What effect would you expect the following changes to have...

What effect would you expect the following changes to have on the rate of the $S_{N} 2$ reaction of 1 -iodo- 2 -methylbutane with cyanide ion? (a) The CN $^{-}$ concentration is halved, and the 1 -iodo- 2 -methylbutane concentration is doubled. (b) Both the $\mathrm{CN}^{-}$ and the 1 -iodo- 2 -methylbutane concentrations are tripled.

What effect would you expect the following changes to have on the rate of the $S_{N} 2$ reaction of 1 -iodo- 2 -methylbutane with cyanide ion?
(a) The CN $^{-}$ concentration is halved, and the 1 -iodo- 2 -methylbutane concentration is doubled.
(b) Both the $\mathrm{CN}^{-}$ and the 1 -iodo- 2 -methylbutane concentrations are tripled.

Key Concepts

Impact of Reactant Concentration on Reaction Rate

Modifying the concentrations of the reactants directly influences the overall reaction rate. For instance, halving one concentration while doubling the other leaves the rate unchanged, whereas tripling both concentrations results in a nine-fold increase in the reaction rate. This concept highlights the multiplicative relationship in the rate law for SN2 reactions.

Bimolecular Reaction Rate Law

The rate of an SN2 reaction is directly proportional to the concentrations of both the substrate and the nucleophile, as described by the rate law Rate = k[substrate][nucleophile]. This reflects the bimolecular nature of the reaction where both molecules are involved in the rate-determining collision.

SN2 Reaction Mechanism

SN2 reactions proceed via a single, concerted step in which the nucleophile attacks the substrate from the side opposite the leaving group, leading to a simultaneous bond formation and breaking. This backside attack leads to inversion of stereochemistry at the reaction center and typically occurs in a single kinetic step.

Transcript

00:01 So we have the following reaction.

00:02 We have one iota 2 methylbutane, and we have our nucleophilic cyanide ion, and we want to know what would happen given the following reaction conditions, but what happened to the rate of the reaction? so we are actually given that this reaction occurs via sn2, so substitution nucleophilic biomolecular.

00:23 So the two here stands for biomolecular.

00:28 And what that means is it relates to the kinetics of the reaction.

00:32 So it means that there are two.

00:34 We have a second order reaction.

00:36 So in other words our reaction rate, which is what we would right here, our reaction rate, is going to depend on a rate constant k, which is going to stay constant, multiplied by our alkyl halide, which we will denote rx here, and our alkyl halide will be this species here.

01:02 So we'll go ahead and write that as rx, and this is also going to a reaction rate will be multiplied by our nucleophile as well, which here we are going to write as our cyanide ion.

01:26 So we're going to go ahead and write this as our concentration in terms of cyanide ion.

01:35 All right.

01:36 So given the following reaction condition, example a, we have half the concentration of our cyanide ion and two times the concentration of our alkyl halide.

01:45 So we can just simply substitute that into our equation for our reaction rate for a bimolecular second order reaction...

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