Question

The total number of optically active isomers for \(\mathrm{CH}_{2} \mathrm{OH}(\mathrm{CHOH})_{3} \mathrm{CHO}\) are (a) 16 (b) 8 (c) 4 (d) 2

Short answer

The total number of optically active isomers for the compound is 8.

Step-by-step solution

Identify Chiral Centers

First, identify the number of chiral centers in the given molecule, which is \( \mathrm{CH}_{2}\mathrm{OH}(\mathrm{CHOH})_{3} \mathrm{CHO} \). A chiral center is a carbon atom attached to four different groups. In this compound, the carbons in the \((\mathrm{CHOH})_{3}\) part are the chiral centers.

Count the Chiral Centers

Count the number of chiral centers identified in Step 1. There are 3 chiral centers in the structure because there are 3 \(\mathrm{CHOH}\) groups, each contributing one chiral center.

Calculate the Maximum Number of Optical Isomers

Use the formula for calculating the maximum number of optical isomers for a compound with \( n \) chiral centers, which is \( 2^n \). Since there are 3 chiral centers, calculate \( 2^3 = 8 \).

Determine Correct Answer

The compound \( \mathrm{CH}_{2}\mathrm{OH}(\mathrm{CHOH})_{3} \mathrm{CHO} \) can have a maximum of 8 optically active isomers. Thus, (b) 8 is the correct answer.

Key concepts

Chiral Centers

Chiral centers are crucial in determining the optical properties of a molecule. A chiral center, sometimes referred to as a stereocenter, is a carbon atom bonded to four different groups. This unique structure allows for non-superimposable mirror images, much like your left and right hands are similar but not identical. This feature is what we call chirality.

In the molecule \( \mathrm{CH}_{2}\mathrm{OH}(\mathrm{CHOH})_{3} \mathrm{CHO} \), the chiral centers are located within the \((\mathrm{CHOH})_{3}\) part. Here, each carbon atom in these groups is attached to four distinct groups: a hydrogen atom, a hydroxyl group (\(-OH\)), another part of the carbon chain, and the remaining segments attached to the central carbon. Thus, we can conclude that there are 3 chiral centers in this particular compound, which are instrumental in exploring its stereochemical properties.

• Each carbon in the \((\mathrm{CHOH})_{3}\) acts as a chiral center.
• The presence of these chiral centers contributes to the molecule's ability to rotate plane-polarized light, which is a characteristic of optically active substances.

Optical Activity

Optical activity is the ability of a molecule to rotate the plane of polarized light. This property is inherently connected to chirality, and therefore, the presence of chiral centers within a molecule. When light waves pass through a chiral compound, the orientation of the light waves is rotated. This rotation can either be dextrorotatory (to the right) or levorotatory (to the left), and it is measured by a polarimeter.

The effectiveness of this rotation depends on the molecule's configuration and the number of chiral centers. With each chiral center, the possible variations and orientations of the molecule increase, thereby influencing the degree of optical rotation the molecule can exhibit. For instance, in our compound \( \mathrm{CH}_{2}\mathrm{OH}(\mathrm{CHOH})_{3} \mathrm{CHO} \), the presence of 3 chiral centers allows for a variety of configurations that contribute to its optical activity.

• Optical isomers are non-superimposable mirror images, each with distinct optical properties.
• By using a polarimeter, one can determine the direction and degree of light rotation.

Stereochemistry

Stereochemistry explores the spatial arrangement of atoms within molecules, significantly impacting chemical behavior and reactions. It deals heavily with the orientation and configuration of molecules, making it essential to understand not only from an academic perspective but also for practical applications, such as drug design in pharmaceuticals.

In molecules like \( \mathrm{CH}_{2}\mathrm{OH}(\mathrm{CHOH})_{3} \mathrm{CHO} \), stereochemistry is governed by the chiral centers. Each unique arrangement of these centers results in different stereoisomers, specifically optical isomers, which are key to the molecule's properties and interactions. The maximum number of optical isomers a compound can have is determined by the formula \( 2^n \), where \( n \) is the number of chiral centers. For our example, with 3 chiral centers, there are \( 2^3 = 8 \) possible stereoisomers.

• Stereochemistry determines how molecules interact with biological systems.
• Understanding stereochemistry is crucial for optimizing the intended effects of bioactive compounds.