The Collision Theory and Activation Energy: Explaining How and Why Factors Affect Reaction Rates

The Collision Theory and
Activation Energy
Explaining how and why factors
affect reaction rates
The Maxwell-Boltzmann apparatus
• Maxwell and Boltzmann performed an
experiment to determine the kinetic energy
distribution of atoms
• Because all atoms of an element have roughly
the same mass, the kinetic energy of identical
atoms is determined by velocity (KE= ½mv2)
The Maxwell-Boltzmann distribution
• The resulting disk looks like this:
Basically, if we plot the
intensity of the dots on a
graph we get a graph of
fraction of atoms/molecules
vs. kinetic energy:
Molecules
Fraction of hit disk first
molecules
Molecules Kinetic energy 
hit disk last
Why is the graph skewed?
• This curve is characteristic of all molecules
• The curve is elongated due to how atoms
collide, and to the units of the graph
• Recall all particles are in motion. An average
speed will be reached.
• The graph is skewed because 0 is the lower
limit, but theoretically there is no upper limit
• More than that the graph is skewed because
the x-axis has units of energy not velocity
Same data, different
axes. E.g. v=1, KE=1
v=2, KE=4
velocity KE v=3, KE=9
Temperature and reaction rate
• By understanding the Maxwell-Boltzmann
distribution, we can begin to understand the
two reasons why an increase in temperature
causes an increase in reaction rate
Q- Look back at the five factors that affect
reaction rates. Three of these factors can be
(at least in part) explained by the collision
theory. Identify the 3 factors and explain how
the affect of each can be explained with
reference to the collision theory
A- Ability to meet (molecules that are well mixed
will have a greater chance of colliding)
Concentration of reactants (more molecules
means more collisions)
Temperature (faster moving molecules means
more collisions per unit of time).
• By increasing the temperature, a small number
of molecules reach Ea. The reaction is
exothermic, further increasing temperature and
causing more molecules to reach Ea, etc.
Shift due to higher

temperature
Fraction of
molecules
Ea
Kinetic energy 
Maxwell–Boltzmann Distributions
This fraction of molecules can be found through the expression
-Ea
RT
f=e
where R is the gas constant and T is the Kelvin temperature.
© 2009, Prentice-Hall, Inc.

Reaction Coordinate Diagrams
It is helpful to
visualize energy
changes throughout a
process on a reaction
coordinate diagram
like this one for the
rearrangement of
methyl isonitrile.

Reaction Coordinate Diagrams
• The diagram shows the
energy of the reactants and
products (and, therefore,
E).
• The high point on the
diagram is the transition
state.
• The species present at the transition state is called the
activated complex.
• The energy gap between the reactants and the activated
complex is the activation energy barrier.

Endothermic Reactions
Exothermic Reactions
The Arrhenius Equation
 Ea / RT
k  Ae
k = rate constant at temperature T
 A = frequency factor
 Ea = activation energy
 R = Gas constant, 8.31451 J/K·mol
The Arrhenius Equation, Rearranged
Ea 1
ln(k )      ln( A)
R T 
 Simplifies solving for Ea
 -Ea / R is the slope when (1/T) is plotted against ln(k)
 ln(A) is the y-intercept
 Linear regression analysis of a table of (1/T) vs. ln(k) can
quickly yield a slope
 Ea = -R(slope)
Arrhenius Equation
Taking the natural
logarithm of both sides,
the equation becomes
Ea
ln k = - ( 1 ) + ln A
R T
y = m x + b
Therefore, if k is determined experimentally at
several temperatures, Ea can be calculated from the
1
slope of a plot of ln k vs. . T

Catalysis
•Catalyst: A substance that speeds up a reaction
without being consumed
•Enzyme: A large molecule (usually a protein) that

catalyzes biological reactions.
•Homogeneous catalyst: Present in the same phase as

the reacting molecules.
•Heterogeneous catalyst: Present in a different phase

than the reacting molecules.
Lowering of Activation Energy
by a Catalyst
Catalysts Increase the Number of
Effective Collisions
Heterogeneous Catalysis
Carbon monoxide and
nitrogen monoxide adsorbed
Step #1: Adsorption on a platinum surface
and activation of the
reactants.
Carbon monoxide and
nitrogen monoxide arranged
Step #2: prior to reacting
Migration of the
adsorbed reactants on
the surface.
Carbon dioxide and nitrogen
form from previous molecules
Step #3:
Reaction of the
adsorbed substances.
Carbon dioxide and nitrogen

gases escape (desorb) from the
platinum surface
Step #4:
Escape, or
desorption, of the
products.

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The Collision Theory and

Shift due to higher

© 2009, Prentice-Hall, Inc.

© 2009, Prentice-Hall, Inc.

© 2009, Prentice-Hall, Inc.

© 2009, Prentice-Hall, Inc.

•Enzyme: A large molecule (usually a protein) that

•Homogeneous catalyst: Present in the same phase as

•Heterogeneous catalyst: Present in a different phase

Carbon dioxide and nitrogen

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