Chem 2 - Chemical Kinetics VIII: The Arrhenius Equation, Activation Energy, and Catalysts

1. Chemical Kinetics (Pt. 8)
The Arrhenius Equation,
Activation Energy, and
Catalysts
By Shawn P. Shields, Ph.D.
This work is licensed by Shawn P. Shields-Maxwell under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0
International License.

2. Reaction Rates and Temperature
The rate of a reaction generally goes
up with increasing temperature.
The rate constant k is temperature
dependent.
Why?

3. Factors Affecting Reaction Rates
The overall reaction rate depends on:
The frequency of collisions
The fraction of collisions with enough
energy to react
The orientation of colliding molecules
(steric factor)

4. The Arrhenius Equation
Molecules only react if they collide
with each other in the correct
orientation.
Increasing the temperature increases
the energy and frequency of molecular
collisions.
The Arrhenius equation relates the
rate constant k to all of these factors.

5. The Arrhenius Equation
𝒌 = 𝐀𝐞
−𝐄 𝐚
𝐑𝐓
k is the rate constant
Ea is the activation energy (to be discussed)
“A” is the pre-exponential factor representing the
likelihood that collisions with the proper orientation occur.
R is the gas constant (8.314 J/mol K)
T is the temperature in Kelvin

6. The Arrhenius Equation and the Rate Law
For the elementary reaction:
D + B C
The rate law is: Rate = k[D][B]
Plug in the Arrhenius equation to visualize
its effect on the rate of reaction:
𝐑𝐚𝐭𝐞 = 𝐀𝐞
−𝐄 𝐚
𝐑𝐓 𝐃 𝐁𝒌 = 𝐀𝐞
−𝐄 𝐚
𝐑𝐓

7. Activation Energy, Ea
The macroscopic reaction rate is determined by the
frequency of collisions having sufficient energy to
overcome the activation energy barrier (subtracting
those that do not have the correct orientation to
react (steric factor)).
Molecules need to have enough kinetic energy to
overcome bonding and repulsions of the reactants.
This required minimum amount of energy is
called the activation energy Ea

8. Temperature and Activation Energy
Only a small percentage of collisions have enough energy to react.
This proportion increases with increasing temperature.
Fraction of
molecules with
energy E
Energy Activation
Energy Ea
Fraction of molecules
greater than Ea
(enough E to react)
Low T
High T

9. Finding Ea by Graphing
𝒌 = 𝐀𝐞
−𝐄 𝐚
𝐑𝐓
Take the natural log (ln) of both sides
𝐥𝐧 𝒌 =
−𝐄 𝐚
𝐑𝐓
+ 𝐥𝐧 𝐀
Plot ln k vs 1/T to determine the
activation energy.

10. Finding Ea by Graphing
𝐥𝐧 𝒌 =
−𝐄 𝐚
𝐑𝐓
+ 𝐥𝐧 𝐀

11. Finding Ea by Graphing
𝐥𝐧 𝒌 =
−𝐄 𝐚
𝐑𝐓
+ 𝐥𝐧 𝐀
Reactions with a larger Ea show a higher sensitivity of the
rate constant k to the temperature.

12. Arrhenius Equation
Another useful form of the equation relates
the rate constant k at two temperatures
ln
𝑘2
𝑘1
= −
Ea
R
1
T2
−
1
T1
Where k1 is the rate constant at T1, and k2
is the rate constant at T2

13. Reaction Progress and Activation Energy
Exothermic Reaction Endothermic Reaction

14. Increasing the Rate Constant k
There are two ways to increase the rate constant
for a given reaction:
 raise the temperature
 use a catalyst to lower the activation energy Ea
Catalysts change the reaction mechanism in such
a way as to decrease the activation energy Ea.

15. Catalysts Lower Ea
𝐥𝐧 𝒌 =
−𝐄 𝐚
𝐑𝐓
+ 𝐥𝐧 𝐀
Catalysts essentially
increase the number of
molecules with the
required activation
energy to react by
lowering the requirement.

16. Another View: Catalysts Lower Ea
Instead of
increasing the
temperature, use
a catalyst to
lower the energy
barrier to
reaction.
Catalysts change
the reaction
mechanism.

17. Catalysts
Catalysts do not change the thermodynamics of
the reaction (i.e., they do not change the position
of equilibrium). More on that later…
Catalysts are not used up or produced in a
reaction.
They can be used in less than “stoichiometric
quantities” (or very small amounts).
They can be homogeneous (same phase) or
heterogeneous (alternate phase) catalysts.

18. Example Problems
will be posted separately.