and structure 3 has \(\text{Cl}\) ligands opposite. We need diagrams or descriptions of arrangements to verify but theoretically this statement could be plausible.

Step 4: Analyzing Statement (b)

Statement (b) claims 1 and 3 are enantiomers. Enantiomers are non-superimposable mirror images, which is possible if complex ion structures have the correct arrangement of ligands (like right and left hand gloves). We examine if structures 1 and 3 have such a relationship in their ligand arrangements.

Step 5: Analyzing Statement (c)

Statement (c) posits that 3 and 4 have identical structures. If structures 3 and 4 have the same spatial arrangement of \(\text{Cl}\) and \(\text{NH}_3\) ligands, this statement is correct. Without specific configurations of these ions for each structure, we assume they can be identical geometrically.

Step 6: Analyzing Statement (d)

Statement (d) suggests 2 and 4 are trans and cis isomers respectively. This implies structure 2 has opposite positioning of \(\text{Cl}\) ions (trans), and structure 4 has adjacent positioning (cis). This statement must be confirmed based on the provided configurations.

Step 7: Evaluating Correctness of Statements

Since we need to find the incorrect statement, we must compare configurations. If 3 and 4 are verified to be identical, statement (c) is correct. If 1 and 3 are indeed enantiomers, (b) holds too. With correct setups for trans and cis, (a) and (d) can also be verified based on ligand positions. Errors arise if any assumption leads to contradiction or inability to conform to specified isomer types.

Key Concepts

Geometric Isomers

Geometric isomers are a fascinating aspect of coordination chemistry. They occur when ligands around a central metal ion can take different spatial arrangements. Imagine these as different ways to arrange elements around a core spot, like rearranging people around a table. These arrangements do not change the connections between atoms, only their spatial orientation.
In an octahedral complex, such as \([\text{Co(NH}_3)_4 \text{Cl}_2]^+\), geometric isomerism is especially prevalent. This is because the six positions around the cobalt ion allow various relative placements of ligands. For instance, two chloride ions can be placed adjacent to each other, or on opposite sides of the cobalt ion, leading to different structures.

• **Cis isomers**: where similar ligands occupy adjacent positions.
• **Trans isomers**: where similar ligands are placed on opposite sides.

Each of these arrangements leads to different chemical properties and reactivity, which makes understanding geometric isomerism essential for predicting the behavior of coordination compounds.

Cis-Trans Isomerism

Cis-trans isomerism is a specific type of geometric isomerism. It focuses on the relative placement of identical ligands in coordination compounds. Understanding this concept is key to grasping different properties and reactivities of these isomers.
In the context of the complex ion \([\text{Co(NH}_3)_4 \text{Cl}_2]^+\), cis isomers appear when the two chlorine atoms are adjacent. This means they are next to each other in the complex, causing a certain spatial configuration. Such configurations can alter the compound’s ability to interact with other molecules, given the available space and the arrangement of charge around the metal ion.
Conversely, trans isomers manifest when these same chloride ligands are positioned opposite each other. This creates a long linear distance between them. Thus, the spatial symmetry differs significantly from cis forms, resulting in different chemical and physical properties.

• In cis, attractive or repulsive forces between same ligands can affect reactions differently than in trans.
• In trans, steric hindrance is often reduced because of the spacing.

Harnessing these differences allows chemists to tailor compounds for specific purposes in both industrial and research contexts.

Enantiomers

Enantiomers are a unique kind of isomers found in coordination chemistry, identified by their property of being non-superimposable mirror images of each other. Imagine trying to lay one over the other, just like trying to place your left hand perfectly over your right without twisting – it simply cannot be done.
They are essentially like a pair of gloves; no matter how similar they appear, they are fundamentally distinct in how they can interact with other chemical species. These interactions often involve light and biological systems. For example, one enantiomer might rotate polarized light in one direction while its mirror image rotates it the opposite way.
The complex \([\text{Co(NH}_3)_4 \text{Cl}_2]^+\) can form enantiomers when ligands are arranged such that two non-superimposable, mirror-image structures arise.

• Enantiomers can have wildly different biological activities. One might be beneficial, while the other could be inactive or harmful.
• Understanding and identifying enantiomers is crucial in industries like pharmaceuticals where the activity of a compound must be controlled.

Seeing how these mirror images behave differently across various scenarios helps in advancing both theoretical and practical chemistry knowledge.