Understanding Activation Energy in Chemical Reactions

1. Kinetics Part IV: Activation EnergyJespersen Chapter 14 Sec 5 & 6 Dr. C. Yau Spring 2013

2. The Collision Theory The rate of a reaction is proportional to the number of effectivecollisions 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. Activation Energy is not affected by increase in temperature. 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 14.11 p.666

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

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. 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)) 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 Then what?... How do we find Ea? Ln k

13. Determination of Ea from k at 2 temperatures Ratio form: Can be used when A isn’t known. For those who like math, turn in a careful derivation for bonus points. You must show every step.. You are not allowed to get help from anyone, due next period.

14. Example Given that k at 25°C is 4.61×10-1M/s and that at 50°C it is 4.64×10-1 M/s, what is the activation energy for the reaction? 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 Given the following data, predict k at 75°C using the graphical approach. Trendline: y = -36.025x – 6.908 k = ? at T = 75oC ANS k=9.01×10-4M/s

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 • -102 kJ • 1004 kJ • -1004 kJ • none of these If we are to determine Ea graphically, what do we graph? Slope = -1.224x104 and y-intercept = 30.9, what are the units? What is Ea? Practice with Example 14.12 p.672, Exer.26,27,28

19. Potential Energy Diagrams

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?

22. PE Reaction Coordinate Catalysts PE Graph • speed a reaction, but are not consumed by the reaction • may appear in the rate law • lower the Eafor the reaction • may be heterogeneous or homogeneous Ea of uncatalyzed rxn Ea of catalyzed rxn

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

24. CatalyticActions • 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. Fe Example of a heterogeneous catalyst Well-known “The Haber Process.” 3H2(g) + N2 (g) 2NH3 (g) Fe Note: Fe is never consumed. Catalysts do not have to be in large amounts.