Question

Answer the following questions for this \(\mathrm{S}_{\mathrm{N}}1\) reaction: (a) What is the rate expression for the reaction? (b) Draw the reaction profile for the reaction. Label all parts. Assume that the products are lower in energy than the reactants. (c) What is the effect on the rate of the reaction of doubling the concentration of 1-bromo-1-methylpentane? (d) The solvent for the reaction is ethanol. What is the effect on the rate of the reaction of adding more ethanol?

Short answer

(a) The rate expression for the reaction is \(Rate = k [1-bromo-1-methylpentane]\). (b) The reaction profile starts with the reactants at a higher energy level, peak at the transition state, and come down to products that are at a lower energy level. (c) The rate of reaction doubles if the concentration of 1-bromo-1-methylpentane is doubled. (d) More ethanol does not affect the rate of reaction as the reaction is dependent only on the concentration of the substrate.

Step-by-step solution

Determine the Rate Expression

For an SN1 reaction, the rate of reaction is only dependent on the concentration of the substrate, in this case, 1-bromo-1-methylpentane. The rate expression is given by: \(Rate = k [1-bromo-1-methylpentane]\)

Draw the Reaction Profile

In an energy diagram for an SN1 reaction, the reactants start at a higher energy level, then there's a hump to represent the transition state, following which the energy level comes down to the products. Since the products are lower in energy than reactants, the change in energy (\(ΔE\)) is negative.

Effect of Doubling Concentration of Substrate

In an SN1 reaction, the rate is proportional to the concentration of the substrate. Therefore, if the concentration of 1-bromo-1-methylpentane is doubled, the rate of reaction will also double.

Effect of Adding More Solvent

In an SN1 reaction, the solvent helps in stabilizing the intermediate carbocation and also helps in breaking the bond of the substrate. Adding more ethanol, in this case, will not affect the rate of the reaction as the reaction is unimolecular and rate of reaction is independent of the concentration of solvent.

Key concepts

Reaction Rate

In the context of an SN1 reaction, understanding the rate at which the reaction proceeds is crucial. The "reaction rate" refers to how quickly reactants are converted into products. For SN1 reactions, the rate is solely dependent on the concentration of the substrate involved.

Let's consider 1-bromo-1-methylpentane as the substrate. Here, the reaction can be expressed with the rate law:

• \(Rate = k [1\text{-}bromo\text{-}1\text{-}methylpentane]\)

Where \(k\) is the rate constant.

This expression highlights the first-order nature of the reaction, where the rate is directly proportional to the concentration of the substrate. If we increase the concentration of the substrate, the reaction rate will also increase proportionally. This is why doubling the concentration of 1-bromo-1-methylpentane results in a doubling of the reaction rate.

Energy Diagram

An energy diagram provides a graphic representation of the energy changes that occur during a chemical reaction. For SN1 reactions, understanding this diagram helps visualize the transition states and energy barriers involved.

In an SN1 energy diagram:

• Reactants start at a higher energy level.
• A peak, representing the transition state, is seen indicating the energy required to form an intermediate.
• The graph then descends to a lower energy level for the products.

This shape is characteristic of SN1 reactions and indicates that the products are more stable than the reactants, hence the overall reaction is exergonic.

The difference in energy levels between the reactants and products is denoted as \(ΔE\), and it is negative for exergonic reactions, meaning energy is released.

Solvent Effect

Solvents play a crucial role in the reactions, especially in SN1 mechanisms. The role of the solvent primarily involves stabilizing the carbocation intermediate formed during the transition state.

In the case of an SN1 reaction taking place in ethanol:

• As ethanol is a protic solvent, it assists in stabilizing the carbocation through hydrogen bonding and polarization effects.
• It also helps in breaking the bond between the leaving group and the substrate, facilitating the formation of the carbocation.

However, adding more ethanol does not affect the rate of the SN1 reaction. This is because the rate is independent of solvent concentration, reaffirming the unimolecular nature of SN1 reactions.

Reaction Kinetics

Understanding reaction kinetics involves studying the rate and steps of a chemical reaction. In SN1 reactions, kinetics are specific because they follow a unimolecular mechanism.

This means:

• The rate-determining step involves only one molecule - the substrate forming a carbocation.
• Subsequent steps, such as the nucleophile attacking the carbocation, occur rapidly.

The kinetics are typically described by a first-order rate law, indicating that the rate of reaction hinges on the concentration of only one reactant.

This makes SN1 reactions distinct from SN2 reactions, which depend on both the substrate and the nucleophile concentrations, highlighting the uniqueness in kinetics of the SN1 mechanism.