1. Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place. Lecture 4

2. Lecture 4 – Tuesday 1/22/2013 2 Block 1 Mole Balances Size CSTRs and PFRs given –r A =f(X) Block 2 Rate Laws Reaction Orders Arrhenius Equation Block 3 Stoichiometry Stoichiometric Table Definitions of Concentration Calculate the Equilibrium Conversion, X e

3. ReactorDifferentialAlgebraicIntegral CSTR PFR Batch X t PBR X W 3 Reactor Mole Balances Summary in terms of conversion, X Review Lecture 2

4. Levenspiel Plots 4 Review Lecture 2

5. 5 PFR Review Lecture 2

6. 6 Reactors in Series Only valid if there are no side streams Review Lecture 2

7. 7 Reactors in Series Review Lecture 2

8. 8 Step 1: Rate Law Step 2: Stoichiometry Step 3: Combine to get Two steps to get Review Lecture 2

9. Building Block 2: Rate Laws 9 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 Review Lecture 3

10. Arrhenius Equation 10 E = Activation energy (cal/mol) R = Gas constant (cal/mol*K) T = Temperature (K) A = Frequency factor (same units as rate constant k) (units of A, and k, depend on overall reaction order) T k Review Lecture 3

11. Reaction Engineering 11 These topics build upon one another Mole BalanceRate LawsStoichiometry Review Lecture 3

12. Algorithm 12 Step 1: Rate Law Step 2: Stoichiometry Step 3: Combine to get How to find Review Lecture 3

13. Building Block 3: Stoichiometry 13 We shall set up Stoichiometry Tables using species A as our basis of calculation in the following reaction. We will use the stoichiometric tables to express the concentration as a function of conversion. We will combine C i = f(X) with the appropriate rate law to obtain -r A = f(X). A is the limiting reactant.

14. Stoichiometry 14 For every mole of A that reacts, b/a moles of B react. Therefore moles of B remaining: Let Θ B = N B0 /N A0 Then:

15. Batch System - Stoichiometry Table 15 SpeciesSymbolInitialChangeRemaining BB N B0 =N A0 Θ B -b/aN A0 X N B =N A0 ( Θ B -b/aX) AAN A0 -N A0 XN A =N A0 (1-X) InertI N I0 =N A0 Θ I ---------- N I =N A0 Θ I F T0 N T =N T0 + δ N A0 X Where: and CC N C0 =N A0 Θ C +c/aN A0 X N C =N A0 ( Θ C +c/aX) DD N D0 =N A0 Θ D +d/aN A0 X N D =N A0 ( Θ D +d/aX) δ = change in total number of mol per mol A reacted

16. Stoichiometry Constant Volume Batch 16 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.

17. Stoichiometry Constant Volume Batch 17 Suppose Batch: Equimolar feed: Stoichiometric feed:

18. Stoichiometry Constant Volume Batch 18 and we have If, then Constant Volume Batch

19. Batch Reactor - Example 19 Consider the following elementary reaction with K C =20 dm 3 /mol and C A0 =0.2 mol/dm 3. Find X e for both a batch reactor and a flow reactor. Calculate the equilibrium conversion for gas phase reaction, X e.

20. Batch Reactor - Example 20 Step 1: Step 2: rate law: Calculate X e

21. Batch Reactor - Example 21 SymbolInitialChangeRemaining B0½ N A0 XN A0 X/2 AN A0 -N A0 XN A0 (1-X) Totals:N T0 =N A0 N T =N A0 -N A0 X/2 @ equilibrium: -r A =0

22. Batch Reactor - Example 22 SpeciesInitialChangeRemaining AN A0 -N A0 XN A =N A0 (1-X) B0+N A0 X/2N B =N A0 X/2 N T0 =N A0 N T =N A0 -N A0 X/2 Solution: At equilibrium Stoichiometry: Constant Volume: Batch

23. Batch Reactor - Example 23

24. Flow System – Stoichiometry Table 24 AAF A0 -F A0 XF A =F A0 (1-X) SpeciesSymbolReactor FeedChangeReactor Effluent BB F B0 =F A0 Θ B -b/aF A0 X F B =F A0 ( Θ B -b/aX) Where:

25. Flow System – Stoichiometry Table 25 SpeciesSymbolReactor FeedChangeReactor Effluent Where: InertIF I0 = A0 Θ I ----------F I =F A0 Θ I F T0 F T =F T0 +δF A0 X CCF C0 =F A0 Θ C +c/aF A0 XF C =F A0 (Θ C +c/aX) DDF D0 =F A0 Θ D +d/aF A0 XF D =F A0 (Θ D +d/aX) and Concentration – Flow System

26. 26 SpeciesSymbolReactor FeedChangeReactor Effluent AAF A0 -F A0 XF A =F A0 (1-X) BBF B0 =F A0 Θ B -b/aF A0 XF B =F A0 (Θ B -b/aX) CCF C0 =F A0 Θ C +c/aF A0 XF C =F A0 (Θ C +c/aX) DDF D0 =F A0 Θ D +d/aF A0 XF D =F A0 (Θ D +d/aX) InertIF I0 =F A0 Θ I ----------F I =F A0 Θ I F T0 F T =F T0 +δF A0 X Where:and Concentration – Flow System Flow System – Stoichiometry Table

27. 27 Stoichiometry Concentration Flow System: Liquid Phase Flow System: Flow Liquid Phase etc. We will consider C A and C B for gas phase reactions in the next lecture

28. Mole Balance Rate Laws Stoichiometry Isothermal Design Heat Effects 28

29. End of Lecture 4 29