$k = Ae^{-E_a/RT}$

Definition

$k = Ae^{-E_a/RT}$ is the rate constant equation, which describes the relationship between the rate constant $k$ and various factors that influence the rate of a chemical reaction. This equation is a fundamental component of collision theory, which explains how the frequency and energy of collisions between reactant molecules determine the overall reaction rate.

5 Must Know Facts For Your Next Test

1. The rate constant $k$ is a measure of the reaction rate, and it increases as the activation energy $E_a$ decreases or the temperature $T$ increases.
2. The pre-exponential factor $A$ represents the frequency of collisions between reactant molecules, and it is influenced by the molecular orientation and the number of available reaction pathways.
3. The exponential term $e^{-E_a/RT}$ represents the fraction of molecules that have sufficient energy to overcome the activation energy barrier and form products.
4. The rate constant equation is derived from the Arrhenius equation, which describes the temperature dependence of the reaction rate.
5. The rate constant equation is a key component of collision theory, which explains how the frequency and energy of collisions between reactant molecules determine the overall reaction rate.

Review Questions

• Explain the relationship between the rate constant $k$ and the activation energy $E_a$ in the rate constant equation $k = Ae^{-E_a/RT}$.
  • The rate constant $k$ is inversely proportional to the activation energy $E_a$ in the rate constant equation. As the activation energy decreases, the exponential term $e^{-E_a/RT}$ increases, leading to a higher value of the rate constant $k$. This means that reactions with lower activation energies will proceed at a faster rate, as the reactant molecules require less energy to overcome the energy barrier and form products.
• Describe the role of the pre-exponential factor $A$ in the rate constant equation $k = Ae^{-E_a/RT}$ and how it relates to the frequency of collisions between reactant molecules.
  • The pre-exponential factor $A$ in the rate constant equation represents the frequency of collisions between reactant molecules. This factor is influenced by the molecular orientation and the number of available reaction pathways. A higher pre-exponential factor indicates that the reactant molecules are colliding more frequently, which can increase the overall reaction rate. However, the pre-exponential factor alone does not determine the rate of the reaction; the activation energy $E_a$ and the temperature $T$ also play crucial roles in determining the value of the rate constant $k$.
• Analyze how changes in temperature $T$ affect the rate constant $k$ in the rate constant equation $k = Ae^{-E_a/RT}$, and explain the underlying principles of collision theory that support this relationship.
  • According to the rate constant equation, as the temperature $T$ increases, the exponential term $e^{-E_a/RT}$ increases, leading to a higher value of the rate constant $k$. This relationship is consistent with the principles of collision theory, which states that higher temperatures result in increased kinetic energy of the reactant molecules. This, in turn, leads to more frequent and energetic collisions between the molecules, increasing the likelihood of them overcoming the activation energy barrier and forming products. The temperature-dependence of the rate constant is a key factor in understanding how reaction rates can be controlled and optimized through the manipulation of reaction conditions.

Related terms

Activation Energy ($E_a$): The minimum amount of energy required for reactant molecules to overcome the energy barrier and form products during a chemical reaction.

Pre-exponential Factor ($A$): A constant that represents the frequency of collisions between reactant molecules, which is influenced by factors such as the molecular orientation and the number of available reaction pathways.

Temperature ($T$): The average kinetic energy of the particles in a system, which affects the frequency and energy of collisions between reactant molecules.