1. ChE 452 Lecture 08 Analysis Of Data From A Batch Reactor 1

2. Objective Data analysis from indirect measurements Essen’s method (learned in p-chem) Does not usually work Van’t Hoff’s method Accurate but amplifies errors in data 2

3. Background: Kinetic Data After Measuring Indirect method – a method where you measure some other property (i.e. concentration vs time) and infer a rate equation. 3 Figure 3.8 Typical batch data for reaction (3.7). Data of Tamaru[1955].

4. Objective For Today: Analysis Of Rate Data Derive basic equations Essen’s method Van’t Hoff’s method 4

5. Derivation Of Performance Equation For A Batch Reactor 5 For A  B, the moles of A reacted/volume/time will equal the reaction rate, i.e. (1) C A is the concentration of A,  is time, and r A is the rate of reaction per unit volume. Figure 3.11 A batch reactor

6. Integration Yields The Following 6 (3.31) Memorize this equation

7. For A First Order Reaction r A = -k 1 C A (3.38) Substituting equation (3.38) into equation (3.31) and integrating yields: 7 Memorize this equation (3.39) Derivation

8. Derivation For A First Order Reaction 8 r A = -k 1 C A

9. For An nth Order Reaction: 9 (3.41) Substituting equation (3.41) into equation (3.31), integrating, and rearranging yields: (3.42) Memorize this equation Derivation

10. Derivation For An nth Order Reaction 10

11. Plots Of Equations 11

12. Table 3.4 Rate Laws For A Number Of Reactions 12 Rate Laws for a number of reactions ReactionRate LawDifferential EquationIntegral Equation A  Products A+B  Products r A =k A A  Products A+B  Products r A =k A [A] A  Products A+B  Products r A =k A [A] n A+B  Products r A =k A [A][B] A+2B  Products r A =k A [A][B] A  B r A =k 1 [A]- k 2 [B]

13. Fitting Batch Data To A Rate Law Steps Start with a batch reactor and measure concentrations vs time. Fit those data to a first order and a second order rate law and see which equation fits better. Whichever rate equation fits best is assumed to be the correct rate equation for the reaction. 13

14. Key Challenge: First And Second Order Data Does Not Look That Much Different 14 Same k(C A 0 ) n-1 Vary k to fit data

15. Essen’s Method 15 First order nth order (3.42) (3.39)

16. Essen’s Method 16 Figure 3.15

17. Example: The Concentration Of Dye As A Function Of Time 17 Table 3.5

18. Essen Plot For Example: 18 r 2 =.984 r 2 =.999 r 2 =.981 No statistically significant difference between results. Figure 3.16

19. Example Shows Essen’s Method Does Not Distinguish Between Models In the literature, Essen’s method is often used. Useful for impressing your boss since it always fits with good r 2 (given good data) It often gives the incorrect answers. 19

20. Van’t Hoff’s Method Take batch data as before. Calculate kone (first order rate constant) ktwo (second order rate). kone should be constant for a first order reaction, ktwo should be constant for a second order reaction. (Use f test to check). 20

21. Equations For kone And ktwo Follow From Before 21 (3.39)(3.51) (3.52) (3.42) Solve for k 1 Solve for k n Derived previously

22. Easy Solution: Define A VB Module In Microsoft Excel 22 Public Function kone(ca0, ca, tau) As Variant kone = Log(ca0 / ca) / tau End Function Public Function ktwo(ca0, ca, tau) As Variant ktwo = ((1# / ca) - (1# / ca0)) / tau End Function Public Function kthree(ca0, ca, tau) As Variant kthree = ((1# / ca) ^ 2 - (1# / ca0) ^ 2) / tau End Function

23. Microsoft Excel/Visual Basic Return Types 23 As VariantGeneral return type (can be an integer, real, vector, matrix, logical or text) As SingleSingle precision real As DoubleDouble precision real As IntegerInteger

24. The Formulas In The Spreadsheet For Van’t Hoff’s Method 24

25. The Numerical Values For Van’t Hoff’s Method 25

26. Van’t Hoff Plot 26 Van’t Hoff’s method is much more accurate than Essens’ method. Essen’s is more common! Figure 3.18 Van’t Hoff plot of the data from tables 3.5 and 3.6

27. Discussion Problem: Use Van’t Hoff’s Method To Determine The Order For The Following Data 27 Table 4.1 Buchanan’s [1871] data for the reaction: CICH 2 COOH + H 2 COOH + HCI at 100º C Time Hours[CICH 2 COOH] gms/liter 0 2 3 4 6 10 13 19 28 34.5 43 48 4 3.80 3.69 3.60 3.47 3.10 2.91 2.54 2.26 1.95 1.59 1.39

28. Solution: 28

29. Solution Continued: 29

30. Van’t Hoff Plot 30 01020304050 0.02 0.03 0.04 0.05 Time, Mins Rate Constant K 3 K 2 K 1 Hydration of Chloracetic Acid Figure 3.18 Van’t Hoff plot of the data from tables 3.5 and 3.6

31. Discussion Problem 2 Ammonium-dinitramide, (ADN) NH 4 N(NO 2 ) 2, is a oxidant used in solid fuel rockets and plastic explosives. ADN is difficult to process because it can blow up. Oxley et. Al., J. Phys chem A, 101 (1997) 5646, examined the decomposition of ADN to try to understand the kinetics of the explosion process. At 160º C they obtained the data in Table P3.20. 31

32. Discussion Problem 2 Continued: a) Is this a direct or indirect measurement of the rate? b) Use Van’t Hoff’s Method to fit this data to a rate equation. c) If you had to process ADN at 160° C, how long could you run the process without blowing anything up? Assume that there is an explosion hazard once 5% of the ADN has reacted to form unstable intermediates. 32

33. This Is An Indirect Measurement! Use Same Spreadsheet As Before To Fit Data 33

34. Solution Cont. 34 Ca0=1 Van't Hoff's timeConcfirstsecondthird ln(ca0/Ca)(Ca0/Ca)-1(CA0/CA)^2-1 01#VALUE! 3000.840.0005810.0006350.001391 6000.70.0005940.0007140.001735 9000.580.0006050.0008050.002192 12000.490.0005940.0008670.002637 15000.410.0005940.0009590.003299 24000.240.0005950.0013190.006817

35. Solution Cont. c) from equ 3.39 35

36. Summary: Two Methods To Fit Rate Data Essen’s Method Most common method Plots look the best Gives great looking results even with incorrect rate equation Van’t Hoff’s Method More accurate than Essen Rare in literature Plots noisier Highlights weaknesses in rate equations 36

37. Class Question What did you learn new today? 37