Problem 170 - Advanced Problems in Organic Chemistry for Competitive Examinations

Question

Which of the following pair represents an example of diastereoisomers (i) (+)-Tartaric acid and meso-tartaric acid (ii) Maleic acid and fumaric acid (iii) \(\mathrm{D}(+)\) -Galactose and \(\mathrm{D}(+)\) -mannose (iv) (+)-Lactic acid and (-)-Lactic acid (a) \(\mathrm{i}\) and \(\mathrm{iii}\) (b) \(\mathrm{i}\), iii and iv (c) \(\mathrm{i}, \mathrm{ii}\) and \(\mathrm{iii}\) (d) iv

Step-by-Step Solution

Answer

Correct answer: (c) i, ii and iii.

Step 1: Understand Diastereoisomers

Diastereoisomers are stereoisomers that are not mirror images of each other. Unlike enantiomers, which come in pairs and are non-superimposable mirror images, diastereoisomers can have different physical properties and are not related by reflection.

Step 2: Analyze Each Pair

Let's analyze each pair to determine if they are diastereoisomers: (i) (+)-Tartaric acid and meso-tartaric acid: These are diastereoisomers because they have the same connectivity but differ in configuration at one or more stereocenters and are not mirror images. (ii) Maleic acid and fumaric acid: These are also diastereoisomers as they are isomers with different geometries around a double bond (cis/trans or Z/E). (iii) (+)-Galactose and (+)-Mannose: They are diastereoisomers because they differ at one or more stereocenters and are not mirror images of each other. (iv) (+)-Lactic acid and (-)-Lactic acid: These are enantiomers, not diastereoisomers, because they are mirror images of each other.

Step 3: Determine the Correct Option

Based on the analysis, pairs (i), (ii), and (iii) are examples of diastereoisomers. Pair (iv) is not, as they are enantiomers. The correct option is therefore the one that includes (i), (ii), and (iii).

Key Concepts

Stereochemistry

Stereochemistry is the branch of chemistry that involves the study of the spatial arrangement of atoms in molecules. It is essential because it helps us understand that molecules with the same molecular formula can have different structures and thus different properties. To explore stereochemistry, we can focus on two main types of stereoisomers:

• Enantiomers: These are mirror images of each other that are not superimposable, much like your left and right hand.
• Diastereoisomers: These are not mirror images, and their spatial arrangements lead to different physical properties.

Understanding stereochemistry is crucial because it impacts how molecules interact with biological systems, influencing things like the scent of substances or the efficacy of drugs in our bodies.
For instance, even a small change in the spatial arrangement of a molecule, such as cis vs trans configurations, can lead to vastly different properties and applications in real-world usage.

Enantiomers

Enantiomers are a fascinating type of stereoisomer where the molecules are non-superimposable mirror images of each other. Think of them as left and right hands; they look alike but cannot be perfectly aligned when placed on top of each other. This property makes enantiomers particularly interesting. The core feature of enantiomers is chirality—a property that refers to a lack of an internal plane of symmetry. Enantiomers often involve a chiral center, typically a carbon atom bonded to four different groups or atoms. This configuration is crucial in determining the way the molecules interact with plane-polarized light; one possible effect is rotating light in different directions, termed optical activity. In practical terms, enantiomers can dramatically affect how a molecule behaves in a biological context. Many drugs have enantiomers, where one may be therapeutic, and the other can be harmful or inactive, showcasing the importance of chirality in pharmacology. In the context of the exercise, (+)-Lactic acid and (-)-Lactic acid are enantiomers, illustrating how small changes can have profound effects.

Geometric Isomerism

Geometric isomerism, sometimes referred to as cis-trans isomerism, occurs in molecules that have restricted rotation, typically around double bonds or within ring structures. This form of isomerism arises because the fixed nature of the bonds means that different spatial arrangements become possible. In geometric isomers:

• Cis-isomers: The substituent groups are on the same side of the double bond or ring.
• Trans-isomers: The substituent groups are on opposite sides.

Such configurations can be crucial in determining the properties of a compound. For example, the difference between cis- and trans- arrangements can affect a compound's boiling point, solubility, and even its biological activity. A clear example from the exercise is the maleic acid and fumaric acid pair. These two acids differ solely in the orientation around their double bond (cis for maleic acid and trans for fumaric acid). Though they have the same molecular formula, their distinct structures give them entirely different properties.