Question

(a) What product would be formed if the reaction of cis- 4-bromocyclohexanol with \(\mathrm{OH}^{-}\) proceeded with inversion? (b) Without inversion? (c) Is it always necessary to use optically active compounds to study the stereochemistry of substitution reactions?

Short answer

(a) If the reaction proceeds with inversion, the product formed would be trans-4-cyclohexanol. (b) Without inversion, the product formed would be cis-4-cyclohexanol. (c) No, it is not always necessary to use optically active compounds to study the stereochemistry of substitution reactions, but they can provide valuable insights into reaction mechanisms and stereochemical outcomes.

Step-by-step solution

Draw the cis-4-bromocyclohexanol structure and label the chiral carbon (Carbon 4) with an asterisk. The compound has a bromine atom and a hydroxyl group on carbon 4, and both atoms are on the same side (cis configuration) of the cyclohexane ring. #Step 2: Reaction with Inversion#

If the reaction of cis-4-bromocyclohexanol proceeds with inversion, an \(\mathrm{OH}^{-}\) ion replaces the bromine atom from the opposite side of where it is attached. In this case, the product formed is trans-4-cyclohexanol. This is because the hydroxyl group and the hydrogen, initially cis to the bromine atom, would now be on opposite sides of the ring. #Step 3: Reaction without Inversion#

If the reaction occurs without inversion, the \(\mathrm{OH}^{-}\) ion attacks and replaces the bromine atom without changing the stereochemistry at the chiral center. In this case, the product remains cis-4-cyclohexanol, as both the hydroxyl group and the hydrogen remain on the same side of the cyclohexane ring. #Step 4: Determining Necessity of Optically Active Compounds for Studying Stereochemistry of Substitution Reactions#

It is not always necessary to use optically active compounds to study the stereochemistry of substitution reactions. However, using optically active compounds can provide valuable insights into the reaction mechanism. By observing how the stereochemistry of the starting material affects the products, conclusions about the mechanism and whether or not inversion has occurred can be drawn. In summary, the reaction of cis-4-bromocyclohexanol with \(\mathrm{OH}^{-}\) will yield trans-4-cyclohexanol if it proceeds with inversion, and cis-4-cyclohexanol without inversion. While using optically active compounds is not always necessary to study the stereochemistry of substitution reactions, it can provide valuable insights into the reaction mechanism and the stereochemical outcomes.

Key concepts

Inversion of Configuration

Understanding the inversion of configuration is crucial when exploring the stereochemical outcomes of substitution reactions. This concept comes into play when a molecule undergoes a type of reaction where a substituent is replaced by another. Most commonly, this occurs in bimolecular nucleophilic substitution reactions, symbolized as SN2 mechanisms.

In an SN2 reaction, the attacking nucleophile approaches the central carbon atom from the opposite side of the leaving group, leading to a 'backside attack'. As a result, the spatial arrangement of the atoms or groups attached to this carbon is inverted like an umbrella flipping inside out on a windy day. For instance, if a molecule initially has a configuration where substituents are arranged in a 'right hand' (R) fashion, the inversion will result in a 'left hand' (L) arrangement.

Take the textbook problem of cis-4-bromocyclohexanol reacting with a hydroxide ion. If this substitution occurs with inversion, the product would be trans-4-cyclohexanol. The hydroxyl group takes the place of the leaving bromine atom, but now it positions itself on the opposite side of the cyclohexane ring, creating a trans configuration.

Cis-Trans Isomerism

Cis-trans isomerism is a form of stereoisomerism that is particularly relevant in the context of cyclic compounds and alkenes. This type of isomerism arises when two substituents are either on the same side (cis) or on opposite sides (trans) of a ring or double bond.

In the context of cyclic compounds like cyclohexanol, the difference between cis and trans isomers can significantly influence the physical and chemical properties of the substance. The 'cis' denotes a configuration where functional groups are on the same side of the cyclohexane ring, while 'trans' indicates they are on opposite sides. For example, trans-4-cyclohexanol will have a higher melting point and may be less soluble than its cis counterpart due to differences in polarity and molecular packing.

The exercise provided illustrates this concept by comparing the outcomes of a substitution reaction with and without inversion. With inversion of configuration, the hydroxyl group ends up on the opposite side of where the bromine was, thereby converting a cis-4-bromocyclohexanol into a trans-4-cyclohexanol.

Optically Active Compounds

Optically active compounds are molecules that have the ability to rotate the plane of polarized light. This optical activity is a consequence of chirality — a property of a substance whereby its mirror image is not superimposable onto itself. In simpler terms, optically active compounds are like your hands; one is the mirror image of the other, yet they cannot be perfectly aligned on top of each other.

Chirality is a ubiquitous concept in stereochemistry and is important for understanding how molecules interact with biological systems. The inclusion of optically active compounds in studies of substitution reactions, particularly when concerned with drugs and biologically active molecules, is instrumental for determining the mechanism and the effects of the reaction outcome on biological activity.

While the study of optically active compounds is not always necessary to explore basic stereochemical concepts, as highlighted in the exercise, it provides a deeper level of understanding, especially when examining complex biological systems or synthetic pharmaceuticals. In conclusively establishing the stereochemistry associated with a substitution reaction, the use of optically active starting materials can be very informative.