Question

How many optically active stereoisomers are possible for butan-2, 3 -diol? (a) 1 (b) 2 (c) 3 (d) 4

Short answer

The number of optically active stereoisomers for butan-2,3-diol is 3.

Step-by-step solution

Identify Chiral Centers

Determine the number of chiral centers in the molecule butan-2,3-diol. The compound has the formula, CH3-CHOH-CHOH-CH3. Each carbon atom with a hydroxyl group (OH) is attached to four different groups: for the second and the third carbon, the groups are (H, OH, CH3, and CHOH). Thus, both of these carbons are chiral centers.

Calculate Maximum Stereoisomers

Use the formula for calculating the maximum number of stereoisomers, which is \(2^n\), where \(n\) is the number of chiral centers. In butan-2,3-diol, \(n = 2\), so the maximum number of stereoisomers is \(2^2 = 4\).

Determine Optically Active Isomers

Optically active isomers are those without an internal plane of symmetry (enantiomers). Draw the structures of each stereoisomer to determine symmetry. Consider that while there are 4 stereoisomers, some are meso compounds which are not optically active due to internal symmetry. Butan-2,3-diol has one meso compound and two pairs of enantiomers.

Count the Optically Active Isomers

Subtract the meso compound (which is not optically active) from the total stereoisomers. Since there is one meso form out of 4 stereoisomers, there are \(4 - 1 = 3\) optical isomers that are optically active.

Key concepts

Chiral Centers

Chiral centers are crucial in understanding the stereochemistry of molecules. A carbon atom is considered a chiral center if it is attached to four different groups. These unique groups create a non-superimposable mirror image, much like your right hand compared to your left hand. In the example of butan-2,3-diol, both the second and third carbon atoms are chiral centers.

This is because each of these carbon atoms is bonded to a hydrogen (H), a hydroxyl group (OH), a methyl group (CH3), and another carbon chain with a hydroxyl group. Identifying these centers is the first step in determining the molecule's ability to form isomers.

Optically Active Isomers

Optically active isomers are molecules that can rotate the plane of polarized light. This property arises due to the lack of an internal plane of symmetry, resulting in two non-superimposable mirror images, known as enantiomers.

For butan-2,3-diol, when you assess its structures, you can find that some of the possible stereoisomers are optically active and capable of affecting polarized light in either a clockwise or counterclockwise direction. These enantiomers form the basis for optical activity in a compound, making it critical to evaluate the symmetry and chiral centers to determine which isomers are optically active.

Meso Compounds

Meso compounds are an interesting exception to the existence of stereochemistry's optically active nature. These compounds, although having chiral centers, are still optically inactive due to an internal plane of symmetry. This symmetry means they are superimposable on their mirror images.

In butan-2,3-diol, one such meso compound exists among the possible stereoisomers. This internal symmetry cancels out any optical activity, despite the presence of chiral centers. Recognizing a meso compound within a set of stereoisomers helps in accurately counting optically active isomers.

Butan-2,3-diol

Butan-2,3-diol is an organic compound with the chemical formula CH3-CHOH-CHOH-CH3. It is a diol, meaning it contains two hydroxyl (OH) groups, which makes it part of the alcohol family.

Butan-2,3-diol is a chiral molecule due to the two chiral centers located at the second and third carbon atoms. Its complex structure allows for the possibility of several stereoisomers. To determine the number of these isomers, the formula \(2^n\) is used, where \(n\) represents the number of chiral centers in the molecule.

Though butan-2,3-diol can have up to four stereoisomers, the presence of one meso compound affects the count of optically active isomers, resulting in three that can rotate polarized light.