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# 18.2: Collision Theory

Difficulty Level: At Grade Created by: CK-12

## Lesson Objectives

The student will:

• define the collision theory.
• describe the conditions for successful collisions.
• explain how the kinetic molecular theory applies to the collision theory.
• describe the rate in terms of the conditions of successful collisions.

## Vocabulary

• activated complex
• activation energy
• collision frequency
• collision theory
• kinetic molecular theory
• threshold energy

## Introduction

Consider the chemical reaction $\mathrm{CH}_4 + 2 \ \mathrm{O}_2 \rightarrow \mathrm{CO}_2 + 2 \ \mathrm{H}_2\mathrm{O}$. In the reactants, the carbon atoms are bonded to hydrogen atoms, and the oxygen atoms are bonded to other oxygen atoms. Each atom in the reactants is bonded to its full capacity and cannot form any more bonds. In the products, the carbon atoms are bonded to oxygen atoms, and the hydrogen atoms are bonded to oxygen atoms. The bonds that are present in the products cannot form unless the bonds in the reactants are first broken, which requires an input of energy.

The energy to break the old bonds comes from the kinetic energy of the reactant particles. The reactant particles are moving around at random with an average kinetic energy related to the temperature. If a reaction is to occur, the kinetic energy of the reactants must be high enough that when the reactant particles collide, the collision is forceful enough to break the old bonds. Once the old bonds are broken, the atoms in the reactants would be available to form new bonds. At that point, the new bonds of the products could be formed. When the new bonds are formed, potential energy is released. The potential energy that is released becomes kinetic energy that is absorbed by the surroundings (primarily the products, the solvent solution if there is one, and the reaction vessel).

Chemists have chosen to give a name to the group of particles that exist for the split second just after the reactant bonds have been broken and just before the product bonds form. This group of un-bonded particles is called the activated complex. The activated part comes from the fact that these atoms are ready to form bonds, and the complex part comes from the fact that the group of particles is a jumble of particles from all the reactant molecules. A successful collision would proceed as follows:

$\text{Reactants} \rightarrow \text{input\ of\ energy} \rightarrow \text{activated\ complex} \rightarrow \text{output\ of\ energy} \rightarrow \text{products}$

The reactants, the activated complex, and the products all have a precise amount of potential energy in their bonds. The potential energy of the activated complex is called the threshold energy. This threshold energy is the minimum potential energy that must be reached in order for a reaction to occur. The input of energy that is necessary to raise the potential energy of the reactants to this threshold energy is called the activation energy. The activation energy must be provided from the kinetic energy of the reactant particles during the collision. In those cases where the reactants do not collide with enough energy to break the old bonds, the reactant particles will simply bounce off each other and remain reactant particles.

## How Reactions Occur

We know that a chemical system can be made up of atoms $(\mathrm{H}_2, \ \mathrm{N}_2, \ \mathrm{K})$, ions $(\mathrm{NO}_3^-, \ \mathrm{Cl}^-, \ \mathrm{Na}^+$), or molecules $(\mathrm{H}_2\mathrm{O}, \ \mathrm{CH}_3\mathrm{CH}_3, \ \mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11})$. We also know that in a chemical system, these particles are moving around at random. The collision theory explains why reactions occur between these atoms, ions, and/or molecules at the particle level. The collision theory provides us with the ability to predict what conditions are necessary for a successful reaction to take place. These conditions include:

1. the particles must collide with each other
2. the particles must have proper orientation
3. the particles must collide with sufficient energy to break the old bonds

A chemical reaction involves breaking bonds in the reactants, re-arranging the atoms into new groupings (the products), and the formation of new bonds in the products. Therefore, not only must a collision occur between reactant particles, but the collision has to have sufficient energy to break all the reactant bonds that need to be broken in order to form the products. Some collision geometries need less collision energy than others, and the optimal collision geometry requires the smallest amount of particle kinetic energy for the reaction to occur. If the reactant particles collide with less than the activation energy, the particles will rebound (bounce off each other), and no reaction will occur.

## The Kinetic Molecular Theory

The kinetic molecular theory provides the foundation for the collision theory. Part of the kinetic molecular theory maintains that the collision between particles are “perfectly elastic.” The term “perfectly elastic” is a term from physics meaning that kinetic energy in conserved in the collision. That is, if no bonds are broken, the colliding particles simply rebound, and the total kinetic energy before and after the collision is exactly the same. The kinetic molecular theory states that gas molecules consist of particles that are moving in random motion. This random motion is always in a straight line, and the particles only deviate when there is a collision with the walls of a container or with another particle. The only collisions of any consequence, however, are those between other particles.

