Collision Theory

We assume that particles must collide in order to react. Thus a first understanding of reaction rates is based on understanding what influences the frequency of collisions.

• Molecularites. This refers to the numbers of molecules (or particles - can also be atoms or ions) involved in the collision.
  • unimolecular - only one molecule involved (there is no collision)
  • bimolecular - 2 body collision
  • termolecular - 3 body collision (this is very rare, essentially never get more than three body collisions)
• Concentration, the rate will depend on concentration. Thus for the bimolecular reaction of A and B
  • rate Z_o[A][B] where Z_o is the collision frequency when [A] = [B] = 1 M
• Not all collisions will lead to reaction. At least two additional factors are important:
  • Activation energy, E_a. This is the energy needed to overcome repulsion, bond strength etc. At any particular temperature the number of particles with a given energy is specified by N = e^-(E_a/RT). Note that
    • as E_a increases the fraction decreases.
    • as T increases, the fraction increases. Arrhenius Equation, k = Ae^-(E_a/RT). Can plot fraction of particles with a given KE vs. T (KE). A crude relation, which holds approximately for many common reactions is the so called Q₁₀. This states that for every 10 °C increase in temperature we get a doubling of reaction rate.
  • Orientation of collision. The steric factor or probability factor (p) is the fraction of collisions which have orientations favorable for reaction. Can range from very small numbers (one atom or molecule must hit another at a very specific place) to about 1.
• Putting these factors together we can then write:

 

r = p (e^-(E_a/RT)) Z_o[A][B]

r = k [A][B]

• Note that for kinetics the stoichiometry of the reaction is not necessarily related to the rate law, rather the rate law is related to a single slow step in the reaction process.

 

 

 

 

 

 

 

 

 

 

public domain image via Wikipedia Creative Commons

 

Arrhenius Equation & Plot

ln k = (-E_a/R) (1/T) + ln A

public domain image via Wikipedia Creative Commons

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Transition States and Reaction Progress (Reaction Coordinate) Diagrams

Reaction with -G:

 

 

 

 

Reaction with +G:

A + B C + D, where r = k[A]²

we could write

2 A C + X

B + X A + D

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A + B C + D

 

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© R A Paselk

Last modified 21 April 2007