Question

In \(\mathrm{S}_{\mathrm{N}} 2\) reactions of alkyl halides, the order of reactivity is \(\mathrm{RI}>\mathrm{RBr}>\mathrm{RCl}>\mathrm{RF}\). Alkyl iodides are considerably more reactive than alkyl fluorides, often by factors as great as \(10^{6}\). All 1-halo-2,4-dinitrobenzenes, however, react at approximately the same rate in nucleophilic aromatic substitutions. Account for this difference in relative reactivities.

Short answer

Question: Explain the difference in reactivities of alkyl halides in SN2 reactions and the fact that all 1-halo-2,4-dinitrobenzenes have similar reaction rates in nucleophilic aromatic substitution reactions. Answer: The difference in relative reactivities for alkyl halides in SN2 reactions is due to the variation in carbon-halogen bond strength, with the order of reactivity being alkyl iodides > alkyl bromides > alkyl chlorides > alkyl fluorides. In 1-halo-2,4-dinitrobenzenes, the strong electron-withdrawing nitro groups have a leveling effect on the differences in carbon-halogen bond strength, resulting in similar reaction rates in nucleophilic aromatic substitution reactions.

Step-by-step solution

Review SN2 Mechanism

SN2 reactions involve a nucleophile (electron-rich species) attacking the carbon atom bonded to the halogen (the electrophilic center) and simultaneously breaking the carbon-halogen bond. The order of reactivity of alkyl halides is determined by the ease of breaking the carbon-halogen bond and electron donation ability of the halogen atom.

Analyze Reactivity of Alkyl Halides

In alkyl halides, the carbon-halogen bond strength decreases in the order of C-F > C-Cl > C-Br > C-I due to the increasing size and decreasing electronegativity of the halogen atom. This means that the carbon-iodine bond is the weakest, making alkyl iodides the most reactive in SN2 reactions, followed by alkyl bromides, alkyl chlorides, and alkyl fluorides.

Nucleophilic Aromatic Substitution Mechanism

Nucleophilic aromatic substitution reactions involve the attack of a nucleophile on the aromatic ring, followed by the removal of a leaving group (the halogen atom) from the ring. This type of reaction is facilitated by the electron-withdrawing effect of the substituents attached to the aromatic ring, which makes the ring more electrophilic and more prone to nucleophilic attack.

Analyze Reactivity of 1-halo-2,4-dinitrobenzenes

1-halo-2,4-dinitrobenzenes have a halogen atom (X) and two nitro groups (-NO2) attached to the aromatic ring. The nitro groups are strong electron-withdrawing groups, which increases the reactivity of the ring towards nucleophilic attack. In these molecules, the reaction rate is mainly determined by the reactivity of electrophilic aromatic ring, rather than the carbon-halogen (C-X) bond strength. The presence of strong electron-withdrawing nitro groups has a leveling effect on the differences in C-X bond strength, making all 1-halo-2,4-dinitrobenzenes react at approximately the same rate in nucleophilic aromatic substitution reactions. In conclusion, the difference in relative reactivities for the given compounds in SN2 and nucleophilic aromatic substitution reactions is due to the variation in carbon-halogen bond strength for alkyl halides and the leveling effect of strong electron-withdrawing nitro groups in 1-halo-2,4-dinitrobenzenes.

Key concepts

SN2 mechanism

The SN2 mechanism, or bimolecular nucleophilic substitution, is a cornerstone of organic chemistry. In this reaction, a nucleophile, which is a species rich in electrons, approaches an electrophilic carbon atom that is attached to a leaving group, typically a halogen. The nucleophile does this in a concerted fashion, meaning the bond formation between the nucleophile and carbon, and the bond breaking between carbon and the leaving group, occur simultaneously.

This reaction occurs in a single step and is characterized by a transition state where the central carbon is pentavalent. As the nucleophile attacks, there's an inversion of stereochemistry at the carbon center, resembling an umbrella turning inside out in a strong wind. The SN2 reaction rate is influenced heavily by steric hindrance; thus, it proceeds most readily with primary alkyl halides and slows considerably or does not occur with secondary and tertiary alkyl halides.

Alkyl halides reactivity

In the context of nucleophilic substitution, the reactivity of alkyl halides is pivotal. Alkyl halides, compounds composed of an alkyl group bonded to a halogen atom, vary widely in their susceptibility to SN2 reactions. Reactivity is often gauged by the bond strength between the alkyl group and the halogen—the weaker this bond, the more reactive the alkyl halide.

Among the halogens, iodine is the least electronegative and forms the weakest bonds with carbon. Consequently, alkyl iodides are the most reactive in SN2 reactions. In contrast, the strong bond between fluorine and carbon in alkyl fluorides results in low reactivity. The trend in reactivity, typically seen as RI > RBr > RCl > RF, reflects the balance between bond strengths, the sizes of the halogen atoms (which impacts the leaving group ability), and the halogen’s ability to stabilize the transition state through electron donation.

Nucleophilic aromatic substitution

Nucleophilic aromatic substitution represents a different pathway compared to its aliphatic counterpart. Unlike the SN2 mechanism that thrives with less hindered, more reactive alkyl halides, the nucleophilic aromatic substitution occurs on benzene rings with electron-withdrawing groups, such as nitro (-NO2) substituents.

Atoms like fluorine, chlorine, bromine, and iodine can be replaced by a nucleophile on an aromatic ring if there are sufficiently strong electron-withdrawing groups in the ortho or para positions. These groups increase the positive charge on the carbon atom holding the leaving group, thereby enhancing its electrophilic character and making it more susceptible to attack by a nucleophile. Despite differences in the carbon-halogen bond strengths, the presence of strong electron-withdrawing groups, like in 1-halo-2,4-dinitrobenzenes, can result in similar reactivity rates among different haloaromatics in nucleophilic aromatic substitution reactions.