Chemical Reaction Engineering Review: Stoichiometry, Equilibrium Conversion, Mole Balances

1. Lecture 4 Kjemisk reaksjonsteknikk Chemical Reaction Engineering • Review of previous lectures • Stoichiometry • Stoichiometric Table • Definitions of Concentration • Calculate the Equilibrium Conversion, Xe

2. Reactor Mole Balances in terms of conversion X Batch t X CSTR W PFR PBR 2

3. Last LectureRelative Rates of Reaction 3

4. Last LectureRate Laws - Power Law Model A reactor follows an elementary rate law if the reaction orders just happens to agree with the stoichiometric coefficients for the reaction as written. e.g. If the above reaction follows an elementary rate law 2nd order in A, 1st order in B, overall third order 4

5. Last LectureArrhenius Equation k is the specific reaction rate (constant) and is given by the Arrhenius Equation. Where: k T 5

6. Reaction Engineering Mole Balance Rate Laws Stoichiometry These topics build upon one another 6

7. How to find Step 1: Rate Law Step 2: Stoichiometry Step 3: Combine to get 7

8. We shall set up Stoichiometry Tables using species A as our basis of calculation in the following reaction. We will use the stochiometric tables to express the concentration as a function of conversion. We will combine Ci = f(X) with the appropriate rate law to obtain -rA = f(X). A is the limiting Reactant. 8

9. For every mole of A that react, b/a moles of B react. Therefore moles of B remaining: Let ΘB = NB0/NA0 Then: 9

10. Batch System Stoichiometry Table Where: and δ = change in total number of mol per mol A reacted 10

11. Constant Volume Batch Note: If the reaction occurs in the liquid phase or if a gas phase reaction occurs in a rigid (e.g. steel) batch reactor Then etc. 11

12. Stoichiometry Suppose Batch: Equimolar feed: Stoichiometric feed: 12

13. Flow System Stochiometric Table Where: 13

14. Flow System Stochiometric Table Where: and 14 Concentration – Flow System

15. Flow System Stochiometric Table Where: and 15 Concentration – Flow System

16. Concentration Flow System: Liquid Phase Flow System: Flow Liquid Phase Liquid Systems etc. 16

17. Liquid Systems If the rate of reaction were then we would have This gives us 17

18. For Gas Phase Flow Systems Combining the compressibility factor equation of state with Z = Z0 Stoichiometry: We obtain: 18

19. For Gas Phase Flow Systems 19

20. For Gas Phase Flow Systems The total molar flow rate is: Substituting FT gives: 20

21. For Gas Phase Flow Systems 21

22. For Gas Phase Flow Systems Concentration Flow System: Gas Phase Flow System: 22

23. For Gas Phase Flow Systems Cj=f(Fj, T, P) =f(x, T,P)

24. For Gas Phase Flow Systems If –rA=kCACB This gives us FA0/-rA X 24

25. Example: Calculating the equilibrium conversion for gas phase reaction in a flow reactor, Xef Consider the following elementary reaction with KC=20 dm3/mol and CA0=0.2 mol/dm3. Calculate Equilibrium Conversion or both a batch reactor (Xeb) and a flow reactor (Xef). 25

26. 26

27. Calculating the equilibrium conversion for gas phase reaction,Xe Batch Reactor Example Consider the following elementary reaction with KC=20 m3/mol and CA0=0.2 mol/m3. Xe’ for both a batch reactor and a flow reactor. 27

28. Batch Reactor Example Calculate Xe Step 1: Step 2: rate law, 28

29. Batch Reactor Example Calculate Xe Totals: NT0=NA0 NT=NA0 -NA0 X/2 @ equilibrium: -rA=0 29

30. Batch Reactor Example Calculating the equilibrium conversion for gas phase reaction At equilibrium Solution: Batch Stoichiometry Constant volume 30

31. BR Example Xeb 31

32. Gas Phase Example Xef Rate law: Solution: 32

33. Gas Flow Example Xef 33

34. Gas Flow Example Xef Stoichiometry: Gas isothermal T=T0, isobaric P=P0 34

35. Gas Flow Example Xef Pure A  yA0=1, CA0=yA0P0/RT0, CA0=P0/RT0 @ eq: -rA=0 35

36. Gas Flow Example Xef Flow: Batch: Recall 36