In the chapter on kinetic-molecular theory, it was discussed that the particles in a sample of material are not all at exactly the same temperature. The particles of the substance actually have a distribution of kinetic energies, and the temperature of the substance is an expression of the average kinetic energy. As a result, some of the particles have more than the average kinetic energy and some have less. Therefore, some of the reactant particles will have sufficient kinetic energy to react, and some of the reactant particles will not.

In a slow reaction, the majority of molecules do not have the minimum amount of energy necessary for a reaction to take place. In the figure below, the graph illustrates the number of molecules in the system versus the kinetic energy of these molecules. The area under the curve represents the total number of particles. The area shaded in red shows the number of molecules that do have sufficient energy for a successful collision.

If the temperature is increased, the average kinetic energy of the particles increases, and the number of molecules with sufficient kinetic energy for a successful collision will also increase. The figure below shows the changes due to the increased temperature.

At the higher temperature $(\mathrm{T}_2)$, the number of molecules with energy greater than the activation energy increases. Therefore, the number of molecules with enough kinetic energy to have successful collisions increases with increasing average kinetic energy.

## Reactions May Occur When Particles Collide

Looking back at the three conditions introduced in the first section, consider the following reaction:

$\mathrm{F}_2 + \mathrm{NO}_2 \rightarrow \mathrm{FNO}_2 + \mathrm{F}$

If there is not enough energy, the particles will simply rebound off each other and bonds will not be broken, as illustrated below. The original reactants will remain.

In order to have a successful collision, the particles must collide with enough energy and with the correct geometry to break the $\mathrm{F}_2$ and $\mathrm{NO}_2$ bonds and form the $\mathrm{FNO}_2$ and $\mathrm{F}$ products, as seen below. The $\mathrm{F}$ would then further react with another element as it is not normally found un-reacted as just $\mathrm{F}$.

## Rate of Reaction Dependent On Various Factors

As stated earlier, there are three conditions that must occur in order for a successful collision to occur. First, the reactant particles must collide. The total number of collisions per second is known as the collision frequency, regardless of whether these collisions are successful or not. The collision frequency depends on the concentration of the particles in the container, the temperature of the reaction, and the size of the particles themselves. Second, the particles must collide with the proper orientation. Third, the particles must collide with sufficient energy. From this knowledge, we can conclude that the rate of the reaction depends on the fraction of molecules that have enough energy and that collide with the proper orientation. The rate depends on the collision frequency itself. Putting this all together we get the following:

$\text{Rate} = \text{collision\ frequency} \times \text{collision\ energy} \times \text{collision\ geometric\ orientation}$

## Lesson Summary

• The collision theory explains why reactions occur between atoms, ions, and/or molecules and allows us to predict what conditions are necessary for a successful reaction to take place.
• The kinetic molecular theory provides the foundation for the collision theory on the molecular level.
• The minimum amount of energy necessary for a reaction to take place is known as the threshold energy.
• With increasing temperature, the kinetic energy of the particles and the number of particles with energy greater than the activation energy increases.
• The total number of collisions per second is known as the collision frequency, regardless of whether these collisions are successful or not.
• $\mathrm{Reaction\ rate} = \mathrm{collision\ frequency}\ \times \ \mathrm{collision\ energy}\ \times \ \mathrm{collision\ geometric\ orientation.}$

## Review Questions

1. According to the collision theory, it is not enough for particles to collide in order to have a successful reaction to produce products. Explain
2. Due to the number of requirements for a successful collision, according to the collision theory, the percentage of successful collisions is extremely small. Yet, chemical reactions are still observed at room temperature and some at very reasonable rates. Explain.
3. What is a basic assumption of the kinetic molecular theory?
1. All particles will lose energy as the velocity increases
2. All particles will lose energy as the temperature increases
3. All particles will increase velocity as the temperature decreases
4. All particles are in random motion
4. According to the collision theory, which of the following must happen in order for a reaction to be successful: i. particles must collide, ii. particles must have proper geometric orientation, iii. particles must have collisions with enough energy?
1. i, ii
2. i, iii
3. ii, iii
4. i, ii, iii
5. What would happen in a collision between two particles if there was insufficient kinetic energy and improper geometric orientation?
1. The particles would rebound and there would be no reaction.
2. The particles would keep bouncing off each other until they eventually react, therefore the rate would be slow.
3. The particles would still collide but the byproducts would form.
4. The temperature of the reaction vessel would increase.
6. Illustrate the successful collision that would occur between the following: $2 \ \mathrm{NO} + 2 \ \mathrm{H}_2 \rightarrow \mathrm{N}_2 + 2 \ \mathrm{H}_2\mathrm{O}$.

Feb 23, 2012

Mar 26, 2015