Question

(a) How many stereoisomers are possible for 4 -methyl-1,2-cyclohexanediol? (b) Which of the possible stereoisomers are formed by oxidation of \((S)-4\)-methylcyclohexene with osmium tetroxide? (c) Is the product formed in part (b) optically active or optically inactive?

Short answer

Is the product optically active or inactive? Answer: There are 4 stereoisomers for 4-methyl-1,2-cyclohexanediol. Two possible stereoisomers are formed by the oxidation of (S)-4-methylcyclohexene with osmium tetroxide, and the product is optically active.

Step-by-step solution

Find the total number of stereoisomers for 4-methyl-1,2-cyclohexanediol

To determine the total number of diastereoisomers, we need to consider the 1,2-cyclohexanediol and the 4-methyl substitution. Diastereoisomers are stereoisomers that are not enantiomers. 1,2-cyclohexanediol possesses two chiral centers at the hydroxyl groups. From the formula 2^n, where n is the number of chiral centers, we calculate the total possible stereoisomers: 2^2 = 4. Therefore, 4-methyl-1,2-cyclohexanediol has four possible stereoisomers, including enantiomers. Answer to (a): There are 4 stereoisomers for 4-methyl-1,2-cyclohexanediol.

Identify the stereoisomers formed by oxidation

Oxidation of \((S)-4\)-methylcyclohex-1-ene with OsO4 results in syn addition of hydroxyl groups. In this case, the hydroxyl groups will be added to the same side of the molecule, either both axial or both equatorial. Considering the chair conformation for the oxidation process, we have two possible oxidation products. One in which the hydroxyl groups and the methyl group are all in the equatorial position (with a more stable conformation), and one where both hydroxyl groups are axial. These two products are diastereoisomers. Answer to (b): Two possible stereoisomers are formed by oxidation of \((S)-4\)-methylcyclohexene with osmium tetroxide.

Determine the optical activity of the product

To determine if the products are optically active or inactive, we need to look for the presence of chiral centers in the molecules. As mentioned earlier, the 1,2-cyclohexanediol has two chiral centers, making it optically active. In the case of the oxidation products, both molecules contain two chiral centers, and therefore, both products formed are optically active. Answer to (c): The product formed in part (b) is optically active.

Key concepts

Diastereoisomers

Diastereoisomers are a type of stereoisomers that have different configurations at some, but not all, of the chiral centers in a molecule. Unlike enantiomers, which are non-superimposable mirror images of each other, diastereoisomers are not mirror images and often have distinct physical and chemical properties. For instance, they can have different boiling points, melting points, and solubilities, making them easier to separate than enantiomers.

When analyzing the complexity of diastereoisomers, it's essential to consider the number of chiral centers in a molecule. The formula \(2^n\), where \(n\) is the number of chiral centers, helps to calculate the maximum number of possible stereoisomers, which includes both enantiomers and diastereoisomers. As we learned from the given exercise, 4-methyl-1,2-cyclohexanediol, with two chiral centers, can have up to four stereoisomers. Out of these, there may be two pairs of enantiomers or a combination of enantiomers and diastereoisomers.

Chiral Centers

Chiral centers, also known as stereocenters or asymmetric centers, are atoms in a molecule that are attached to four different substituents, leading to non-superimposable mirror images called enantiomers. A molecule can have one or more chiral centers, and the presence of multiple chiral centers adds complexity to the molecule's stereochemistry.

Identifying chiral centers is crucial for understanding the behavior of molecules, especially in organic chemistry, where chirality plays a significant role in the activity and properties of organic compounds. The molecule of 4-methyl-1,2-cyclohexanediol contains two chiral centers, which are the basis for its potential to form four stereoisomers. Each chiral center has two possible configurations, 'R' or 'S', based on the Cahn-Ingold-Prelog priority rules, which define how substituents are ranked around a chiral center.

Optical Activity

Optical activity refers to the ability of a molecule to rotate the plane of polarization of plane-polarized light. This property is observed in compounds that contain chiral centers. A substance that can rotate the plane of polarized light is described as optically active, and the direction of rotation determines if the compound is 'dextrorotatory' (rotating clockwise) or 'levorotary' (rotating counter-clockwise).

The optical activity is measured using a polarimeter, and the degree of rotation is dependent on several factors, including the concentration of the chiral compound, the length of the light path through the sample, and the wavelength of light used. Stereochemistry plays a critical role in this property because the arrangement of atoms in the molecule determines how it interacts with light. In our exercise, the optically active products of oxidation with osmium tetroxide demonstrate that the presence of chiral centers in a molecule directly leads to optical activity.