Problem 101 - Chemistry Structure and Properties

Question

This reaction has an activation energy of zero in the gas phase. $$\mathrm{CH}_{3}+\mathrm{CH}_{3} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}$$ \begin{equation} \begin{array}{l}{\text { a. Would you expect the rate of this reaction to change very much }} \\ {\text { with temperature? }} \\ {\text { b. Why might the activation energy be zero? }} \\ {\text { c. What other types of reactions would you expect to have little or no }} \\ {\text { activation energy? }}\end{array} \end{equation}

Step-by-Step Solution

Answer

a. The rate of the reaction is not expected to change significantly with temperature. b. The activation energy could be zero due to the direct combination of reactants without an energy barrier. c. Diffusion-controlled and highly exothermic reactions typically have little or no activation energy.

Step 1: Understanding Activation Energy

Activation energy is the minimum energy required to initiate a chemical reaction. A reaction with an activation energy of zero implies that it can occur spontaneously without any energy barrier to overcome.

Step 2: Temperature Dependence of Reaction Rates

For reactions with non-zero activation energy, increasing the temperature typically increases the reaction rate because more molecules have the necessary energy to overcome the energy barrier. However, if a reaction has zero activation energy, it suggests that the reaction rate will not be significantly affected by temperature changes because there is no energy barrier that molecules are struggling to overcome.

Step 3: Reasons for Zero Activation Energy

A reaction may have zero activation energy because it involves a simple collision between molecules leading to a chemical reaction without any energy barrier, which could be due to a highly favorable physical orientation or a very exothermic reaction pathway.

Step 4: Types of Reactions with Low or No Activation Energy

Reactions that are diffusion-controlled or have very exothermic reaction pathways where the reactants have enough kinetic energy to react upon contact are examples of reactions you would expect to have little or no activation energy.

Key Concepts

Chemical Reaction Rates

Chemical reaction rates refer to how fast a chemical reaction occurs. This rate can be influenced by various factors such as the concentration of reactants, the presence of a catalyst, surface area, and temperature, among others. A vital concept within this topic is the activation energy, which is the minimum amount of energy required for reactants to transform into products.

In the context of the exercise, a chemical reaction with an activation energy of zero means that the reaction can proceed without any additional input of energy, which is quite unusual. The rate of this reaction is determined primarily by the frequency and orientation of collisions between the reactive molecules, CH₃ radicals in this case. However, with zero activation energy, the temperature's effect on the reaction rate becomes less critical because the molecules don't need to gain additional energy to react.

Temperature Dependence in Reactions

The temperature dependence in reactions is explained by the Arrhenius equation, which shows that an increase in temperature typically leads to an increase in the reaction rate. This is because higher temperatures provide more energy to the reactant molecules, allowing them to move faster, collide more often, and with greater energy. These more frequent and energetic collisions can result in more reactant molecules having enough energy to overcome the activation barrier of the reaction.

For a reaction with an activation energy of zero, as noted in the exercise, we would not expect the rate to change much with temperature because there is no barrier for the reactants to overcome. This implies that such reactions could occur readily at a wide range of temperatures, perhaps only limited by the availability of reactants and possibly other reaction mechanisms such as diffusion.

Exothermic Reactions

Exothermic reactions are chemical reactions that release energy, usually in the form of heat, to the surroundings. This release of energy happens when the total energy of the products is less than that of the reactants. Such reactions often occur spontaneously and can be highly favorable, both thermodynamically and kinetically.

It is possible for exothermic reactions to have low or even zero activation energy, as the released energy might provide the necessary boost for the reaction to proceed without an additional energy input. The reaction in the exercise, where two CH₃ radicals combine to form C₂H₆, might be inherently exothermic, enabling the reaction to proceed with no activation energy. This scenario aligns well with other diffusion-controlled reactions or those with a highly exothermic pathway, where reactants react as soon as they come into contact without a significant energy barrier.