14-8 Theoretical Models for Chemical Kinetics

1. 14-8 Theoretical Models for Chemical Kinetics • Kinetic-Molecular theory can be used to calculate the collision frequency. • In gases 1030 collisions per second. • If each collision produced a reaction, the rate would be about 106 M s-1. • Actual rates are on the order of 104 M s-1. • Still a very rapid rate. • Only a fraction of collisions yield a reaction. Collision Theory General Chemistry: Chapter 14

2. Activation Energy • For a reaction to occur there must be a redistribution of energy sufficient to break certain bonds in the reacting molecule(s). • Activation Energy: • The minimum energy above the average kinetic energy that molecules must bring to their collisions for a chemical reaction to occur. General Chemistry: Chapter 14

3. Activation Energy General Chemistry: Chapter 14

4. Kinetic Energy General Chemistry: Chapter 14

5. Collision Theory • If activation barrier is high, only a few molecules have sufficient kinetic energy and the reaction is slower. • As temperature increases, reaction rate increases. • Orientation of molecules may be important. General Chemistry: Chapter 14

6. Collision Theory General Chemistry: Chapter 14

7. Transition State Theory • The activated complex is a hypothetical species lying between reactants and products at a point on the reaction profile called the transition state. General Chemistry: Chapter 14

8. -Ea 1 ln k = + lnA R T 14-9 Effect of Temperature on Reaction Rates • Svante Arrhenius demonstrated that many rate constants vary with temperature according to the equation: k = Ae-Ea/RT General Chemistry: Chapter 14

9. -Ea = -1.2104 K R Arrhenius Plot N2O5(CCl4)→ N2O4(CCl4) + ½ O2(g) -Ea = 1.0102 kJ mol-1 General Chemistry: Chapter 14

10. -Ea 1 ln k = + ln A R T 1 -Ea 1 -Ea ln k2– ln k1 = + ln A - - ln A T2 R T1 R k1 1 1 -Ea ln = - k2 T1 T2 R Arrhenius Equation k = Ae-Ea/RT General Chemistry: Chapter 14

11. 14-10 Reaction Mechanisms • A step-by-step description of a chemical reaction. • Each step is called an elementary process. • Any molecular event that significantly alters a molecules energy of geometry or produces a new molecule. • Reaction mechanism must be consistent with: • Stoichiometry for the overall reaction. • The experimentally determined rate law. General Chemistry: Chapter 14

12. Elementary Processes • Unimolecular or bimolecular. • Exponents for concentration terms are the same as the stoichiometric factors for the elementary process. • Elementary processes are reversible. • Intermediates are produced in one elementary process and consumed in another. • One elementary step is usually slower than all the others and is known as the rate determining step. General Chemistry: Chapter 14

13. d[HI] = k[H2][ICl] H2(g) + ICl(g) HI(g) + HCl(g) dt HI(g) + ICl(g) I2(g) + HCl(g) d[I2] = k[HI][ICl] dt d[P] = k[H2][ICl] dt Slow Step Followed by a Fast Step d[P] H2(g) + 2 ICl(g) → I2(g) + 2 HCl(g) = k[H2][ICl] dt Postulate a mechanism: slow fast H2(g) + 2 ICl(g) → I2(g) + 2 HCl(g) General Chemistry: Chapter 14

14. Slow Step Followed by a Fast Step General Chemistry: Chapter 14

15. d[P] = -kobs[NO2]2[O2] dt k1 2NO(g) N2O2(g) fast k-1 d[NO2] k2 k1 slow N2O2(g) + O2(g) 2NO2(g) = k2[N2O2][O2] [N2O2] [NO]2 = K[NO]2 = dt k1 [N2O2] k-1 K = = d[I2] k1 k-1 [NO] = k2 [NO]2[O2] dt k-1 Fast Reversible Step Followed by a Slow Step 2NO(g) + O2(g) → 2 NO2(g) Postulate a mechanism: 2NO(g) + O2(g) → 2 NO2(g) General Chemistry: Chapter 14

16. Catalytic Converters • Dual catalyst system for oxidation of CO and reduction of NO. cat CO + NO CO2 + N2 General Chemistry: Chapter 14

17. 14-5 Catalysis General Chemistry: Chapter 14

18. Worked Examples Follow: General Chemistry: Chapter 14

19. General Chemistry: Chapter 14

20. General Chemistry: Chapter 14

21. General Chemistry: Chapter 14

22. CRS Questions Follow: General Chemistry: Chapter 14

23. X+Y Energy A+B reaction coordinate Energy Energy A+B A+B X+Y X+Y reaction coordinate reaction coordinate 1. 2. A+B Energy The reaction between A and B is determined to be a fairly fast reaction and slightly exothermic. Which of the following potential energy surfaces fit this description? X+Y reaction coordinate 3. 4. General Chemistry: Chapter 14

24. X+Y Energy A+B reaction coordinate Energy A+B X+Y reaction coordinate 1. 2. A+B Energy The reaction between A and B is determined to be a fairly fast reaction and only slightly exothermic. Which of the following potential energy surfaces fit this description? X+Y reaction coordinate 3. 4. Energy A+B X+Y reaction coordinate General Chemistry: Chapter 14

25. A particular reaction was found to have forward and reverse activation energies of 60 and 140 kJ mol-1, respectively. The enthalpy change for the reaction is, (do not use a calculator) R Energy 1. DH = 60 kJ mol-1 2. DH = -60 kJ mol-1 P 3. DH = 80 kJ mol-1 reaction coordinate 4. DH = -80 kJ mol-1 5. DH = 140 kJ mol-1 General Chemistry: Chapter 14

26. A particular reaction was found to have forward and reverse activation energies of 60 and 140 kJ mol-1, respectively. The enthalpy change for the reaction is, (do not use a calculator) R Energy 1. DH = 60 kJ mol-1 2. DH = -60 kJ mol-1 P 3. DH = 80 kJ mol-1 reaction coordinate 4. DH = -80 kJ mol-1 5. DH = 140 kJ mol-1 General Chemistry: Chapter 14

27. 1. A+B Energy X+Y reaction coordinate A+B Energy X+Y Energy X+Y A+B reaction coordinate reaction coordinate 2. A+B Energy X+Y In which diagram to the right does the dashed line best represent the catalyzed version of the reaction’s potential energy profile? reaction coordinate 3. 4. General Chemistry: Chapter 14

28. 1. A+B Energy X+Y reaction coordinate A+B Energy X+Y Energy X+Y A+B reaction coordinate reaction coordinate 2. A+B Energy X+Y In which diagram to the right does the dashed line best represent the catalyzed version of the reaction’s potential energy profile? reaction coordinate 3. 4. General Chemistry: Chapter 14

29. Textbook End of Chapter ?’s: • P.611- #1, 3, 11, 13, 17, 19, • 21, 33, 47, 51, 55, 100, 101, • 102, 103, 104, 105 General Chemistry: Chapter 14