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# Collision Theory I

Proposed by Max Trautz and William Lewis in the early 1900s, collision theory is an aspect of kinetic-molecular theory; it is strongly interconnected with chemical kinetics. The theory is used to explain how different variables affect the rate of reaction. This theory is built on the idea that reactant particles must collide for a reaction to occur, but only a small percentage of the total collisions have appropriate energies and "orientations" to effectively cause the reactants to form into the products. The field of study involving molecular collisions developed quickly in the 1980s because of modern electronic and vacuum instrumentation.

### Collision Theory

For a reaction to occur, molecules must collide. The collision frequency describes how many times a particular molecule collides with others per unit of time. However, not all collisions result in a reaction. In order for molecules to react, a physical chemist named Svante Arrhenius explained, the colliding molecules must possess enough kinetic energy to overcome the repulsive and bonding forces of the reactants. The minimum amount of energy required for a chemical reaction to occur is known as the activation energy, denoted $$E_a$$.

The higher the $$E_a$$ of a reaction, the smaller the amount of energetic collisions present, and the slower the reaction. Energetic collisions are collisions between molecules with enough kinetic energy to cause the reaction to occur. Not all collisions are energetic collisions because they do not provide the necessary amount of $$E_a$$, so not all collisions lead to reactions and product formation. In contrast, the lower the $$E_a$$ of a reaction, the greater the amount of energetic collisions present, and the faster the reaction.

### Effects of Energy

A reaction cannot occur if the particles do not collide with the activation energy of the reaction. If the atoms collide with less energy, the atoms simply bounce away from each other. Only collisions with energy that is equal to or greater than the activation energy will create a reaction. Ultimately, chemical reactions involve the breaking of some bonds (which takes energy) and making new bonds (which releases energy). Activation energy is the key to breaking the initial bonds. When collisions are too gentle, the adequate amount of energy is not brought to the bonds and a reaction fails to occur. The activation energy is crucial in the reaction rate because depending on how much kinetic energy is brought to the collision, the reaction will vary in speed and frequency.

### Molecularity of a Reaction

A unimolecular reaction occurs when a single reactant molecule transforms into one or more products. Examples of a unimolecular reaction include racemization, thermal decomposition, and isomerization.

A bimolecular reaction occurs when two reactant molecules collide in one elementary step. Bimolecular reactions are the most common reactions. An example of a bimolecular reaction is the collision of N2O and NO, forming the products N2 and NO2​. Another is the collision of glucose and O2, forming CO2 and water.

The rate constant for a bimolecular gas phase reaction as predicted by collision theory is defined as follows:

$k = Ae^{-\frac{E_a}{RT}}$

where:

• k is the rate constant.
• A is the product of the collision frequency and the fraction of molecules with enough kinetic energy to cause a reaction to occur -- the likelihood of molecules with sufficient kinetic energy will collide, causing a reaction to occur.
• Ea is the activation energy of the reaction.
• T is the temperature (in Kelvin).
• R is the gas constant, 8.314 J mol​-1 K-1.

A termolecular reaction occurs when three reactant molecules collide simultaneously to cause a reaction and formation of products. Termolecular reactions are extremely rare.

No reactions with more than three reactant molecules colliding simultaneously are known, and as such, no reactions with molecularities higher than three have yet been observed.

### Maxwell-Boltzmann Distribution

It is useful to know the proportion of atoms that have high enough energies to cause a chemical reaction in a collision. Gases can be plotted on a graph called the Maxwell-Boltzmann distribution. It shows different atoms or particles, and their energies.

Figure 1 - Number of Particles vs. Energy

From Figure 1, three observations can be made:

1. Most of the particles have a moderate amount of energy.
2. Only a select few have very high energies.
3. Few particles have very low energies.

The rate of almost all chemical reaction increases with an increase in temperature. Particles that move more quickly collide more often and with greater kinetic energy. The number of effective collisions increases exponentially with an increase in temperature (Figure 2). At a certain temperature, only a  fraction of the molecules possess enough energy for collisions (Figure 3).

Figure 2 - Temperature and Rate of Reaction                           Figure 3 - Maxwell-Boltzmann Distribution

### Effects of Orientation

In any collision involving unsymmetrical atoms, the orientations of the atoms during collision determine whether a reaction occurs; without the proper orientations during the collision, the reaction will not occur at all.

Figure 4: Collisions need to be oriented in a specific way to generate a reaction.

