When ethyl bromide is added to potassium tert-butoxide, the product is ethyl tert-butyl ether.
CH₃CH₂–Br + (CH₃)₃C–O^–K⁺ → (CH₃)₃C–O–CH₂CH₃ ethyl bromide potassium tert-butoxide ethyl tert-butyl ether
a. What happens to the reaction rate if the concentration of ethyl bromide is doubled?

Verified step by step guidance

1. Step 1: Recognize that this reaction is an example of a Williamson ether synthesis, which proceeds via an SN2 (bimolecular nucleophilic substitution) mechanism.
2. Step 2: Recall that the rate of an SN2 reaction depends on the concentrations of both the nucleophile (potassium tert-butoxide) and the electrophile (ethyl bromide). The rate law for an SN2 reaction is: $r=k\cdot {[}_{\mathrm{RBr}}\cdot {[}_{\mathrm{Nu}}$, where $\mathrm{RBr}$ is the alkyl halide (ethyl bromide) and $\mathrm{Nu}$ is the nucleophile (tert-butoxide).
3. Step 3: Analyze the effect of doubling the concentration of ethyl bromide. Since the rate law is directly proportional to the concentration of ethyl bromide, doubling its concentration will double the reaction rate, assuming the concentration of potassium tert-butoxide remains constant.
4. Step 4: Understand that this proportional relationship is a hallmark of the SN2 mechanism, where the reaction rate depends on the simultaneous interaction of the nucleophile and the electrophile in the rate-determining step.
5. Step 5: Conclude that if the concentration of ethyl bromide is doubled, the reaction rate will also double, as per the rate law for an SN2 reaction.

Key Concepts

Reaction Rate

The reaction rate refers to the speed at which reactants are converted into products in a chemical reaction. It is influenced by factors such as concentration, temperature, and the presence of catalysts. In this context, understanding how the concentration of ethyl bromide affects the reaction rate is crucial for predicting the outcome of the reaction.

Concentration and Rate Law

The rate law expresses the relationship between the concentration of reactants and the rate of the reaction. For a reaction involving ethyl bromide, if the rate law indicates a first-order dependence on its concentration, doubling the concentration would double the reaction rate. This concept is essential for analyzing how changes in reactant concentrations impact the overall reaction kinetics.

Nucleophilic Substitution Mechanism

The reaction between ethyl bromide and potassium tert-butoxide involves a nucleophilic substitution mechanism, where the nucleophile (tert-butoxide) attacks the electrophilic carbon in ethyl bromide. Understanding this mechanism helps in predicting how the reaction proceeds and how the concentration of reactants influences the rate of product formation.