1. ERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY
Lecturer: Miss Anis Atikah Ahmad
Tel:

2. Outline PART 1: Rate Laws PART 2: Stoichiometry
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
EXERCISE
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?

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

8. 2. Reaction Order & Rate Law
Rate law is a kinetic expression that gives the relationship between reaction rate, -rA, and concentration.
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
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. Thermodynamic Equilibrium Relationship
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 The rate of disappearance of benzene;
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 rxn btween diphenyl & 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 = J/mol-K = 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
Energy barier
-total no of collision
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:
Species
Initially (mol)
Change (mol)
Remaining (mol) A B C D I
Totals

26. 4. Batch Systems Stoichiometric Table
aA + bB  cC + dD
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
Species
Initially (mol)
Change (mol)
Remaining (mol) A B C D I -
Totals

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??
Species
Initially
Change
Remaining
Concentration A B C D I
Totals

32. 4. Batch Systems Stoichiometric Table
Concentration of each species in terms of conversion can be expressed as:
Recall from stoichiometric table
Remaining (mol) A B C D

33. 4. Batch Systems Stoichiometric Table

34. 4. Batch Systems Stoichiometric Table

35. 4. Batch Systems Stoichiometric Table
Species
Initially
Change
Remaining
Concentration A B C D I -

36. 4. Batch Systems Stoichiometric Table
Species
Initially
Change
Remaining
Concentration A B C D I -

37. 4. Batch Systems Stoichiometric Table
EXAMPLE
Given the saponification for the formation of soap from aqueous caustic soda & glyceryl stearate 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. 4. Batch Systems Stoichiometric Table
EXAMPLE
Species
Initially
Change
Remaining
Concentration A B C D I -
Total

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

41. 5. Flow Systems Stoichiometric Table
Components of stoichiometric table:
Species
Feed rate to reactor
(mol/time)
Change within the reactor (mol/time)
Effluent rate from reactor (mol/time) A B C D I
Totals

42. 5. Flow Systems Stoichiometric Table
Species
Feed rate to reactor
(mol/time)
Change within the reactor (mol/time)
Effluent rate from reactor (mol/time)
Concentration
(mol/L) A B C D I -
Totals

43. 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.

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

45. Answer for quiz 5 A B C D Totals Species Feed rate to reactor
(mol/time)
Change within the reactor (mol/time)
Effluent rate from reactor (mol/time) A B C D
Totals

46. Answer for quiz 5 Substituting the numerical values; A B C D Totals
Species
Feed rate to reactor
(mol/time)
Change within the reactor (mol/time)
Effluent rate from reactor (mol/time) A B C D
Totals

47. 6. Concentration in terms of conversion
1. For liquid phase:
Batch System:

48. 6. Concentration in terms of conversion
1. For liquid phase:
Flow System -

49. 6. Concentration in terms of conversion
2. For gas phase:
Batch System
Need to substitute V from gas law equation
From equation of state;
At any time t,
At initial condition (t=0)
T= temperature, K
P= total pressure, atm (1 atm= kPa)
Z= compressibility factor
R= gas constant = dm3-atm/mol-K
(1)
(2)

50. 6. Concentration in terms of conversion
2. For gas phase:
Batch System
Dividing (1) by (2);
(1)
(2)
Recall from stoichiometric table
(4)
(3)
Dividing (4) by NT0 ;

51. 6. Concentration in terms of conversion
2. For gas phase:
Batch System
Applies for both batch and flow systems
Will be substitute
in (3)
Rearranging;
At complete conversion (for irreversible rxn): X=1, NT=NTf

52. 6. Concentration in terms of conversion
2. For gas phase:
Batch System
Substituting the expression for NT/NT0 in (3),
(3)
If the compressibility factor are not change significantly during rxn, Z0⩳Z
(5)

53. 6. Concentration in terms of conversion
2. For gas phase:
Flow System
Need to substitute υ from gas law equation
From gas law, at any point in the reactor,
At the entrance of reactor;
(1)
(2)
Dividing (1) by (2)
(3)

54. 6. Concentration in terms of conversion
2. For gas phase:
Flow System
Substituting for FT;
Recall from stoichiometric table
(4)

55. 6. Concentration in terms of conversion
2. For gas phase:
Flow System
Substituting υ & Fj;
Need to substitute υ from gas law equation
(5)
(4)
Stoichiometric coefficient
(d/a, c/a, -b/a, -a)

56. 6. Concentration in terms of conversion
2. For gas phase:
Flow System
Concentration for each species:
aA + bB  cC + dD

57. Summary
Relative rate of reaction:
Power Law Model:

58. Summary Elementary rate law:
The rxn that in which its stoichiometic coefficients are IDENTICAL to the reaction order of each species.
Non-elementary rate laws:
The reactions that do not follow simple rate laws (power rate laws) in which its stoichiometic coefficients are NOT IDENTICAL to the reaction order of each species.
Reversible reaction:
All rate laws must reduce to the thermodynamic relationship relating the reacting species concentrations at equilibrium.
Power Law Model:

59. Summary E ⬆, k ⬆, -r ⬆ Reaction Rate Constant, k
The larger the activation energy, the more sensitive k is, (towards the change in temperature)

60. Summary Stoichiometric Table for Batch Systems A B C D I - Species
Initially
Change
Remaining A B C D I -

61. Summary Stoichiometric Table for Flow Systems A B C D I - Totals
Species
Feed rate to reactor
(mol/time)
Change within the reactor (mol/time)
Effluent rate from reactor (mol/time) A B C D I -
Totals

62. Summary
Expression of V and υ in calculating the concentration of each species:
Batch systems
Liquid phase:
Gas phase:
Flow systems

63. Quiz 6
Derive a concentration for each species for the isothermal gas phase reaction below, neglecting the pressure drop:
A + B  C