Question

A sample of \((R)-\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}\left(\mathrm{CH}_{3}\right) \mathrm{Cl}\) reacts with \(\mathrm{CH}_{3} \mathrm{O}^{-}\) in dimethyl sulfoxide, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SO},\) a convenient solvent for organic reactions. The resulting solution is optically active. (a) Write the formula of the product. (b) By which mechanism does this nucleophilic substitution reaction occur?

Short answer

The formula of the product is \((R)-\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}\left(\mathrm{CH}_{3}\right) \mathrm{OCH_{3}}\). This nucleophilic substitution reaction occurs through an SN2 mechanism.

Step-by-step solution

Writing the Product's Formula

The nucleophile in this case is methoxide (\(\mathrm{CH}_{3} \mathrm{O}^{-}\)). When the nucleophone performs a nucleophilic substitution on the given sample, it will replace the Chlorine atom attached to the chiral carbon. Hence, the product is \((R)-\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}\left(\mathrm{CH}_{3}\right) \mathrm{OCH_{3}}\) because Methoxide (\(\mathrm{CH}_{3} \mathrm{O}^{-}\)) replaces Chlorine.

Determining the Mechanism

We need to identify whether this is an SN1 or SN2 reaction. In an SN1 reaction, the stereochemistry (R or S configuration) of the product can be inverted or retained because it passes through a planar intermediate step. However, it is given that the resulting solution is optically active. Thus, the chiral carbon must have retained its configuration. The mechanism is therefore an SN2 reaction, during which the nucleophile attacks from the back of the carbon atom bonded to the leaving group (Chlorine, in this case), causing an inversion in configuration. In this circumstance, however, because the nucleophile and leaving group are both (R)-configured, the inversion leads to another (R)-configured product, and the optical activity of the solution remains unchanged.

Key concepts

SN1 and SN2 Mechanisms

Understanding the landscape of nucleophilic substitution reactions begins with differentiating the SN1 and SN2 mechanisms, two pivotal processes in organic chemistry.

In SN2 mechanisms, the characterizing feature is the simultaneous bond-breaking and bond-forming that occurs in one concerted step. This 'bimolecular' reaction depends heavily on the concentration of both the substrate and the nucleophile. It requires a strong, unhindered nucleophile to effectively displace the leaving group. A classic indication of an SN2 reaction is the inversion of stereochemistry at the chiral center, often compared to an 'umbrella flipping inside out' during a windy storm.

On the other hand, SN1 reactions proceed through two distinct steps. The first step is the formation of a carbocation intermediate, which is planar and thus susceptible to attack from either side. This results in a mixture of retention and inversion of stereochemistry, often leading to racemization in chiral centers. The rate of SN1 reactions is dependent only on the concentration of the substrate, rendering it 'unimolecular'. Factors favoring SN1 include a stable carbocation intermediate and a polar solvent.

By evaluating aspects such as the solvent type, the structure of the substrate, and the nature of the nucleophile and leaving group, chemists can often predict which mechanism will dominate in a nucleophilic substitution reaction.

Optical Activity

Optical activity offers a window into the structural orientation of molecules, specifically involving chirality. A compound is considered optically active if it can rotate the plane of polarized light, a property measured using a polarimeter.

This phenomenon arises from the presence of chiral centers within a molecule, leading to two non-superimposable mirror images known as enantiomers. Each enantiomer will rotate polarized light to an equal degree but in opposite directions, a property known as specific rotation. For instance, the designation of (R) or (S) correlates with the direction in which enantiomers rotate light - either to the right (dextrorotatory) or to the left (levorotatory).

In the context of nucleophilic substitution reactions, the preservation of optical activity post-reaction can signal that the stereochemistry of the chiral center was maintained. In the case of the exercise provided, the retention of optical activity after the reaction implies the SN2 mechanism, where the stereospecific 'backside attack' leads to the preservation of the (R) configuration, even though the inversion of configuration is typically expected.

Chiral Carbons

Chiral carbons are the cornerstone of molecular asymmetry in organic chemistry. A carbon atom becomes chiral when it is attached to four different substituents, creating an environment where it has non-superimposable mirror images, much like human hands.

These chiral centers are liable for the optical activity of organic molecules. When light passes through a solution containing a chiral molecule, the differing spatial arrangements of the atoms cause the light to rotate. The importance of chirality extends beyond optical activity; it plays a crucial role in the biological activity of molecules, as enzymes and receptors often distinguish between different enantiomers.

In any chemical reaction involving chiral molecules, it's essential to consider the fate of the chiral centers. As indicated in the exercise, the nucleophilic substitution at a chiral center retains the (R) configuration in an SN2 reaction, unexpectedly maintaining the solution's optical activity. This outcome underlines the nuance in predicting reactions involving chiral centers, as it may not always result in an inversion of configuration typically expected in SN2 reactions.