Question

Answer the following questions for this E2 reaction: $$\begin{aligned} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br}+\mathrm{NaOH} & \longrightarrow \mathrm{CH}_{3} \mathrm{CH}= \mathrm{CH}_{2}+\mathrm{NaBr}+\mathrm{H}_{2} \mathrm{O} \end{aligned}$$ (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 \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br} ?\) (d) What is the effect on the rate of the reaction of halving the concentration of \(\mathrm{NaOH} ?\)

Short answer

(a) Rate = k[\(CH_{3} CH_{2} CH_{2} Br\)][\(NaOH\)]\n(b) The reaction profile starts at a high energy level (reactants), reaches a peak (transition state) and ends at a lower energy level (products).\n(c) If the concentration of \(CH_{3} CH_{2} CH_{2} Br\) is doubled, the reaction rate doubles.\n(d) If the concentration of \(NaOH\) is halved, the reaction rate halves.

Step-by-step solution

Determining the Rate Expression

The rate expression for an E2 reaction is given by Rate=k[\(CH_{3} CH_{2} CH_{2} Br\)][\(NaOH\)]. The rate of reaction is directly proportional to the concentration of substrate and the base.

Drawing the Reaction Profile

The reaction has one transition state, thus there's a single peak on the reaction profile. The reactants are at higher energy level and products are at lower energy level. Therefore, the plot starts high and ends lower, with one peak representing the transition state in between.

Analyzing the effect of doubling the concentration of \(CH_{3} CH_{2} CH_{2} Br\)

According to the rate expression, if the concentration of \(CH_{3} CH_{2} CH_{2} Br\) is doubled, the rate of the reaction will also double.

Analyzing the effect of halving the concentration of \(NaOH\)

Similarly, from the rate expression, if the concentration of \(NaOH\) is halved, the rate of the reaction will decrease by half.

Key concepts

Chemical Kinetics

Understanding the speed or rate at which chemical reactions occur is the essence of chemical kinetics. It’s a field of study that can explain how different experimental conditions can affect the speed of a chemical reaction and help predict the rates of new reactions.

For instance, in the given E2 reaction where an alkyl halide, \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br} \), reacts with a base, \( \mathrm{NaOH} \), to produce an alkene, \( \mathrm{CH}_{3} \mathrm{CH}= \mathrm{CH}_{2} \), alongside sodium bromide (\(\mathrm{NaBr}\)) and water (\(\mathrm{H}_{2}\mathrm{O}\)). The rate of this reaction is influenced by the concentrations of the reactants. In chemical kinetics, the rate expression links the rate of reaction to the molarity of the reactants, showing that as the concentration of \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br} \) or \( \mathrm{NaOH} \) changes, so does the reaction rate.

This observation is key to predicting how the reaction will behave under different conditions, which is crucial for synthesizing compounds in chemistry labs and industry effectively.

Reaction Mechanism

A reaction mechanism isn't just a one-step process—it's a series of steps that show the detailed path a reaction takes from reactants to products. Each step of a mechanism can involve the formation and breaking of bonds, which typically occur one at a time.

In an E2 reaction, the mechanism involves the concerted removal of a proton by a base and the loss of a leaving group from the substrate to form a double bond. This single-step process is termed 'concerted' because these two events happen simultaneously. Understanding the reaction mechanism offers us a molecular-level view, which is useful when trying to control or optimize a reaction.

Transition State Theory

Transition state theory helps us visualize and understand the energy changes that occur during a chemical reaction. It posits that there is a high-energy, temporary state—the transition state—between the reactants and the products.

When drawing a reaction profile for an E2 reaction, we illustrate this as a peak on the energy diagram. The transition state is the highest point on this peak because it represents the point at which the old bonds are breaking, and new ones are forming—all before the molecule settles into a more stable configuration as the products. This highest energy state does not last long and cannot be isolated, but it's crucial because the reaction cannot progress without it.

For our given E2 reaction, the energy diagram would start at a higher level (representing the reactants), peak at the transition state, and then descend to a lower level representing the products, consistent with the assumption that products are lower in energy than the reactants.