Question

Which reaction in each of the following pairs would you expect to be faster? (a) The \(\mathrm{S}_{\mathrm{N}} 2\) displacement by \(\mathrm{I}^{-}\) on \(\mathrm{CH}_{3} \mathrm{Cl}\) or on \(\mathrm{CH}_{3} \mathrm{OTos}\) (b) The \(\mathrm{S}_{\mathrm{N}}^{2}\) displacement by \(\mathrm{CH}_{3} \mathrm{CO}_{2}^{-}\) on bromoethane or on bromocyclohexane (c) The \(\mathrm{S}_{\mathrm{N}}\) 2 displacement on 2 -bromopropane by \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{O}^{-}\) or by CN \(^{-}\) (d) The \(\mathrm{S}_{\mathrm{N}} 2\) displacement by \(\mathrm{HC}=\mathrm{C}^{-}\) on bromomethane in benzene or in acetonitrile

Short answer

(a) CH3OTos, (b) Bromoethane, (c) CN-, (d) Acetonitrile.

Step-by-step solution

Understanding S_N2 Mechanism

The S_N2 reaction is a bimolecular nucleophilic substitution reaction. It involves a single step where the nucleophile attacks the electrophile, causing the leaving group to leave. The reaction rate depends largely on the concentration of both the substrate and the nucleophile, steric hindrance, and the strength of the nucleophile.

Comparing Leaving Groups

(a) Compare \(CH_3Cl\) and \(CH_3OTos\). Tosylate (OTos) is a better leaving group compared to chloride (Cl) due to its larger size and ability to stabilize the negative charge. Therefore, the S_N2 displacement by \(I^-\) on \(CH_3OTos\) is faster.

Considering Electrophile Structure

(b) Bromoethane vs. Bromocyclohexane: Bromoethane is less hindered than bromocyclohexane. The reaction is faster with bromoethane because S_N2 reactions are slower with more steric hindrance.

Evaluating Nucleophile Strength

(c) Compare nucleophiles \(CH_3CH_2O^-\) and CN \(^-\). CN \(^-\) is a stronger nucleophile due to its ability to donate a lone pair of electrons more effectively. Therefore, the S_N2 displacement on 2-bromopropane by CN \(^-\) will be faster.

Solvent Effects on Reaction Rate

(d) Benzene vs. Acetonitrile: Acetonitrile is a polar aprotic solvent, which increases the nucleophilicity of \(HC=C^-\), promoting the S_N2 reaction. In contrast, benzene is nonpolar and less effective in facilitating the reaction, making the reaction faster in acetonitrile.

Key concepts

Nucleophile Strength

Nucleophiles are the key players in \( ext{S}_N2\) reactions. They are atoms or molecules rich in electrons, making them eager to donate their extra electrons to form new bonds. Nucleophile strength is determined by several factors, including:

• The availability of a lone pair of electrons for bonding.
• The size of the nucleophile, affecting how easily it can approach and react with the substrate.
• The basicity of the nucleophile, which is often directly related to its strength in solution.

For instance, in an \( ext{S}_N2\) reaction scenario, \(CN^-\) is a highly effective nucleophile. This is because it not only holds a lone pair of electrons ready for donating but also features a strong ability to polarize, enhancing its attack on the substrate. \(CH_3CH_2O^-\), being bulkier and less electronically excited compared to \(CN^-\), acts as a weaker nucleophile. Thus, in any competitive \( ext{S}_N2\) context, \(CN^-\) would usually ensure faster reaction rates than \(CH_3CH_2O^-\), emphasizing its superior nucleophilic strength.

Leaving Groups

In \( ext{S}_N2\) reactions, a leaving group is the part of the substrate that exits once the nucleophile forms a new bond. The efficiency of a \( ext{S}_N2\) reaction often hinges on the quality of the leaving group. Key qualities of good leaving groups include:

• Stability once free from the substrate.
• Ability to stabilize the negative charge they acquire post their departure.

Take tosylate (OTos) for example; it stands out as a superior leaving group compared to chloride (Cl). It is highly stable when separated, efficiently spreading out any negative charge due to its large surface area and resonance stabilization. Thus, in reactions involving \( ext{S}_N2\), substrates with OTos as the leaving group tend to undergo faster reactions compared to those with Cl, given equally favorable conditions. This highlights the importance of choosing substrates with strong leaving groups to optimize \( ext{S}_N2\) reaction speeds.

Steric Hindrance

Steric hindrance plays a vital role in determining the rate of \( ext{S}_N2\) reactions. This term refers to the spatial congestion around the reactive center of the substrate, which could impede the approaching nucleophile from effectively attacking the electrophile. Key points to consider include:

• Less crowded substrates are more prone to fast reactions.
• Bulky groups near the reaction site slow down the process.

Consider bromoethane versus bromocyclohexane: bromoethane offers a less cluttered environment for the nucleophile, allowing swifter nucleophilic attacks compared to the bulkier bromocyclohexane. Thus, steric hindrance significantly influences the success rate of the reaction, with less hindrance ensuring a faster reaction process.

Solvent Effects

Solvents can dramatically alter the outcome of \( ext{S}_N2\) reactions, primarily by influencing nucleophile strength and reaction kinetics. Different solvents will have different effects:

• Polar aprotic solvents enhance nucleophilicity and reaction speed.
• Nonpolar solvents offer less support for the nucleophilic attack.

Considering solvents like acetonitrile and benzene, acetonitrile, known for its polar and aprotic characteristics, accelerates the \( ext{S}_N2\) reactions by enhancing the nucleophilicity of species like \(HC=C^-\). Conversely, benzene, largely nonpolar, doesn't significantly aid the nucleophile’s performance. Hence, reactions tend to proceed more rapidly in polar aprotic solvents such as acetonitrile compared to their nonpolar counterparts like benzene.