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ERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY
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1. ERT 316: REACTION ENGINEERINGCHAPTER 3RATE LAWS & STOICHIOMETRY Lecturer: Miss Anis Atikah Ahmad Email: anisatikah@unimap.edu.my Tel: +604 976 3245

2. Outline • PART 1: Rate Laws • Relative Rates of Reaction • Reaction Order & Rate Law • Reaction Rate Constant, k • PART 2: Stoichiometry • Batch System Stoichiometric Table • Flow System Stoichiometric Table • Calculation for Concentration in terms of Conversion

3. 1. Relative Rates of Reaction Reaction Stoichiometry EXAMPLE If NO2 formed at 4 mol/m3/s (r NO2= 4 mol/m3/s), what is the rate of formation of NO?

4. 1. Relative Rates of Reaction If NO2 formed at 4 mol/m3/s (r NO2= 4 mol/m3/s), what is the rate of formation of NO?

5. 1. Relative Rates of Reaction • The Reaction: is carried out in a reactor. If at a particular point, the rate of disappearance of A is 10 mol/dm3/s, what are the rates of B and C? EXERCISE

6. 1. Relative Rates of Reaction • The relative rates are • Given, the rate of disappearance of A, -rA, is 10mol/dm3/s • Thus, solving the rates of B & C; r A= -10 mol/dm3/s

7. Rate law is a kinetic expression that gives the relationship between reaction rate, -rA, and concentration. 2. Reaction Order & Rate Law • The reaction rate (rate of disappearance) depends on temperature and composition. • It can be written as the product of reaction rate constant, kAand a function of concentrations (activities) of the reactants involved in the reaction:

8. Rate law is a kinetic expression that gives the relationship between reaction rate, -rA, and concentration. 2. Reaction Order & Rate Law • For reaction in which the stoichiometric coefficient is 1 for ALL species: we shall delete the subscript on the specific reaction rate, (e.g.; A in kA) to let

9. 2.1 Power Law Models & Elementary Rate Laws • Power Law Model: The rxn is 𝛂 order wrt reactant A AND The rxn is 𝛃 order wrt reactant B The overall order of the reaction, n;

10. 2.1 Power Law Models & Elementary Rate Laws • The unit of the specific reaction, k, will vary with the order of reaction. Products Zero order (n=0) First order (n=1) Second order (n=2) Third order (n=3)

11. 2.1 Power Law Models & Elementary Rate Laws • Elementary reaction: a chemical reaction in which one or more of the chemical species react directly to form products in a single reaction step and with a single transition state. • Elementary rate law: The rxn is said to follow the elementary rate law if the stoichiometic coefficients are IDENTICAL to the reaction order of each species. Products Unimolecular reaction Products Bimolecular reaction Non-elementary rxn But follows the elementary rate law!

12. Examples of Reaction Rate Laws

13. Examples of Reaction Rate Laws

14. Examples of Reaction Rate Laws

15. 2.2 Non-Elementary Rate Laws • Non-elementary rate laws: reactions that do not follow simple rate laws (power rate laws). • Example 1: Homogeneous Rxn The kinetic rate law is: Rxn order: first order wrt to CO, three-halves order wrt Cl2, five-halves order overall. Gas phase synthesis of phosgene

16. 2.2 Non-Elementary Rate Laws Gas-solid catalyzed rxn: Hydrodemethylation of toluene (T) • Example 2: Heterogeneous Rxn The rate of disappearance of toluene per mass of catalyst is: where KB & KT is the adsorption constants. In terms of partial pressure rather than concentrations

17. 2.3 Reversible Reactions ⇌ • For reversible rxn, all rate laws must reduce to the thermodynamic relationship relating the reacting species concentrations at equilibrium. Thermodynamic Equilibrium Relationship

18. 2.3 Reversible Reactions EXAMPLE: combination rxn of 2 mol of benzene to form 1 mol H2 and 1 mol diphenyl. kB ⇌ k-B kB ⇌ symbolically; k-B The rate of disappearance of benzene; OR The reverse rxnbtweendiphenyl & hydrogen; k-B ⇌ The rate of formation of benzene (in reverse direction);

19. 2.3 Reversible Reactions The net rate of formation of benzene is; Multiplying both sides by -1, we obtain the rate law of disappearance of benzene, -rB

20. 2.3 Reversible Reactions Replacing the ratio of the reverse & forward rate law constant by equilibrium constants; where Concentration equilibrium constant

21. 3. The Reaction Rate Constant Arrhenius equation A= preexponential factor or frequency factor E= activation energy, J/mol or cal/mol R=gas constant = 8.314 J/mol-K = 1.987 cal/mol-K T= absolute temperature, K -no of collision -probability that the collision will result in a reaction

22. 3. The Reaction Rate Constant • Activation energy is a measure of the minimum energy that the reacting molecules must have in order for the reaction to occur (energy required to reach transition state). Transition state - no of collision that result in a rxn -total no of collision Energy barier probability that - the collision will result in a rxn Reactants Products

23. 3. The Reaction Rate Constant Taking a natural logarithm; The larger the activation energy, the more temperature sensitive k and thus the reaction rate. • E ⬆, k ⬆, -r = ⬆

24. 4. Batch Systems Stoichiometric Table • Purpose of developing stoichiometric table: • To determine the no of moles of each species remaining at a conversion of X.

25. 4. Batch Systems Stoichiometric Table refers to moles of species reacted or formed • Components of stoichiometric table:

26. aA + bB cC + dD 4. Batch Systems Stoichiometric Table • Recall from Chapter 2: • Factorizing; moles of A reacted moles of A remaining in the reactor at a conversion of X

27. 4. Batch Systems Stoichiometric Table Moles B reacted, NB Moles B reacted Moles A reacted Moles A reacted Moles C formed, NC Moles D formed, ND

28. 4. Batch Systems Stoichiometric Table moles B remaining in the system, NB moles of B reacted moles of B initially in the system NC moles of C formed ND moles of D formed

29. 4. Batch Systems Stoichiometric Table

30. 4. Batch Systems Stoichiometric Table • Total no of moles per mole of A reacted can be calculated as: where Change in the total number of moles per mole of A reacted

31. 4. Batch Systems Stoichiometric Table Can we express concentration of each species??

32. 4. Batch Systems Stoichiometric Table • Concentrationof each species in terms of conversion can be expressed as: Recall from stoichiometric table

33. 4. Batch Systems Stoichiometric Table

34. 4. Batch Systems Stoichiometric Table

35. 4. Batch Systems Stoichiometric Table

36. 4. Batch Systems Stoichiometric Table

37. 4. Batch Systems Stoichiometric Table EXAMPLE Given the saponification for the formation of soap from aqueous caustic soda & glycerylstearate is: Letting X the conversion of sodium hydroxide, set up a stoichiometric table expressing the concentration of each species in terms of its initial concentration and the conversion.

38. 4. Batch Systems Stoichiometric Table EXAMPLE We know that this is a liquid-phase reaction. Therefore, V=V0

39. 5. Flow Systems Stoichiometric Table • Purpose of developing stoichiometric table: • To determine the effluent flow rate of each species at a conversion of X.

40. 5. Flow Systems Stoichiometric Table • Components of stoichiometric table:

41. 5. Flow Systems Stoichiometric Table

42. QUIZ 5 • Given a liquid phase reaction: A+ 2B  C + D The initial concentration of A and B are 1.8 kmol/m3 and 6.6 kmol/m3 respectively. Construct a stoichiometric table for a flow system considering A as the basis of calculation.

43. Answer For Quiz 5 A+ 2B  C + D Given: From stoichiometry, we know that, Since C & D are products.