Question

A sample of 1 -chloro-1-phenylethane with an \([\alpha]_{25}^{\mathrm{D}}\) of \(-94.8^{\circ}\) is reacted with \(\mathrm{NH}_{3}\) in methanol/water solvent. The major substitution product of the reaction is 1-phenyl-1-ethylamine with an \([\alpha]_{25}^{D}\) of \(-8.6^{\circ} .\) Given that optically pure (R) 1-chloro-1-phenylethane has a specific rotation of \(-109.0^{\circ}\) and that optically pure (R) 1-phenyl-1-ethylamine has a specific rotation of \(+39.3^{\circ} .\) Which of the following statements best describes this reaction? (A) Net inversion \(25 \%\) with \(75 \%\) racemization \(-\mathrm{S}_{\mathrm{N}} 1\) mechanism (B) Net inversion \(12 \%\) with \(88 \%\) racemization \(-\mathrm{S}_{\mathrm{N}} 1\) mechanism (C) Net inversion \(75 \%\) with \(25 \%\) racemization \(-\mathrm{S}_{\mathrm{N}} 2\) mechanism (D) Net inversion \(12 \%\) with \(88 \%\) racemization \(-\mathrm{S}_{\mathrm{N}} 2\) mechanism

Short answer

The best statement that describes this reaction is (C) Net inversion 75% with 25% racemization - SN2 mechanism.

Step-by-step solution

Calculate enantiomeric excess (ee) of the reactant and product

To compare the specific rotations of the reactant and the product, we need to calculate the enantiomeric excess (ee) for both. The formula for enantiomeric excess is: \(ee = \frac{\text{observed specific rotation}}{\text{specific rotation of the pure enantiomer}} \times 100\%\) For the reactant, 1-chloro-1-phenylethane, \(ee_{\text{reactant}} = \frac{-94.8}{-109.0} \times 100\% ≈ 87\%\) For the product, 1-phenyl-1-ethylamine, \(ee_{\text{product}} = \frac{-8.6}{39.3} \times 100\% ≈ -22\%\) (The negative sign indicates the sample is a mixture of R and S enantiomers.)

Calculate the net inversion

Net inversion can be calculated using the enantiomeric excess of the reactant and product as follows: Net inversion = \(|ee_{\text{reactant}} - ee_{\text{product}}|\) Net inversion = \(|87 - (-22)| = 109\%\)

Determine the extent of racemization

Since racemization is the process of converting enantiomers into a racemic mixture, the racemization percentage can be calculated by subtracting the net inversion from 100%. Racemization = \(100\% - \text{net inversion} = 100\% - 109\% = -9\%\) (The negative sign indicates excess inversion rather than racemization.)

Identify the best statement

Now, let's analyze the given statements: (A) Net inversion 25% with 75% racemization - SN1 mechanism (B) Net inversion 12% with 88% racemization - SN1 mechanism (C) Net inversion 75% with 25% racemization - SN2 mechanism (D) Net inversion 12% with 88% racemization - SN2 mechanism Based on our calculations, the net inversion in the reaction is 109%, and racemization is -9%. The statement that best matches our calculations is (C) Net inversion 75% with 25% racemization - SN2 mechanism. Although the calculated percentages do not match exactly, this option is the closest to our results, indicating that this reaction follows an SN2 mechanism with a high extent of inversion and a low extent of racemization.

Key concepts

Enantiomeric Excess

Enantiomeric excess (ee) is a crucial concept in the realm of stereochemistry and chiral molecules. It provides a measure of the purity of an enantiomer in a mixture, as compared to its mirror image.

Put simply, it refers to the excess of one enantiomer over the other expressed in percentage terms. Enantiomeric excess is calculated using the formula:
\(ee = \frac{\text{observed specific rotation}}{\text{specific rotation of the pure enantiomer}} \times 100\%\).

In our textbook example, the reaction showed that the starting material and the product had different degrees of enantiomeric excess, which suggests a change in the stereochemistry during the reaction. Understanding this change is pivotal in determining the reaction mechanism at play. The concept of enantiomeric excess is also intertwined with optical purity and is especially relevant in the pharmaceutical industry where the efficacy and safety of a drug can depend on the enantiomeric composition of a compound.

Optical Activity in Organic Chemistry

Optical activity is a manifestation of chirality in molecules. A substance that can rotate the plane of polarized light is described as optically active. The rotation can be either to the left (levorotatory) or right (dextrorotatory), indicated by negative and positive angles, respectively.

The specific rotation, denoted as \([\alpha]\), provides a quantitative measure of a compound's optical activity under specific conditions. In the provided exercise, the optical activity was used to assess the stereochemical outcomes of a substitution reaction.

By examining the specific rotations given for pure enantiomers and reaction mixtures, students can gain insights into the molecular changes happening during a chemical reaction. This information is crucial, especially when differentiating between SN1 and SN2 reaction pathways, where each mechanism has distinct consequences on the compound's stereochemistry.

Racemization

Racemization is a process where an optically active compound, possessing enantiomeric excess, is converted into a racemic mixture—a 1:1 mixture of enantiomers with no net optical activity. It occurs when a reaction allows for the interconversion of enantiomers.

In stereoselective reactions, the degree of racemization can indicate whether the reaction followed an SN1 or SN2 mechanism. SN1 reactions often lead to higher levels of racemization, due to the formation of a planar carbocation intermediate which can be attacked from either side. Contrastingly, SN2 reactions are characterized by backside attacks that tend to preserve or invert the configuration, resulting in less racemization.

The exercise improvement lies in understanding that net inversion calculated from enantiomeric excess helps in determining the extent of racemization, and thus, the reaction mechanism. If net inversion is high and racemization is low, as in the textbook example, it points towards an SN2 mechanism, contrary to an SN1 mechanism which would yield more racemization.

Stereochemistry

Stereochemistry involves the study of the spatial arrangement of atoms within molecules and how this arrangement affects the physical and chemical properties of those molecules. It is an essential aspect of organic chemistry, especially when dealing with chiral molecules or stereoisomers.

Considering the SN1 and SN2 mechanisms, stereochemistry plays a pivotal role. These mechanisms differ not only in their mechanistic steps but also in their stereochemical outcomes. The SN1 mechanism typically results in a racemic mixture due to the generation of a planar intermediate, whereas the SN2 mechanism usually leads to inversion of configuration due to backside nucleophilic attack.

Deciphering the stereochemical course of the reaction as it goes from reactants to products helps chemists understand and predict the behavior of molecules in biological systems and in the development of pharmaceuticals. In the provided textbook exercise, analyzing stereochemistry helps in solving the puzzle of whether the reaction went through an SN1 or SN2 pathway, which has substantial implications for synthesis and product formation.