1. Kinetics Part IV: Activation Energy Jespersen Chapter 14 Sec 5 & 6
Dr. C. Yau
Spring 2014

2. The Collision Theory
The rate of a reaction is proportional to the number of effective collisions per second among the reactant molecules. We already know concentration plays an important part in rxn rate: Conc Freq Collision Rxn Rate Only EFFECTIVE collisions lead to products. Only a small fraction of collisions lead to products, based on two other factors: 1) Activation Energy 2) Molecular Orientation

3. Kinetic Energy Distribution
Ea = Activation energy = minimum energy needed for collision to be effective
REMEMBER: This is the graph for Kinetic Energy.
Don’t confuse with graph for Potential Energy.
Fig p.666
Activation Energy is not affected by increase in temperature.

4. Collision Theory Of Reactions
For a reaction to occur, three conditions must be met:
Reactant particles must collide.
Collision energy must be enough to break bonds/initiate.
Particles must be oriented so that the new bonds can form.
e.g. NO2Cl + Cl NO2 + Cl2
Figure 13.9 The importance of molecular orientation during a collision in a reaction. The key step in the decomposition of NO2Cl to NO2 and Cl2 is the collision of a Cl atom with a NO2Cl molecule. (a) A poorly oriented collision. (b) An effectively oriented collision.

5. Eqn Summarizing 3 Factors in Collision Theory
Particulate Level:
Rxn Rate (molecules L-1 s-1) =
N x forientation x fKE
N = # collisions per second per liter of mixture
forientation = fraction of collisions with effective orientation
fKE = fraction of collisions with sufficient kinetic energy for effective collision (area under the curve with KE  Ea

6. has been found to be related to Ea and T in this equation:
Mathematically, fKE
has been found to be related to Ea and T in this equation:
Still remember what fKE stands for?

7. Eqn Summarizing 3 Factors in Collision Theory
Macroscopic Level: Equation has to be in terms of moles instead of molecules. Conversion factor is So we divide the previous equation by Avogadro’s number to get reaction rate in units of mol L-1 s-1

8. Temperature Effects
Changes in temperature affect the rate constant, k, according to the
Arrhenius equation:
p is the steric factor
Z is the frequency of collisions.
Ea is the activation energy
R is the Ideal Gas Constant (8.314 J/(mol K)
T is the temperature (K)
We substitute A (the frequency factor) for (pZ))
Activation Energy (Ea) : The energy needed for the reaction to proceed. Includes the energy needed to break the bonds in the reactant molecules.
Frequency Factor (A) : The relative probability that the reactant molecules will collide in the proper orientation to initiate product formation.
This is an important equation to remember!

9. Graphical Determination of Ea
You are expected to be able to derive this yourself.
How exactly do we determine Ea?
What do we plot on the x-axis? on the y-axis?
How do we find Ea on the graph?

10. Example 14.12 p.670: Determine Ea in kJ/mol
What do we do with this data?

12. Ln k vs. 1/T
Ln k
Then what?...
How do we find Ea?

13. Determination of Ea from k at 2 temperatures
Ratio form: Can be used when A isn’t known.
You should be able to derive this equation for yourself. We did a similar derivation earlier this semester for Hvap, VP and T.
ChemFAQ: Calculate k at a selected temperature, given Ea and k at another temperature.

14. Example
Given that k at 25°C is 4.61×10-1 M/s and that at 50°C it is 4.64×10-1 M/s, what is the activation energy for the reaction?
ChemFAQ: Calculate k at a selected temperature, given Ea and k at another temperature.
Ea= 188 J/mol = 2 x102 J/mol
Can you think of a reason why the graphical method would give a more accurate value for Ea?

16. Working With The Arrhenius Equation
k (M/s)
T °C 25 50
100
150
Given the following data, predict k at 75°C using the graphical approach.
Trendline gives Ea/R and lnA. Substitute in 1/T in kelvin and solve for k.
Trendline: y = x – 6.908
k = ? at T = 75oC
ANS k=9.01×10-4M/s

17. T deg C k
1/T (in K-1)
ln k 25 50
150
100

18. In the reaction 2N2O5(g) 4 NO2(g) + O2(g) the following temperature and rate constant information is obtained. What is the activation energy of the reaction?
102 kJ mol-1
-102 kJ mol-1
1004 kJ mol-1
-1004 kJ mol-1
none of these
T (K)
k (s-1)
338
328
318
4.87(10-3)
1.50(10-3)
4.98(10-4)
Slope of plot = ; slope = -Ea/R ; R=8.314e-3 kJ/molK. Incorrect answers from other version of R
If we are to determine Ea graphically, what do we graph?
Slope = x104 K and y-intercept = 30.9, what are the units? What is Ea?
Practice with Example p.672, Exer.26,27,28

19. Potential Energy Diagrams
                                                                                                                                                                                                                                                                                                
The product is said to be “thermodynamically favored” over the reactant. LEARN THIS TERMINOLOGY.
Figure Potential-energy diagram for an exothermic reaction.

20. Potential Energy Diagrams
demonstrate the energy needs and products as a reaction proceeds
tell us whether a reaction is exothermic or endothermic
tell us if a reaction occurs in one step or several steps
show us which step is the slowest
Do not confuse PE diagram with KE diagram! Learn the terminology!
So, remember which is the KE diagram?

21. Potential Energy Diagram
What would the potential energy diagram look like for an endothermic reaction? Make a sketch of a PE diagram for an endothermic reaction. Where do we look to find the activation energy? Where do we look to find the heat absorbed during the reaction? What is thermodynamically favored?

22. Catalysts speed a reaction, but are not consumed by the reaction
PE Graph
speed a reaction, but are not consumed by the reaction
may appear in the rate law
lower the Ea for the reaction
may be heterogeneous or homogeneous PE
Reaction Coordinate
Ea of uncatalyzed rxn
Ea of catalyzed rxn
Figure Effect of a catalyst on a reaction. (a) The catalyst provides an alternative, low-energy path from the reactants to the products.

23. KE Graph: Effect of Catalyst
Fraction of Molecules
Kinetic Energy
Ea without catalyst
Ea with catalyst
000
000

24. Catalytic Actions may serve to weaken bonds through induction
may serve to change polarity through amphipathic/surfactant effects
may reduce geometric orientation effects
Heterogeneous catalyst: reactant and product exist in different states.
Homogeneous catalyst: reactants and catalyst exist in the same physical state

25. Example of a heterogeneous catalyst
Well-known “The Haber Process.” Fe
3H2 (g) + N2 (g) NH3 (g) Fe
Figure The Haber process. Catalytic formation of ammonia molecules from hydrogen and nitrogen on the surface of a catalyst.
Note: Fe is never consumed.
Catalysts do not have to be in large amounts.