Question

The compound which does not have exactly 4 optical isomers is (A) \(1,2,3\)-trichloropentane (B) \(2,3,4\)-trichloropentane (C) \(1,2,4\)-trichloropentane (D) \(1,2,5\)-trichloropentane

Short answer

The compound that does not have exactly 4 optical isomers is (D) \(1,2,5\)-trichloropentane.

Step-by-step solution

Identify Chiral Centers

For each given compound, identify the chiral centers. Chiral centers are carbon atoms with four different groups attached to them. (A) \(1,2,3\)-trichloropentane: The chiral centers are C1, C2, and C3. (B) \(2,3,4\)-trichloropentane: The chiral centers are C2, C3, and C4. (C) \(1,2,4\)-trichloropentane: The chiral centers are C1, C2, and C4. (D) \(1,2,5\)-trichloropentane: The chiral centers are C1 and C2.

Find the Number of Optical Isomers

For each compound, calculate the number of optical isomers using the formula \(2^n\), where n is the number of chiral centers. (A) \(1,2,3\)-trichloropentane: \(2^3 = 8\) optical isomers. (B) \(2,3,4\)-trichloropentane: \(2^3 = 8\) optical isomers. (C) \(1,2,4\)-trichloropentane: \(2^3 = 8\) optical isomers. (D) \(1,2,5\)-trichloropentane: \(2^2 = 4\) optical isomers.

Identify the Compound Without 4 Optical Isomers

According to the calculated number of optical isomers, the compounds (A), (B), and (C) all have 8 optical isomers, while the compound (D) has 4 optical isomers. So, the compound that does not have exactly 4 optical isomers is: (D) \(1,2,5\)-trichloropentane.

Key concepts

Chiral Centers Identification

Understanding chiral centers is fundamental in organic chemistry as they are the key to comprehending optical activity in molecules. A chiral center, often a carbon atom, is one that has four distinct substituents, leading to a molecule that is not superimposable on its mirror image. Identifying chiral centers in a compound is the first step towards determining its chirality.

When faced with the task of identifying these unique centers within a compound, one must inspect each carbon atom and discern whether it is bonded to four different groups. For example, in the compound 1,2,3-trichloropentane, the carbon atoms at positions 1, 2, and 3 are each attached to different groups, making them chiral centers. On the other hand, in 1,2,5-trichloropentane, only carbons 1 and 2 are chiral centers as they meet the criteria for chirality.

Knowing how to pinpoint these chiral centers is crucial, as they form the basis for the next steps in analyzing stereoisomerism in organic compounds.

Calculation of Optical Isomers

Once chiral centers have been identified in a molecule, the next intriguing question is to determine how many stereoisomers, specifically optical isomers, the molecule can have. Optical isomers are molecules that differ only in their ability to rotate plane-polarized light in different directions. The simplest rule of thumb for this calculation is the use of the formula \(2^n\), where \(n\) represents the number of chiral centers.

For instance, if a molecule has two chiral centers, there can be up to \(2^2 = 4\) optical isomers. These isomers include both right-handed (dextrorotatory) and left-handed (levorotary) configurations, as well as their corresponding mirror images. This basic mathematical approach provides a quantitative understanding of the molecule's stereoisomer complexity and is an indispensable tool for students grappling with the intricacies of optical isomerism in chemistry.

Stereoisomerism in Organic Compounds

Stereoisomerism is a fascinating aspect of organic chemistry that involves the study of different isomers of a compound which have the same molecular formula and sequence of bonded atoms (constitution), but differ in the three-dimensional orientations of their atoms in space. This spatial diversity can lead to variations in physical and chemical properties, making the study of stereoisomerism incredibly important.

There are two main types of stereoisomers: enantiomers and diastereomers. Enantiomers are mirror images, like left and right hands, and cannot be superimposed on one another. In contrast, diastereomers are not mirror images and have different arrangements in space. The existence of these isomers can profoundly affect the behavior of molecules in biological systems, underlining the importance of accurate chiral center identification and the calculation of possible optical isomers for students and researchers alike.