Question

Acid-catalyzed hydrolysis of a 1,2 -epoxycyclohexane produces a transdiaxial 1,2 -diol. What product would you expect to obtain from acidic hydrolysis of cis-3-tert-butyl-1,2-epoxycyclohexane? (Recall that the bulky tert-butyl group locks the cyclohexane ring into a specific conformation.) (a) Draw the epoxide, showing stereochemistry. (b) Draw and name the product, showing stereochemistry. (c) Is the product chiral? Explain. (d) Is the product optically active? Explain.

Short answer

The product is 3-tert-butyl-cyclohexane-1,2-diol, trans-diols are not chiral and not optically active.

Step-by-step solution

Draw the Epoxide

Start by drawing the structure for cis-3-tert-butyl-1,2-epoxycyclohexane. The cyclohexane ring should be in its chair conformation. The epoxide group is attached at positions 1 and 2, creating a bridge across two carbon atoms on the ring. Make sure to place the tert-butyl group in the equatorial position at carbon 3 since it's bulky. Both the any substituents involved in the epoxide (like hydrogen, if they are explicit) on the ring are directed either both up or both down representing 'cis' stereochemistry.

Predict the Product from Hydrolysis

During the acid-catalyzed hydrolysis of the epoxide, the epoxide ring opens. The nucleophile (water) will attack the less substituted carbon (position 1 here) of the epoxide in a mechanism that opens the ring to form a 1,2-diol. This ring opening occurs such that the nucleophile attacks from the opposite side to avoid any steric hindrance caused by groups in axial positions on the cyclohexane. Therefore, the hydroxyl groups (-OH) will be trans to each other.

Draw and Name the Product

The product will be 3-tert-butyl-cyclohexane-1,2-diol. Draw this structure, ensuring the stereochemistry: the hydroxyl groups at positions 1 and 2 should be trans to each other. Typically, in the chair conformation, one hydroxyl group will be axial and the other equatorial to achieve trans-diol configuration.

Determine if the Product is Chiral

To determine chirality, check if the molecule has a plane of symmetry. In 3-tert-butyl-cyclohexane-1,2-diol, the tertiary butyl group creates significant steric hindrance that forces the cyclohexane into a specific conformation, however, if the diol is trans and symmetrical, the molecule may not be chiral. In this case, the overall molecule is not chiral due to the symmetry introduced by the identical -OH groups.

Determine if the Product is Optically Active

Optical activity depends on chirality. Since we have concluded the product is not chiral due to a plane of symmetry, it is not optically active. Chiral molecules without internal planes of symmetry are optically active, and since this molecule can be superimposed on its mirror image, it does not meet that criteria.

Key concepts

Acid-Catalyzed Reaction

An acid-catalyzed reaction involves the use of an acid to speed up a chemical reaction, usually by providing a more favorable pathway with lower activation energy. In the case of epoxide hydrolysis, an acid, such as a proton donor, facilitates the opening of the strained three-membered epoxide ring. This protonation increases the electrophilicity of the epoxide, making it easier for a nucleophile such as water to attack one of the carbons participating in the ring.

The mechanism typically follows these steps:

• Protonation: The acidic condition causes the epoxide oxygen to accept a proton, enhancing its positive charge.
• Nucleophilic attack: Water acts as a nucleophile and attacks the carbon atom that has less steric hindrance or substitution, leading to the opening of the ring.
• Ring opening: The epoxide ring opens to form a diol, which means two hydroxyl (-OH) groups will end up on adjacent carbons.

This reaction is crucial in organic synthesis for converting epoxides to valuable diol compounds, which are useful intermediates in the synthesis of various chemicals.

Cyclohexane Stereochemistry

Cyclohexane rings can adopt conformations that minimize steric strain and torsional strain, with the chair conformation being the most stable. In chair conformation, the ring's carbons are not all in the same plane. This allows substituents to be positioned in either axial (up and down) or equatorial (in the plane of the ring) positions.

• Axial positions are more crowded because they are aligned with the overall axis of the ring.
• Equatorial positions are less hindered and are often preferred by bulky substituents, such as a tert-butyl group, which stabilizes the cyclohexane ring by reducing steric hindrance.

In this exercise, we deal with the stereochemistry of a cis-epoxide in a cyclohexane ring. To preserve stability, the tert-butyl group is placed in the equatorial position. When the epoxide undergoes hydrolysis, the trans configuration of the resulting diol ensures that one hydroxyl group is axial and one is equatorial, further optimizing stability.

Chiral Molecules

Chirality in molecules arises when a molecule cannot be superimposed on its mirror image. Such molecules have a chiral center, which typically is a carbon with four different substituents. Chiral molecules exhibit enantiomeric forms—deeply relating chemistry to optical properties.

• To check for chirality, look for a plane of symmetry. If a plane can divide the molecule into two symmetrical halves, it’s considered achiral.
• If a molecule has no internal plane of symmetry and four different groups on a central atom, it’s chiral.

In the solution provided, the molecule 3-tert-butyl-cyclohexane-1,2-diol is analyzed for chirality. The identical hydroxyl groups contribute to a plane of symmetry within the molecule. Because of this symmetry, the molecule is considered achiral. Despite having a stereocenter, the diol product does not meet the criteria to be chiral due to its symmetrical nature.

Optical Activity

Optical activity refers to a molecule's ability to rotate plane-polarized light. This property is intrinsically tied to the chirality of a compound. If a molecule is chiral, it typically shows optical activity because such a molecule exists in two enantiomeric forms that can rotate light in different directions.

• Optically active compounds lack internal planes of symmetry, which ensure that their mirror images can’t be superimposed.
• Molecules that are symmetric, like meso compounds, do not exhibit optical activity, even if they contain stereogenic centers.

In the case of 3-tert-butyl-cyclohexane-1,2-diol, despite the presence of an asymmetric carbon due to the hydroxyl groups, the overall symmetry introduced by these groups results in an achiral molecule. Consequently, this molecule is not optically active because it can be superimposed on its mirror image, demonstrating that identical planes of symmetry prevent the rotation of plane-polarized light.