Question

\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Br}+\mathrm{KI} \stackrel{\text { acetone }}{\longrightarrow} \mathrm{C}_{2} \mathrm{H}_{5}-\mathrm{I}+\mathrm{KBr} \quad \rightarrow(\mathrm{I})\) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{Br}+\mathrm{KI} \stackrel{\text { acetone }}{\longrightarrow}\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{I}+\mathrm{KBr} \quad \rightarrow(\mathrm{II})\) Reaction (II) is much slower than reaction (I) because (a) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}\) is sparingly soluble in acetone. (b) (I) follows \(\mathrm{S}_{\mathrm{N}} 1\) and (II) follows \(\mathrm{S}_{\mathrm{N}} 2\) mechanism. (c) (I) follows \(\mathrm{S}_{\mathrm{N}} 2\) and (II) follows \(\mathrm{S}_{\mathrm{N}} 1\) mechanism. (d) steric hindrance in the case of reaction (II).

Short answer

Answer: Reaction (II) is slower than reaction (I) due to steric hindrance caused by the bulky tert-butyl group in (CH3)3CBr, which makes the SN1 mechanism more favorable, leading to a slower reaction rate compared to reaction (I). In reaction (I), the primary alkyl halide, C2H5Br, favors the faster SN2 mechanism.

Step-by-step solution

Identify Key Information About the Reactions

We have two reactions involving alkyl halides with the same reactants. The difference between the reactions lies in their organic reactants (C2H5Br and (CH3)3CBr). Reaction (I) involves ethyl bromide (C2H5Br) as the alkyl halide, while reaction (II) involves tert-butyl bromide ((CH3)3CBr) as the alkyl halide.

Comparison of Alkyl Halides Reactivity

Ethyl bromide, as a primary alkyl halide, can follow both the SN1 and SN2 mechanisms, but in general, SN2 mechanisms are faster for primary alkyl halides. Tert-butyl bromide, as a tertiary alkyl halide, can undergo both SN1 and SN2 mechanisms as well, but the presence of bulky substituents around the carbon makes it more favorable for SN1 mechanism, which is generally slower than SN2.

Evaluating the Reasons

Now, let's evaluate the options given: (a) Solubility in acetone is not relevant as both reactions are taking place in the same solvent, acetone. (b) As explained in Step 2, primary alkyl halides favor SN2 while tertiary alkyl halides favor SN1. This statement is incorrect. (c) This statement is opposite to the one explained in Step 2, so it's incorrect as well. (d) The steric hindrance in the case of reaction (II) is due to the bulky (CH3)3C group, which makes SN1 more favorable and slows down the reaction rate.

Choose the Correct Reason

The correct option for the reason why reaction (II) is slower than reaction (I) is (d) steric hindrance in the case of reaction (II). This steric hindrance results from the bulky tert-butyl group in (CH3)3CBr, which makes SN1 mechanism more favorable, leading to a slower reaction rate compared to reaction (I) where the primary alkyl halide, C2H5Br, favors the faster SN2 mechanism.

Key concepts

SN1 and SN2 Mechanisms

The SN1 and SN2 are two primary mechanisms by which alkyl halides can react. Understanding these mechanisms is crucial to comprehending how these reactions proceed and predict which reaction types will dominate in different scenarios.

In the SN2, or bimolecular nucleophilic substitution, reaction speed is dependent on the concentration of both the substrate (the alkyl halide) and the nucleophile. This mechanism involves a single concerted step where the nucleophile attacks the electrophilic carbon, displacing the leaving group, in this case, the halide, and resulting in an inversion of the chiral center. As such, these reactions are generally faster for primary alkyl halides due to less steric hindrance, which enables the nucleophile to access the electrophilic carbon atom more easily.

By contrast, the SN1, or unimolecular nucleophilic substitution, involves two steps. The first is the slow dissociation of the alkyl halide to form a carbocation intermediate, followed by the rapid attack of the nucleophile. The rate of SN1 reactions is only dependent on the concentration of the alkyl halide. Tertiary alkyl halides, such as tert-butyl bromide, tend to undergo SN1 reactions because the bulky groups stabilize the carbocation intermediate through hyperconjugation and inductive effects.

Steric Hindrance

Steric hindrance is a concept which refers to the prevention of chemical reactions by the physical size of groups within molecules. Larger groups can impede the access of reactants to a particular part of the molecule, notably the reactive center. This phenomenon is highly relevant in understanding why certain alkyl halides react more slowly than others.

In the context of nucleophilic substitution reactions, the presence of bulky substituents around the carbon atom that holds the leaving group can slow down or even prevent an SN2 mechanism. The nucleophile struggles to approach and react with the carbon center. In our example, the tert-butyl group in (CH_3)_3CBr presents significant steric hindrance, making it less reactive via the SN2 pathway. Instead, the SN1 mechanism becomes dominant because it does not involve a direct attack on the hindered carbon but rather a step-wise process starting with the formation of a carbocation.

Reaction Rate

The reaction rate in chemical reactions dictates how quickly reactants are transformed into products. Factors influencing reaction rates include concentration of reactants, temperature, presence of a catalyst, and the nature of the reactants themselves.

In the case of nucleophilic substitution reactions, the reaction rate can vary significantly between the SN1 and SN2 mechanisms. The SN2 mechanism's rate is proportional to the concentrations of both the alkyl halide and the nucleophile due to its bimolecular nature. Conversely, the SN1 reaction rate is only proportional to the concentration of the alkyl halide since it proceeds through a rate-determining step that forms a carbocation.

The rate of reaction is also influenced by steric and electronic factors. Steric hindrance slows reaction rates for SN2 reactions, while electron-donating groups attached to the alkyl halide can stabilize carbocations and increase the rate of SN1 reactions. In our exercise, the primary alkyl halide (C2H5Br) has a faster reaction rate through the SN2 pathway compared to the tertiary alkyl halide (CH3)3CBr, which proceeds more slowly through the SN1 pathway due to steric hindrance.