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

8 optically active isomers.

Step-by-step solution

Identify Chiral Centers

To determine the number of optically active isomers, we first need to identify the chiral centers in the compound. The compound given is \( \mathrm{CH}_{2}\mathrm{OH}(\mathrm{CHOH})_{3} \mathrm{CHO} \), which is a sugar molecule (an aldotetrose). We can see that it has three chiral centers at each of the \( \mathrm{CHOH} \) groups.

Calculate Maximum Optical Isomers

Each chiral center can have two possible configurations (R or S), so the total maximum number of optical isomers is calculated using \( 2^n \), where \( n \) is the number of chiral centers. For this compound, with 3 chiral centers, the calculation is \( 2^3 = 8 \).

Consider Only D and L Isomers

Since optical isomers come in pairs as mirror images (D and L), the number of optically active isomers remains 8 because each configuration is distinctively different and optically active.

Key concepts

Chiral Centers

In the world of organic chemistry, chiral centers are essential players. A chiral center, often called an asymmetric carbon, is a carbon atom bonded to four different atoms or groups. This unique structure allows for the possibility of different spatial arrangements. These spatial differences are what make molecules chiral, and as such, they can have optical activity—meaning they can rotate plane-polarized light in different directions.

For the compound \( \mathrm{CH}_{2}\mathrm{OH}(\mathrm{CHOH})_{3} \mathrm{CHO} \), each \( \mathrm{CHOH} \) group contains a chiral center, making a total of three chiral centers. Identifying chiral centers in complex organic structures is crucial because it is the first step in determining the number of optical isomers a compound can have.

Optical Isomers Calculation

Once chiral centers are identified, calculating the maximum number of optical isomers follows. Each chiral center can have two configurations: either "R" (rectus) or "S" (sinister), referring to their specific orientation. Therefore, the number of possible optical isomers for a molecule is determined by the formula \( 2^n \), where \( n \) is the number of chiral centers.

Applying this to the aldotetrose structure \( \mathrm{CH}_{2}\mathrm{OH}(\mathrm{CHOH})_{3} \mathrm{CHO} \), we find there are 39 possible optical isomers. This calculation acknowledges the maximum potential number before considering special cases or configurations that might reduce this number. This method is essential for chemists as they explore how molecular structure affects properties like taste, smell, and pharmacological activity.

Aldotetrose Structure

In carbohydrate chemistry, an aldotetrose is a type of sugar that is significant due to its simple yet effective structure. An aldotetrose contains four carbon atoms, and among them, the presence of three \( \mathrm{CHOH} \) groups signifies the locations of the chiral centers.

The structure is also defined by its aldehyde group (\( \mathrm{CHO} \)). Specifically, for \( \mathrm{CH}_{2}\mathrm{OH}(\mathrm{CHOH})_{3} \mathrm{CHO} \), it represents a straightforward sugar molecule from which more complex carbohydrates are derived. Understanding such foundational structures helps in areas like biochemistry and nutrition, as sugars are central to energy production and metabolism.

D and L Isomers

When discussing carbohydrates, particularly sugars, the terms "D" and "L" are commonly used to describe the absolute configuration of the chiral centers in relation to glyceraldehyde, a standard reference sugar. The designations "D" and "L" originate from Latin 'dextro' meaning right, and 'levo' meaning left, describing the direction each isomer rotates polarized light.

The difference between D and L isomers is found in the spatial arrangement around the chiral centers. For example, in D-glyceraldehyde and L-glyceraldehyde, the OH group can be found on the right for D and on the left for L isomers. For the compound in question, with 3 chiral centers and the capacity for 8 isomers based on \( 2^n \) calculation, you'll find that these isomers naturally divide into D and L forms, each of which is optically active. This distinction is vital for them to interact adequately in biological systems, showcasing the significance of chirality in nature.