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
b. What happens to the rate if the concentration of potassium tert-butoxide is tripled and the concentration of ethyl ­bromide is doubled?
c. What happens to the rate if the temperature is raised?

Verified step by step guidance

1. Step 1: Identify the reaction type. This reaction is an SN2 (bimolecular nucleophilic substitution) mechanism. In SN2 reactions, the rate depends on the concentration of both the nucleophile (potassium tert-butoxide) and the electrophile (ethyl bromide). The rate law can be expressed as: $\mathrm{Rate}=k[\mathrm{CH}$₃CH₂⁢Br]⁢[(CH₃³C)⁢O^-].
2. Step 2: Analyze part b. If the concentration of potassium tert-butoxide is tripled and the concentration of ethyl bromide is doubled, the rate will increase proportionally to the product of these changes. Specifically, the rate will be multiplied by 3 (from potassium tert-butoxide) and 2 (from ethyl bromide), resulting in a total increase of 6 times the original rate.
3. Step 3: Analyze part c. Raising the temperature generally increases the rate of reaction. This is because higher temperatures provide more kinetic energy to the reactants, increasing the frequency and energy of collisions. The rate constant ($k$) in the rate law is temperature-dependent and follows the Arrhenius equation: $k=A{e}^{-}$_a/RT, where $E$_a is the activation energy, $R$ is the gas constant, and $T$ is the temperature in Kelvin.
4. Step 4: Explain the effect of temperature on the reaction rate. As temperature increases, the exponential factor in the Arrhenius equation becomes larger, leading to an increase in the rate constant ($k$). This results in a faster reaction rate, assuming the reaction mechanism remains unchanged.
5. Step 5: Summarize the findings. For part b, the rate increases by a factor of 6 when the concentrations of potassium tert-butoxide and ethyl bromide are tripled and doubled, respectively. For part c, raising the temperature increases the reaction rate due to the temperature dependence of the rate constant as described by the Arrhenius equation.

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 changes in the concentrations of ethyl bromide and potassium tert-butoxide affect the rate of ether formation is crucial for predicting the outcome of the reaction.

Concentration Effects

Concentration effects describe how the amount of reactants present in a reaction influences the rate of that reaction. According to the rate law, if the concentration of a reactant is increased, the rate of reaction typically increases, assuming the reaction order with respect to that reactant is greater than zero. In this case, tripling the concentration of potassium tert-butoxide and doubling ethyl bromide will have a specific impact on the overall reaction rate.

Temperature and Reaction Kinetics

Temperature plays a significant role in reaction kinetics, as it affects the energy of the molecules involved. Generally, increasing the temperature increases the kinetic energy of the reactants, leading to more frequent and effective collisions, which can accelerate the reaction rate. Understanding how temperature changes influence the rate of the reaction is essential for predicting the behavior of the system under different conditions.