1. ChE 452 Lecture 03 Variations In Rate With Temperature 1

2. Objectivge For Today Review Arrhenius’ law Develop some rules of thumb that allow one to estimate activation barriers from very little data. 2

3. Variations in Rate With Temperature Huge Rate variations with temperature are much larger than variations in rate with concentration Factor of two in concentration gives factor of 2-4 in rate Factor of 2 in temperature gives 10 7 variation in rate 3

4. Homogeneous Reactions Rate increases with increasing temperature 4 Figure 2.10 The rate of E. Coli growth as a function of temperature adapted from Bailey and Ollis [1977].

5. Heterogeneous Reactions Rate has a maximum at intermediate temperatures 5 Figure 2.18 The rate of the reaction CO + 2 O 2  CO 2 on Rh(111). Data of Schwartz, Schmidt and Fisher[1986].

6. Models For Variations In Rate With Temperature Key processes Molecules get hot Cross a barrier 6

7. Models For Variations In Rate With Temperature Key processes Molecules get hot Cross a barrier Models Perrin’s Model: energy transfer dominates Arrhenius’ Model: barrier dominates 7

8. Perrin’s Model Assume energy transfer dominates. k = k T T n k = rate constant k T = preexponential n = constant between 1 and 4 8 (2.24)

9. Arrhenius’ Model Assume barrier dominates k = k o exp(-E a /k B T) k o = preexponential E a = activation barrier, kJ/molecule k B = Boltzman’s constant, 1.381x10 -23 J/K T = temperature (K) 9 (2.26)

10. Arrhenius’ Model In Kcal/mole Assume barrier dominates k = k o exp(-E a /RT) k o = preexponential E a = activation barrier, kcal/molecule R = Gas law constant, 1.98x10 -3 kcal/mole/K T = temperature (K) 10

11. Real Data Somewhere In Between 11 Figure 2.6 The rate of the reaction CH + N 2  HCN + N as a function of the temperature. Data of Becker, Gelger and Wresen[1996].

12. Best Fit Of Real Data Uses A Combined Expression 12 Arrhenius’ effect much larger than Harcourt and Essen (2.28)

13. Rates Double Or Triple When The Temperature Rises By 10 K 13 ReactionTemperature range,  C Rate Change with a 10- K Temperature Change 3.6-30.42.03 23.5-43.62.87 24.5-43.62.68 0-613.0 Table 2.6 The variation in rate of a series of reactions with a 10-K change in temperature

14. Also Works For Biological Processes 14 Table 2.7 The variation in the respiration rate of plants with a 10  change in temperature. Data of Clausen[1890]. Wheat2.47 Lilac2.48 Lupine2.46 Figure 2.10 The rate of E. Coli growth as a function of temperature adapted from Bailey and Ollis [1977].

15. Crickets Chirping Example 15 Figure 2.11 The rate that crickets chirp as a function of temperature. Data for field crickets (Gryllys pennsylvanicus)

16. Examples From You Own Life Why does bread taste better warm? Why does beer taste better cold? Why do you refrigerate, freeze food? Why do you maintain a body temperature? Why do amphibians stop moving when it is cold Why a fever? 16

17. Next Key Implications Of Arrhenius’ Law 17 (2.32) (2.33) Figure 2.8 A plot of  ½ vs. E A at 100, 200, 300, 400, and 500 K. (2.31)

18. Example Question Assume that you are measuring the kinetics of sponification of ethyl acetate in the unit ops lab, and you find that you get 50% conversion in 20 minutes at 25  C. What is the activation energy of the reaction? How long should it take to get to 50% conversion at 35  C. 18

19. Example Assume that a reaction has an activation barrier of 35 kcal/mole. Approximately what temperature do we want to run it? 19

20. Summary: Cont Arrhenius’ law and Perrin’s model Arrhenius: barrier dominates Perrin: energy transfer dominates Truth in between Biological processes follow the same rate laws as chemical processes Leads to simple ways to estimate activation barriers 20