The reaction is an SN2SN2 methylation of an enolate, so the rate is fastest in polar aprotic solvents that strongly solvate the cation (Na+Na+) but leave the anionic nucleophile “free”; among the given choices, the correct order of rate is DMSO > DMF > DME > THF > benzene, so option (A) is correct.​​

Introduction

The solvent effect on enolate methylation is a classic concept question that links nucleophilic substitution (SN2SN2) mechanisms with solvent properties such as polarity, dielectric constant and ability to solvate ions. In this IIT‑JAM style problem, the sodium enolate of cyclohexanone reacts with methyl iodide in different aprotic solvents (benzene, THF, DME, DMSO, DMF), and the task is to predict how the reaction rate changes with solvent.​

Step‑wise analysis of the reaction

• The substrate is methyl iodide, a primary alkyl iodide that reacts via a one‑step SN2SN2 pathway with strong nucleophiles.​

• The nucleophile is the sodium enolate of cyclohexanone, essentially an ion pair: Na+ − ⁣O-C6H9Na+−O-C6H9, where the negative charge is delocalised between oxygen and the α‑carbon.​

• The rate‑determining step is the bimolecular attack of the enolate on methyl iodide; therefore, reaction rate depends strongly on the “nakedness” and nucleophilicity of the enolate anion and on how well the ionic reagent is dissolved.​

For SN2SN2 reactions with anionic nucleophiles:

• Polar aprotic solvents (DMSO, DMF, DME, THF, etc.) are best, because they do not hydrogen‑bond to anions, so they leave the nucleophile highly reactive while solvating the cation.​

• Within polar aprotic solvents, increasing dielectric constant and ion‑solvating ability aid separation of ion pairs and increase nucleophile availability, usually increasing rate.​

Approximate dielectric constants at room temperature illustrate this trend:

Thus the expected rate order is:

$$\text{DMSO}>\text{DMF}>\text{DME}>\text{THF}>\text{benzene}$$

which matches option (A).​

Detailed discussion of each option

Option (A): DMSO > DMF > DME > THF > Benzene (Correct)

• DMSO and DMF are highly polar aprotic solvents that strongly solvate cations but not anions, giving a relatively free enolate anion; this maximises nucleophilicity and SN2SN2 rate.​

• DME and THF are less polar ethers; they solvate the sodium cation but, because of their much lower dielectric constant, they separate ion pairs less efficiently, so the nucleophile is somewhat less reactive.​

• Benzene is nearly non‑polar, dissolves ionic sodium enolates poorly, and keeps the ion pair tightly bound, giving the slowest reaction.​

• Therefore this option correctly orders solvents from most to least effective for the SN2SN2 methylation of the enolate.​

Option (B): Benzene > THF > DME > DMF > DMSO (Incorrect)

• This option places non‑polar benzene as the fastest solvent, which contradicts the requirement that ionic nucleophiles need polar media for good dissolution and high reactivity.​

• It also implies that increasing solvent polarity and ion‑solvating power (from ethers to DMF/DMSO) would decrease the SN2SN2 rate, whereas well‑established data show polar aprotic solvents accelerate SN2SN2 reactions with anionic nucleophiles.​

Option (C): DME > DMSO > DMF > THF > Benzene (Incorrect)

• Here DME is predicted to be faster than DMSO, which is unreasonable because DME has a much lower dielectric constant and weaker ability to separate the sodium enolate into free ions.​

• Experimental and textbook discussions consistently state that DMSO and DMF are superior to ether solvents like DME or THF for SN2SN2 reactions involving anionic nucleophiles such as enolates.​

Option (D): THF > Benzene > DME > DMSO > DMF (Incorrect)

• This option wrongly suggests that less polar solvents (THF, benzene) give higher rates than the more polar aprotic solvents DMSO and DMF.​

• In reality, moving from benzene or THF to DMSO/DMF generally increases the rate of enolate alkylation because the enolate is better solvated as a free anion and thus more nucleophilic.​

Key takeaways for exam preparation

• For ionic nucleophiles (e.g., enolates, alkoxides, halides), polar aprotic solvents like DMSO and DMF usually give the fastest SN2SN2 reactions.​

• Within aprotic solvents, higher dielectric constant and cation‑solvating ability generally correlate with higher reaction rates for such substitutions.​

• Non‑polar solvents such as benzene dramatically slow these reactions because they cannot effectively dissolve and separate ionic reagents, a crucial point to remember for multiple‑choice questions on solvent effects.​