# SN2 - Second-order Nucleophilic Substitution

## Kinetics of $SN2$ Reactions

In SN reactions, two borderline cases of are possible. In the first case, the reaction rate depends on the concentrations of both starting products. Such a reaction is called bimolecular nucleophilic substitution, or $SN2$ reaction. In contrast, if the reaction rate is influenced only by the the substrate's (alkyl halide's), and not the nucleophile's concentration, the reaction is called unimolecular nucleophilic substitution, or $SN1$ reaction.

### Hydrolysis of chloromethane

The conversion of chloromethane into methanol is a typical $SN2$ reaction. The reaction can be carried out in water, though the solubility of chloromethane in water is only very small. Nevertheless, the chloromethane concentration is large enough to obtain a noticeable reaction rate. Additional chloromethane is permanently dissolved, as it is consumed by the reaction and consequently removed from the solution equlibrium.

Fig.1
Hydrolysis of chloromethane.

The $OH−$ ion concentration is controlled by the addition of sodium hydroxide. In order to increase the reaction rate, the reaction should be carried out at an elevated temperature. The reaction rate may be determined by measuring the chloromethane concentration during the reaction time.

Tab.1
Initial reaction rates of chloromethane hydrolysis at different initial chloromethane and hydroxide concentrations.
ExperimentInitial concentration [$CH3Cl$]Initial concentration [$OH−$]Initial reaction rate [mol/(l*s)]
1 0.001 1.0 4.9E-7
2 0.002 1.0 9.8E-7
3 0.001 2.0 9.8E-7
4 0.002 2.0 19.9E-7

It is obtained by the kinetic investigation on chloromethane hydrolysis that in doubling the substrate's ($CH3Cl$) or nucleophile's ($OH−$ ) concentration, the reaction rate is also doubled. Likewise, if the concentrations of both starting products are doubled, the reaction rate is increased by four times.

Thus, the reaction rate depends on the concentration of both starting products. Therefore, the rate law is:

Reaction rate = k [$CH3Cl$] [$OH−$],

where k is the proportionality constant of the equation, called the rate constant, or rate coefficient. The rate constant of cloromethane hydrolysis, that has been mentioned above, amounts to k = 4.9-4 l/(mol*s).

The chloromethane hydrolysis is a bimolecular reaction, or second-order reaction, as both starting products participate in the rate-determining step. The reaction rate depends directly on the suitable reactants's number of collisions. Therefore, doubling the concentration of one starting product also doubles the reaction rate, while doubling the concentration of both starting products increases the reaction rate by four times.

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