ChE 452 Lecture 04

1. ChE 452 Lecture 04 Measuring Rate Data

2. Objective • General concepts in measurement of rate data • Compendium of methods (language) • Direct vs indirect • Design of experiments

3. General Approach Initiate reaction measure concentration vs time fit data to calculate rates

4. Rate Measurements: An Old Topic Figure 3.1 Wilhelmy’s [1850] measurements of the changes in sucrose concentration in grape juice after acid is added.

5. Many Methods To Do Measurements • Techniques include: conventional, stopped flow, temperature jump… • Differ via time scale of reaction • Need to mix reactants and initiate reaction before reaction is done • Different techniques used for fast reactions than slow ones

6. Batch Methods To Measure Reaction Rates Table 3.1

7. Batch Methods Continued

8. Flow Methods To Measure Reaction Rates

9. How Do You Decide What Experimental Method To Use? Key Issues: • Direct method or indirect method • Can measurement be done on an appropriate time scale?

10. Direct vs Indirect Methods Recall – rate equation is the rate as a function of the concentrations • Direct method - any method where you actually measure the rate as a function of concentration • Indirect method - a method where you measure some other property (i.e. concentration vs time) and infer a rate equation.

11. Example: Consider Arsine Doping Of Silicon Figure 3.6 A typical arsine decomposition reactor.

12. Direct Measurement Figure 3.7 A possible apparatus to examine the decomposition of arsine (AsH3) on silicon.

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

14. A Comparison Of The Advantages And Disadvantages Of Direct And Indirect Methods Direct Method Advantages • Get rate equation directly • Easy to fit data to a rate law • High confidence on final rate equation Disadvantages • Difficult experiment • Need many runs • Not suitable for very fast or very slow reactions Indirect Method Disadvantages • Must infer rate equation • Hard to analyze rate data • Low confidence on final rate equation Advantages • Easier experiment • Can do a few runs and get important information • Suitable for all reactions including very fast or very slow ones

15. Other Notation Direct method • differential method • differential reactor Indirect method • integral method

16. Initial Rate Method • Start with multiple parallel reactors • Fill each with a different concentration • Let reaction go & measure conversion vs time • Get rate from slope extrapolated to zero

17. Next: Start Analysis Of Data From Indirect Reactors: Which is easier to analyze? • Direct method (rate vs concentration • Indirect method (concentration vs time) Direct is easier to analyze.

18. Analysis Of Data From A Differential Reactor General method – least squares with rate vs time data Figure 3.10 The rate of copper etching as a function of the oxygen concentration. Data of Steger and Masel [1998].

19. Next: Multiple Variable Analysis • Rates of reaction usually strongly effected by many variables • Temperature: concentration, solvents, inpurities, catalysts, …… • So far only consider one variable: Concentration

20. Example: Develop A Rate Equation For The Growth Of Grass Variables • Sunlight • Rain • Amount of grass seed • Number of birds and insects • Fertilizer • Soil type • Soil bacteria How do we proceed to measure a rate?

21. Usual Technique: Initial Rate Method • Start with multiple parallel reactors • Fill each with a different concentration • Let reaction go & measure conversion vs time • Get rate from slope extrapolated to zero

22. If We Have Several Variables, What Do We Measure? General approach • Take some preliminary data to determine what variables are important • Usually requires multiple iterations • Take more detailed measurements on the variables that are most important

23. Design Of Experiments To Determine Which Variables Are Important • 2n designs • Pick two values of each of the variables • Look at two possibilities for each variable • Do experiments for all combinations • Do analysis to decide which variables are important

24. Example: How Does Temperature And Concentration Affect Selectivity Of A Reaction • Pick two values of each variable Temperature + = higher temperature Temperature - = lower temperature Concentration + = higher concentration Concentration - = lower concentration • Look at all possibilities

25. Table of All Possibilities

26. How Do We Analyze The Data? • Look at the deviation from the mean • Calculate row averages

27. For Our Example, Mean=45%

28. Calculate Row Averages

29. First Conclusion • Want temperature to be low • Cannot tell about concentration

30. Calculate Row Averages

31. Is It True That We Do Not Care About Concentration? Answer no: If the temperature is low, can improve conversion by keeping the concentration high – it is just that the opposite effect occurs when the temperature is high

32. Lets Examine The Effect Of TC (Simultaneous Variation of T+C) Want T – and TC -

33. Can Extend Process To Several Variables Gives too many runs

34. Software To Help • Concept: we usually want to fit the data to a simple function: Response=C1+C2A+C3B+… Only need enough runs to fit constants accurately

35. Echip Software Example

36. Software Setup

37. Number of Runs Substantially Reduced • 4 variables, 4 values with 3 replicates gives (4)4 + 3*4 = 268 runs • Echip achieves almost the same accuracy with 23 runs!

38. Summary • Single variables use ANOVA to check models • Multivariable problems • Use design of experiments to see which variables are important (2n) designs • Software can simplify runs • Use variances to fit models (automatic in software)

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