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 \(\mathrm{CH}_{3}\) 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 \(\mathrm{CN}^{-}\) (d) The \(S_{N} 2\) displacement by \(H S^{-}\) on bromomethane in toluene or in acetonitrile

Short answer

(a) \(\mathrm{CH}_{3} \mathrm{OTos}\); (b) Bromoethane; (c) \(\mathrm{CN}^{-}\); (d) Acetonitrile.

Step-by-step solution

Analyze Structure and Leaving Group for Pair (a)

In the first pair, we compare the substrates \(\mathrm{CH}_{3} \mathrm{Cl}\) and \(\mathrm{CH}_{3}\mathrm{OTos}\). The tosylate group (OTos) is a better leaving group than chlorine, as it is more stable when separated from the organic moiety. Therefore, the \(S_N2\) reaction on \(\mathrm{CH}_{3}\mathrm{OTos}\) will proceed faster.

Consider the Reactivity of Different Substrates for Pair (b)

Compare the bromoethane and bromocyclohexane. Bromoethane is a primary alkyl halide which is less hindered, making it easier for the nucleophile \(\mathrm{CH}_{3}\mathrm{CO}_2^-\) to attack than on bromocyclohexane, a secondary halide with more steric hindrance. Thus, the reaction with bromoethane is faster.

Compare Nucleophiles for Pair (c)

We need to compare the nucleophiles \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{O}^{-}\) and \(\mathrm{CN}^{-}\). \(\mathrm{CN}^{-}\) is a stronger nucleophile due to its higher charge density and is less sterically hindered compared to ethoxide. Hence, the reaction with \(\mathrm{CN}^{-}\) will be faster on 2-bromopropane.

Consider Solvent Effects for Pair (d)

The solvents toluene and acetonitrile differ in polarity. Acetonitrile is a polar aprotic solvent, which enhances the nucleophilicity of \(HS^-\) compared to toluene, a non-polar solvent. Thus, the reaction proceeds faster in acetonitrile.

Key concepts

Nucleophile Reactivity

In an SN2 reaction, the nucleophile plays a crucial role in determining the reaction rate. The strength of a nucleophile is affected by several factors, including charge, electronegativity, and sterics. In general, a negatively charged nucleophile will be stronger than a neutral one because it has a higher electron density. For example, in the given pair \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{O}^{-}\) and \(\mathrm{CN}^{-}\), \(\mathrm{CN}^{-}\) is a stronger nucleophile than ethoxide due to its higher charge density and relative lack of steric hindrance. This allows it to attack the electrophile more effectively, leading to a faster reaction.
It's also important to consider the size of the atom that holds the charge. Bigger atoms can distribute the charge more easily, which usually makes them better nucleophiles in protic solvents. However, in aprotic solvents, smaller, more basic nucleophiles are often more reactive as they are less solvated.

Leaving Group Ability

The leaving group in an SN2 reaction must be able to leave the substrate, creating space for the nucleophile to attack. Good leaving groups are typically weak bases, as they can stabilize the negative charge after departure. In the example given in pair (a), the tosylate \(\mathrm{OTos}\) is a much better leaving group than chloride \(\mathrm{Cl}^{-}\).
Why is tosylate better, you might ask? It's because tosylate can stabilize the negative charge over a larger area due to resonance within its structure. Conversely, a halide like chloride has no resonance and cannot stabilize the charge as effectively. When the leaving group can leave easily, the reaction proceeds faster.

Steric Hindrance

Steric hindrance refers to the physical obstruction a nucleophile faces when approaching the electrophilic center. In SN2 reactions, steric effects play a significant role because the reaction occurs in a single step where the nucleophile directly displaces the leaving group. For example, in pair (b), you're comparing bromoethane and bromocyclohexane.
**Less Hindrance Equals Faster Reactions**
Bromoethane is a primary alkyl halide, meaning its electrophilic carbon is less surrounded by large groups, allowing nucleophiles easier access. Bromocyclohexane, on the other hand, has a secondary carbon, which is more crowded, making nucleophilic attack harder. This crowding slows down the reaction.

Solvent Effects in Reactions

The choice of solvent in SN2 reactions can drastically alter the reaction's pathway and speed. Solvents are categorized based on their ability to stabilize ions. Polar aprotic solvents like acetonitrile enhance the reactivity of nucleophiles by not forming strong interactions with them.
**Polar Aprotic are Game-Changers**
In pair (d), the solvent acetonitrile is polar aprotic, which means it can stabilize the substrate without stabilizing the nucleophile. This allows \(\mathrm{HS}^{-}\) to remain highly reactive, facilitating a faster reaction. Conversely, toluene is non-polar and doesn't provide such stabilization, which makes nucleophiles in such environments less reactive. Knowing the right solvent helps optimize reaction conditions.