Problem 90 - Advanced Problems in Organic Chemistry for Competitive Examinations

Question

Which of the following statements are true? (i) Structural isomers are compounds with the same molecular formula, but are different in the connectivity (order of attachment) of their atoms. (ii) Stereoisomers are compounds with the same molecular formula and same order of attachment of their atoms, but are different in the orientation of their atoms or groups in space. (iii) Enantiomers are stereoisomers whose molecules are mirror images of each other. (iv) Diastereomers are stereoisomers whose molecules are not mirror images of each other. (v) A molecule with two chiral centres designated as \((\mathrm{R}, \mathrm{R})\) will have an enantiomer with two chiral centres designated as \((\mathrm{S}, \mathrm{R})\). (vi) Cis-1,2-dichlorocyclopentane and trans-1,2-dichlorocyclopentane are enantiomer to each other. (a) \(\mathrm{i}, \mathrm{ii}, \mathrm{iv}, \mathrm{vi}\) (b) \(\mathrm{i}, \mathrm{ii}, \mathrm{iii}, \mathrm{iv}\) (c) \(\mathrm{i}, \mathrm{ii}, \mathrm{iii}, \mathrm{iv}, \mathrm{vi}\) (d) \(\mathrm{ii}, \mathrm{iii}, \mathrm{iv}, \mathrm{vi}\)

Step-by-Step Solution

Answer

Option (b) is correct: i, ii, iii, iv are true.

Step 1: Evaluate Statement (i)

Structural isomers have the same molecular formula but differ in the connectivity of their atoms. This statement matches the definition and is true.

Step 2: Analyze Statement (ii)

Stereoisomers have the same molecular formula and connectivity, differing only in the arrangement in space. This accurately describes stereoisomers, making the statement true.

Step 3: Consider Statement (iii)

Enantiomers are indeed stereoisomers that are mirror images of each other. This matches the standard definition and is true.

Step 4: Review Statement (iv)

Diastereomers are stereoisomers that are not mirror images of each other, which is correct according to standard chemistry definitions. Therefore, this statement is true.

Step 5: Examine Statement (v)

An enantiomer of a molecule with two chiral centers designated as (R,R) would actually have them as (S,S), since enantiomers are mirror images. Thus, (S,R) would not be its enantiomer and this statement is false.

Step 6: Evaluate Statement (vi)

Cis-1,2-dichlorocyclopentane and trans-1,2-dichlorocyclopentane are not mirror images of each other but are diastereomers. Therefore, this statement is false.

Step 7: Choose the Correct Option

From the analysis: statements i, ii, iii, and iv are true, while v and vi are false. The correct option matching true statements i, ii, iii, and iv is (b).

Key Concepts

Structural Isomers

Structural isomers, also known as constitutional isomers, are compounds that have the same molecular formula but differ in the way their atoms are connected. This means that, although they have identical numbers of each type of atom, the atoms are arranged in different ways. For example, consider the molecular formula C you can have a straight chain of carbon atoms or a branched chain, both differing in the connectivity of their atoms.
Identifying structural isomers involves examining the bonds between atoms, as these differences in connectivity give rise to different physical and chemical properties.

• Same molecular formula
• Different connectivity
• Diverse physical and chemical properties due to different structures

This concept is crucial in organic chemistry, where even a small change in structure can significantly alter how a compound behaves and interacts.

Stereoisomers

Stereoisomers are fascinating compounds because they have the same molecular formula and connectivity of atoms but differ in their spatial arrangement. This type of isomerism doesn't involve breaking any bonds; instead, it revolves around how atoms or groups are oriented in three-dimensional space. Before understanding stereoisomers, it's important to note that this category includes two main types: enantiomers and diastereomers.

• Same connectivity
• Different spatial arrangement

The differences in spatial arrangement can lead to vastly different physiochemical properties and biological activities. For instance, the flavor of certain molecules in food can change significantly based on their spatial arrangement, even if their chemical formulas remain identical.

Enantiomers

Enantiomers are a kind of stereoisomer that are mirror images of each other but are not superimposable. Think of your left and right hands; they are the same yet opposite, unable to perfectly align with one another when placed on top of each other. Similarly, enantiomers have this mirror-image relationship, which exists at chiral centers within molecules.
These chiral centers, typically carbon atoms bound to four different groups, create asymmetry. An enantiomer's physical and chemical properties can be remarkably similar, but their interaction with polarized light varies; one rotates light clockwise and the other counterclockwise. Additionally, enantiomers can exhibit very different biological activities.

• Mirror images
• Not superimposable
• Affect light rotation differently

Diastereomers

Diastereomers are stereoisomers that are not mirror images of one another. While they share similar connectivity, the spatial arrangement between diastereomers differs in multiple places, not just at one single chiral center. Unlike enantiomers, diastereomers don't have to be paired in mirror-image sets, and they do not generally share similar physical or chemical properties.
Examples include compounds that possess multiple chiral centers; changes in any but all of these centers can result in diastereomers. This variety leads to different boiling and melting points, solubility, and other attributes, making diastereomers particularly useful in material and chemical processes.

• Not mirror images
• Multiple chiral centers involved
• Variable physical properties

This specific kind of isomerism is important in the study of materials and biological systems, providing insights into how structure can influence function at a molecular level.