Example 1: A collision occurs between two molecules, ethene (CH2=CH2), and hydrogen chloride (HCl), and the reaction produces chloroethane. Because of the collision, the double bond in the middle of the two carbons is changed into a single bond. A hydrogen atom is attached to one of the carbon atoms, and a chlorine atom is attached to the other. If the hydrogen side of the H-Cl bond meets the carbon-carbon (double bond), a reaction can occur. If it does not align in such a way, it will not react. This is illustrated in the figure below.

Figure 5 - The Collision of Hydrogen Chloride with ethene:
(Carbon is shown in black, hydrogen in pink, and chloride in green.)

Example 2: When two hydrogen atoms combine together to create a hydrogen molecule, no bonds are destroyed (an H-H bond is created). Hydrogen atoms are spherical and completely symmetrical; the orientation is therefore the same no matter how the hydrogen atoms collide (Figure 6). The reaction will take place as quickly as the collision.

Figure 6 -  Collision Between Two Hydrogen Atoms

Example 3: The collision theory implicates that the orientations of NO2 and NO at the time of collision will determine if the reaction proceeds. In (A), the oxygen is pushed off the nitrogen of the N2O on the nitrogen of the NO. This reaction occurs and products form. Therefore, this reaction occurs due to a favorable collision. Both (B) and (C) have unfavorable collisions because the same element in each reactant molecule collides, and the two molecules simply deflect off each other. The collisions do not produce enough activation energy to allow the reaction to occur. The figure below demonstrates that the number of unfavorable collisions in a mixture of reactants is greater than the number of favorable collisions, which further demonstrates that most collisions may not cause reactions to occur.

Figure 7 - The Collision of Nitrous Oxide with Nitric Oxide:
(Please note that nitrogen is shown in blue, oxygen is in red, and the yellow arrows depict the direction of movement of the molecule.)
*** Similar to FIGURE 14-9 on p. 624 of General Chemistry, Principles & Modern Applications 10th Edition, by Petrucci, 2007, 2002, 1997. .....skhdd

### References

• Collision Theory, Goldberg, Watson, 1964
• Atomic and Molecular Collison Theory, Gianturco, 1980
• General Chemistry, Principles & modern Applications,Petrucci,2007,2002, 1997

### Problems

Example #1: In a classroom there is a group of blindfolded students made to walk around the room at a slow pace. A pair of students will bump into each other occasionally. If the students start to run around the room at a higher pace (higher pace = more energy for collision), then a collision is more likely to be successful. If a portion of students move around fast, while others move about at a more sluggish pace, successful reactions will still occur, but not as often as if all students are running. How do the concepts of energy and speed, in the context of this classroom, directly affect a successful or unsuccessful collision?

Solution: The students are walking around at a fairly high speed but not running. If an arm to arm collision happens, then this is considered an unsuccessful reaction. However, if one student steps on another's shoe, a successful collision occurs. Of the collisions that occur, only a few will involve one student stepping on another's toes. This shows you that collisions must occur with the correct orientation. Many collisions between students will occur, but only a select few will be successful!

Example #3: Which beaker will have more collisions, and thus more chance of reactivity?

Beaker A: 10 ml beaker filled with 10 ml of a mixture.

Beaker B: 20 ml beaker filled with 10 ml of the same mixture.

Solution: Beaker A. The concentration is increased with less space, thus giving the atoms a higher chance of having enough energy and hitting at the correct orientation.

Example #4: When vinegar is added to baking soda, does the collision theory apply?

Solution: Yes, the fizzing and bubbling of the reaction is due to the collision theory, and is a good real-life example of the theory.

Example #5:When using a pipet to distribute HCl into an ice bath of Mg and boiling bath of Mg, which reaction will occur faster?

Solution: The boiling Mg will push the reaction to occur more quickly because higher heat results in higher kinetic energy.

Example #6: Does the collision theory apply to enzymes in the human body?

Solution: Yes. Enzymes are biological molecules that act as catalysts. Enzymes catalyze chemical reactions within the human body by decreasing the activation energy (Ea) required for a reaction to proceed. By lowering the Ea of the reaction taking place, there is a greater amount of energetic collisions present, and the reaction occurs at a faster rate.

### Contributors

• Kelly Cox, Asadullah Awan, Joslyn Wood, Sukhjeet Pabla

10:24, 31 Oct 2014

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This material is based upon work supported by the National Science Foundation under Grant Numbers 1246120, 1525057, and 1413739.