Question

In a classic experiment in physical organic chemistry, \((R)-2\) -iodooctane was allowed to react (non-enzymatically) with a radioactive isotope of iodide ion, and the researchers monitored how fast the radioactive iodide was incorporated into the alkane (the rate constant of incorporation, \(\mathrm{k}_{i}\) ) and also how fast optical activity was lost (the rate constant of racemization, \(\mathrm{k}_{r}\) ). They found that the rate of racemization was, within experimental error, equal to twice the rate of incorporation. Discuss the significance of this result - what does it say about the actual mechanism of the reaction?

Short answer

Answer: The result implies that there are two separate reaction pathways in this experiment, with racemization being more favored compared to the incorporation step. The reaction mechanism most likely involves a two-step nucleophilic substitution followed by racemization.

Step-by-step solution

Understanding incorporation and racemization

Incorporation is a process in which a new atom or group of atoms is introduced within the structure of a molecule, leading to the formation of a new molecule or compound. In this case, the radioactive iodide ion is being incorporated into the alkane. Racemization is the process of converting an optically active compound (one that can rotate plane-polarized light) into an optically inactive compound, typically by transforming it into a racemic mixture (a 1:1 mixture of enantiomers). In the context of this experiment, racemization refers to the loss of optical activity as the \((R)-2\) -iodooctane reacts.

Analyze the given data

The researchers found that the rate of racemization \((\mathrm{k}_{r})\) is approximately equal to twice the rate of incorporation \((\mathrm{k}_{i})\). In other words, \(\mathrm{k}_{r} \approx 2\mathrm{k}_{i}\).

Interpret the significance of the rates

The fact that the rate of racemization is approximately twice the rate of incorporation suggests that there are two separate reaction pathways in this experiment. In one pathway, the iodide ion incorporates into the alkane forming a new product, while in the other pathway, racemization occurs as the initial \((R)-2\) -iodooctane compound converts into its enantiomer, with no incorporation of the iodide ion.

Discuss the reaction mechanism

Based on the information provided, we can deduce that this reaction most likely involves a two-step mechanism. In the first step, the \((R)-2\) -iodooctane undergoes a nucleophilic substitution (SN1 or SN2) with the radioactive iodide ion, leading to the formation of a new compound that incorporates the iodide ion and racemizing the alkane. In the second step, the racemized alkane can either proceed through another nucleophilic substitution pathway with iodide ion, thus incorporating another iodide ion and producing another racemized compound, or simply return to its original conformation via racemization without incorporating the iodide ion. The fact that the rate of racemization is approximately twice the rate of incorporation implies that the reaction has a preference for the pathway that causes racemization without incorporation of the iodide ion. This information leads us to conclude that the actual reaction mechanism involves a two-step nucleophilic substitution followed by racemization, with the racemization step being more favored compared to the incorporation step.

Key concepts

Racemization in Organic Chemistry

Racemization in organic chemistry refers to the process by which an optically active, chiral molecule is converted into an optically inactive mixture that has equal amounts of both left- and right-handed enantiomers—a racemic mixture.

When observing racemization in a laboratory setting, scientists track how a substance that can initially rotate plane-polarized light (show optical activity) gradually loses this ability. This loss of optical activity occurs because the mixture of enantiomers, which are mirror images of each other, rotate light in opposite directions, canceling each other's effect.

In the experiment involving (R)-2-iodooctane, the rate of racemization being double the rate of incorporation indicates a likelihood that for every incorporation event that generates a molecule with a new iodine, there are two events leading to the conversion of the molecule into its mirror image without incorporating new iodine. This implies the presence of an intermediate that can easily invert its configuration, leading to the formation of equal amounts of both enantiomers and resulting in a racemic mixture.

Rate Constant Monitoring

Rate constant monitoring is an essential technique in the study of chemical kinetics to understand the speed of a chemical reaction. The rate constant, symbolized by (mathrm{k}), is a proportional factor that quantifies the rate of a chemical reaction at a given temperature and for a specific reaction step.

In the example of the (R)-2-iodooctane reaction, scientists monitored two rate constants: the rate constant of incorporation (mathrm{k}_{i}), which measures how quickly the radioactive iodide is added to the molecule, and the rate constant of racemization (mathrm{k}_{r}), determining how fast the optical activity is lost.

The discovery that (mathrm{k}_{r} approx 2mathrm{k}_{i}) provides an insight into the reaction's mechanism. It suggests that the racemization step happens more frequently compared to the incorporation step, and this must be accounted for in any proposed reaction mechanism to accurately reflect the observed kinetics.

Optical Activity

Optical activity is a term used to describe the ability of a compound to rotate the plane of polarized light. This property is exhibited by chiral substances—molecules that are not superimposable on their mirror images, much like a pair of hands.

A compound can be optically active if it exists as one of two enantiomers, each rotating light in a specific direction, either to the left (levorotatory) or to the right (dextrorotatory). When equal amounts of both enantiomers are present, as is the case in a racemic mixture, their optical activities cancel each other out, and the overall solution becomes optically inactive.

The experiment with (R)-2-iodooctane illustrates this concept well. Initially, the pure enantiomer shows optical activity. As the reaction progresses and the racemization rate exceeds the incorporation rate, more of the opposite enantiomer is formed, leading to a decrease in optical activity, which eventually disappears when the mixture becomes racemic.