Activation Energy and Collision Theory for the ESAT

The Collision Theory of Reaction Rates

Chemical reactions do not happen spontaneously just because reactants are mixed. According to collision theory, for a reaction to occur, reactant particles must collide with each other. However, the majority of collisions are unsuccessful and do not lead to a reaction. For a collision to be successful, or effective, the particles must meet two specific criteria: they must collide with the correct orientation, and they must possess a minimum amount of kinetic energy.

Defining Activation Energy ($E_a$)

The minimum energy that colliding particles must have in order to react is called the activation energy, represented by the symbol $E_a$. This energy is required to start breaking the chemical bonds in the reactants so that new bonds can form in the products. If the colliding particles have energy less than the activation energy, they will simply bounce off each other unchanged. You can think of the activation energy as an energy barrier or a hill that the reactants must climb over to reach the product state.

The Relationship between $E_a$ and Reaction Rate

The rate of a reaction is determined by the frequency of successful collisions. If the activation energy for a reaction is high, very few particles will have enough energy to overcome the barrier at a given temperature, making the reaction slow. Conversely, a reaction with a low activation energy will proceed more quickly as a larger proportion of particles will possess the necessary energy upon collision. While temperature affects the kinetic energy of particles, the $E_a$ itself is a constant for a given reaction pathway.

Activation Energy on Energy Level Diagrams

Energy level diagrams, also known as reaction profile diagrams, plot the enthalpy of the chemicals against the progress of the reaction. These diagrams visually represent the activation energy as the difference in energy between the reactants and the highest point on the curve, known as the transition state or the activated complex. On these graphs, the vertical axis represents energy and the horizontal axis represents the path of the reaction.

Exothermic Reaction Profiles

In an exothermic reaction, the products have less energy than the reactants because energy is released to the surroundings. On the diagram:

1. The reactants are shown as a horizontal line at a higher energy level than the products.
2. A curve rises from the reactant level to a peak before falling to the product level.
3. The activation energy ($E_a$) is shown as an upward arrow starting from the reactant line and ending at the peak of the curve.
4. The enthalpy change ($\Delta H$) is the vertical distance between the reactant level and the product level, which is negative for exothermic reactions.

Endothermic Reaction Profiles

In an endothermic reaction, the products have more energy than the reactants because energy is absorbed from the surroundings. On the diagram:

1. The reactants are shown as a horizontal line at a lower energy level than the products.
2. The curve rises from the reactants to a peak that is higher than the products.
3. The activation energy ($E_a$) is still measured from the reactant line to the peak. In endothermic reactions, $E_a$ is always greater than the enthalpy change ($\Delta H$) because the system must reach a peak higher than the final product energy.

Worked Example: Interpreting a Reaction Profile

Consider a reaction where the energy of the reactants is $150$ kJ mol$^{-1}$ and the energy of the products is $100$ kJ mol$^{-1}$. The peak of the energy curve reaches $300$ kJ mol$^{-1}$.

1. To find the activation energy ($E_a$), calculate the difference between the peak energy and the reactant energy: $300 - 150 = 150$ kJ mol$^{-1}$.
2. To find the enthalpy change ($\Delta H$), calculate the difference between the product energy and the reactant energy: $100 - 150 = -50$ kJ mol$^{-1}$.

Because the value for $\Delta H$ is negative, the reaction is exothermic. Note that $E_a$ is always a positive value because it represents the energy that must be absorbed to reach the peak of the barrier.