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ChemWiki: The Dynamic Chemistry E-textbook > Physical Chemistry > Kinetics > Modeling Reaction Kinetics > Collision Theory > Collision Theory I

Collision Theory I

Proposed by Max Trautz and William Lewis in the early 1900's, the collision theory is essentially a detailed section of the kinetic-molecular theory; it is strongly interconnected to chemical kinetics. The theory is basically used to explain how different variables change the rate of reaction. This theory is based on the idea that reactant particles must collide for a reaction to occur, but only a small percentage of the total collisions have the energy and "orientation" to connect effectively and cause the reactants to form into the products. The field of study involving molecular collisions developed vigorously in the 1980’s 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. To create a reaction, species need to collide. However, not all collisions result in a reaction. In order for molecules to react, a physical chemist named Svante Arrhenius explains that the colliding molecules must possess enough kinetic energy to overcome the repulsive and bonding forces of the reactants. This minimum amount of energy required for a chemical reaction to occur is known as the activation energy.


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Ea > repulsive and bonding forces of the reactants

The higher the Ea 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 Ea, so not all collisions lead to reactions and product formation. Reversely, the lower the Ea of a reaction, the greater the amount of energetic collisions present, and the faster the reaction.

Effects of Energy

A reaction will not be able to occur if the particles do not collide with the activation energy of the reaction, which is the minimum amount of energy above the average kinetic energy needed for a reaction to occur.

If the atoms collide with less energy than the activation energy, the atoms simply bounce off and away from each other. Only the 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 whentwo reactant molecules collide in one elementary step. Bimolecular reactions are the most common type of reaction molecularity. 
An example of a bimolecular reaction would be the collision of N2O and NO, forming the products N2 and NO2
Another example would be the collision of glucose and O2, forming the products CO2 and water.

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

k = Ae(-Ea/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/molK.

A termolecular reaction occurswhen 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. No reactions with molecularities higher than three have yet been observed.

Maxwell-Boltzmann Distribution

It is very useful to know the types of proportion of atoms that have high enough energies to cause a chemical reaction when colliding. 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

File:Physical_Chemistry/Kinetics/Rate_Laws/Gas_Phase_Kinetics/Collision_Theory/Collision_Theory_I/Maxwell-Boltzmann.bmp

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

The rate of almost all chemical reaction increases with an increase in temperature. Particles that move fast collide more often and with greater kinetic energy. Effective collisions will increase 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

                                      graph 2.jpg

 

 

Effects of Orientation

In any collision with unsymmetrical atoms, the orientations of the atoms during collision are crucial in creating a reaction. The reaction rate is affected by the orientation because without the proper orientation during collision, the reaction will not occur at all.

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

orientation.jpg

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 carbons 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:
(Please note that carbon is in black, hydrogen in pink, and chloride in green.)

collision!.bmp

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 all spherical and symmetrical in every way; this means that the orientation will be 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

hydrogen.bmp

 

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 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

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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 are a group of blindfolded students and you have them walk around the room at a slow pace. A pair of students will bump in 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 most likely going 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. Do you see the concept of energy and speed, and how they directly affect a successful or unsuccessful collision?

Solution: The students are walking around at a pretty high speed but not running. If an arm to arm collision happens, then this is considered an unsuccessful reaction. On the other hand if one student steps on another's shoe, a successful collision occurs. You will see that of the  collisions that happen, only a few will be 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 is going to have more collisions, 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 is the correct answer because 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 you add vinegar to baking soda does the collision theory take place?

Solution: Yes, the fizzing and bubbling of the reaction requires the collision theory to occur in every facet. This is a real-life example of the collision 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 ,remember, higher heat tends to result 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

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21:49, 21 Feb 2014

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