S_N2 Reaction: Kinetics

Kinetic Studies and Significance

In a chemical reaction, a relationship exists between the concentration of reactants and the rate at which the reaction proceeds. The study to measure this relationship is known as the kinetics of a chemical reaction. Kinetic studies are used to deduce the rate law of a chemical reaction, which provides information about the species involved during the transition state of the rate-determining step. Thus, kinetic studies help to derive the mechanism of a reaction.

Kinetic Studies: How to Measure the Rate?

A chemical reaction proceeds at a certain rate at a given temperature, pressure, and solvent.  The rate of a reaction can only be identified experimentally. To do so, the rate at which the reactants disappear or the rate at which the products appear in the reaction mixture is measured. In specific time intervals, aliquots are withdrawn from the reaction mixture and analyzed for the concentration of the reactants or the products formed. Further, while keeping the temperature and solvent conditions the same, the reaction's initial concentration is varied to observe the effect on the rate of the reaction.

Nucleophilic Substitution Reactions and Kinetics

In the 1930s, British chemists Sir Christopher Ingold and Edward D. Hughes studied rate kinetics of various substitution reactions to understand the probable mechanism of nucleophilic substitution reactions. They observed that a nucleophilic substitution reaction of an alkyl halide proceeded by two possible mechanisms – either in single-step or via two steps.

For specific reactions, such as chloromethane and sodium hydroxide, the reaction rate depended on the concentration of both the nucleophile and the alkyl halide. Specifically, they observed that when the concentration of either of the reactants was doubled, the reaction rate doubled. Furthermore, when the concentration of both reactants was doubled, the rate increased four times, as shown in Table 1.

Table 1. Rate study of the reaction between chloromethane and hydroxide ions at 60 °C

Thus, the rate equation was found to be:

Rate ∝ [CH₃Cl][HO⁻]

This shows that the rate is first order with respect to each reactants' concentration and second-order overall. 

S_N2 Reactions and Kinetics

• •  The kinetics of the above reaction suggest that for the substitution to occur, the nucleophile and the alkyl halide collide in a single step to form the product.
• •  The molecularity of such reactions is said to be bimolecular as two species are involved in the rate-limiting step.
• •  Thus, the reaction between chloromethane and sodium hydroxide is an S_N2 reaction, where S stands for Substitution, N for Nucleophilic, and 2 for a bimolecular reaction.