ChE 551 Lecture 05

1. ChE 551 Lecture 05 Analysis Of Data From A Batch Reactor

2. 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. Figure 3.8 Typical batch data for reaction (3.7). Data of Tamaru[1955].

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

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

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

6. For A First Order Reaction rA = -k1CA (3.38) Substituting equation (3.38) into equation (3.31) and integrating yields: Memorize this equation (3.39) Derivation

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

8. Plots Of Equations

9. Table 3.4 Rate Laws For A Number Of Reactions

10. 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.

11. Key Challenge: First And Second Order Data Does Not Look That Much Different Vary k to fit data Same k(CA0)n-1

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

13. Essen’s Method Figure 3.15

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

15. Essen Plot For Example: r2=.984 r2=.999 r2=.981 Figure 3.16 No statistically significant difference between results.

16. Example Shows Essen’s MethodDoes Not Distinguish Between Models • In the literature, Essen’s method is often used. • Useful for impressing your boss since it always fits with good r2 (given good data) • It often gives the incorrect answers.

17. 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).

18. Equations For kone And ktwo Follow From Before Solve for k1 (3.39) (3.51) Derived previously Solve for kn (3.52) (3.42) Derived previously

19. Easy Solution: Define A VB Module In Microsoft Excel 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

20. Microsoft Excel/Visual Basic Return Types

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

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

23. Van’t Hoff Plot 0.2 K Oxidation of 3 Red Dye 0.15 Rate Constant K 2 0.1 K 1 0.05 0 5 10 15 Time, Mins Figure 3.18 Van’t Hoff plot of the data from tables 3.5 and 3.6 Van’t Hoff’s method is much more accurate than Essens’ method. Essen’s is more common!

24. Discussion Problem: Use Van’t Hoff’s Method To Determine The Order For The Following Data

25. Solution:

26. Solution Continued:

27. Van’t Hoff Plot 0.05 Hydration of K 3 Chloracetic Acid 0.04 Rate Constant K 2 0.03 K 1 0.02 0 10 20 30 40 50 Time, Mins Figure 3.18 Van’t Hoff plot of the data from tables 3.5 and 3.6

28. Discussion Problem 2 Ammonium-dinitramide, (ADN) NH4N(NO2)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.

29. 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.

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

31. Ca0= 1 Solution Cont. Van't Hoff's time Conc first second third ln(ca0/Ca) (Ca0/Ca)-1 (CA0/CA)^2-1 0 1 #VALUE! #VALUE! #VALUE! 300 0.84 0.000581 0.000635 0.001391 600 0.7 0.000594 0.000714 0.001735 900 0.58 0.000605 0.000805 0.002192 1200 0.49 0.000594 0.000867 0.002637 1500 0.41 0.000594 0.000959 0.003299 2400 0.24 0.000595 0.001319 0.006817

32. Solution Cont. c) from equ 3.39

33. 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

34. Class Question • What did you learn new today?