1. Kinetics of Complex Reactions
Chemistry 232
Kinetics of Complex Reactions

2. The Pre-Equilibrium Approximation
Examine the following process

3. Pre-Equilibrium (II)
B is obviously an intermediate in the above mechanism.
Could use SSA.
What if the initial equilibrium is fast?
Step 2 is the rds!

4. Pre-Equilibrium (III)
We now have a simple expression for the [B]; hence

5. Lindemann-Hinshelwood Mechanism
An early attempt to explain the kinetics of complex reactions.
Mechanism
Rate Laws

6. The ‘Activated’ Intermediate
Formation of the product depends directly on the [A*].
Apply the SSA to the net rate of formation of the intermediate [A*]

7. Is That Your ‘Final Answer’?
Substituting and rearranging

8. The ‘Apparent Rate Constant’ Depends on Pressure
The rate laws for the Lindemann-Hinshelwood Mechanism are pressure dependent.
High Pressure Case
Low Pressure Case

9. The Pressure Dependence of k’
In the Lindemann-Hinshelwoood Mechanism, the rate constant is pressure dependent.

10. Catalysts
So far, we have considered one way of speeding up a reaction (i.e. increasing T usually increases k). Another way is by the use of a catalyst.
A catalyst - a substance that speeds up the rate of the reaction without being consumed in the overall reaction.

11. A+B ® C rate constant with catalyst is kcat
look at the following two reactions
A+B ® C rate constant k
A+B ® C rate constant with catalyst is kcat
NOTE: RATE WITH CATALYST > RATE WITHOUT CATALYST

13. Types of Catalyst
We will briefly discuss three types of catalysts. The type of catalyst depends on the phase of the catalyst and the reacting species.
Homogeneous
Heterogeneous
Enzyme

14. Homogeneous Catalysis
The catalyst and the reactants are in the same phase
e.g. Oxidation of SO2 (g) to SO3 (g)
2 SO2(g) + O2(g) ® 2 SO3 (g) SLOW
Presence of NO (g), the following occurs.
NO (g) + O2 (g) ® NO2 (g)
NO2 (g) + SO2 (g) ® SO3 (g) + NO (g) FAST

15. SO3 (g) is a potent acid rain gas
H2O (l) + SO3 (g)  H2SO4 (aq)
Note the rate of NO2(g) oxidizing SO2(g) to SO3(g) is faster than the direct oxidation.
NOx(g) are produced from burning fossil fuels such as gasoline, coal, oil!!

16. Heterogeneous Catalysis
The catalyst and the reactants are in different phases
adsorption the binding of molecules on a surface.
Adsorption on the surface occurs on active sites
Places where reacting molecules are adsorbed and physically bond to the metal surface.

17. The hydrogenation of ethene (C2H4 (g)) to ethane
C2H4 (g) + H2(g)  C2H6 (g)
Reaction is energetically favourable
rxnH = kJ/mole of ethane.
With a finely divided metal such as Ni (s), Pt (s), or Pd(s), the reaction goes very quickly .

18. There are four main steps in the process
the molecules approach the surface;
H2 (g) and C2H4 (g) adsorb on the surface;
H2 dissociates to form H(g) on the surface; the adsorbed H atoms migrate to the adsorbed C2H4 and react to form the product (C2H6) on the surface
the product desorbs from the surface and diffuses back to the gas phase

20. Simplified Model for Enzyme Catalysis
E º enzyme; S º substrate; P º product
E + S ® ES
ES ® P + E
rate = k [ES]
The reaction rate depends directly on the concentration of the substrate.

21. Enzyme Catalysis Enzymes - proteins (M > 10000 g/mol)
High degree of specificity (i.e., they will react with one substance and one substance primarily
Living cell > 3000 different enzymes

22. The Lock and Key Hypothesis
Enzymes are large, usually floppy molecules. Being proteins, they are folded into fixed configuration.
According to Fischer, active site is rigid, the substrate’s molecular structure exactly fits the “lock” (hence, the “key”).

23. The Lock and Key (II)

24. The Michaelis-Menten Mechanism
Enzyme kinetics – use the SSA to examine the kinetics of this mechanism.
ES – the enzyme-substrate complex.

25. Applying the SSA to the Mechanism
Note that the formation of the product depends directly on the [ES]
What is the net rate of formation of [ES]?

26. ES – The Intermediate
Apply the SSA to the equation for d[ES]/dt = 0

27. Working Out the Details
Let [E]o = [E] + [ES]
Complex concentration
Initial enzyme concentration
Free enzyme concentration
Note that [E] = [E]o - [ES]

28. The Final Equation
Substituting into the rate law vp.

29. The Michaelis Constant and the Turnover Number
The Michaelis Constant is defined as
The rate constant for product formation, k2, is the turnover number for the catalyst.
Ratio of k2 / KM – indication of catalytic efficiency.

30. The Maximum Velocity As [S]o gets very large.
Note – Vmax is the maximum velocity for the reaction. The limiting value of the reaction rate high initial substrate concentrations.

31. Lineweaver-Burk Equation
Plot the inverse of the reaction rate vs. the inverse of the initial substrate concentration.

32. Chain Reactions Classifying steps in a chain reaction. Initiation
C2H6 (g) 2 CH3•
Propagation Steps
C2H6 + •CH3  •C2H5 + CH4
Branching Steps
H2O + •O•  2 •OH

33. Chain Reactions (Cont’d)
Retardation Step
HBr + H•  H2 + Br•
Terminations Steps
2 CH3CH2•  CH3CH2CH2CH3
Inhibition Steps
R• + CH3•  RCH3

34. The H2 + Br2 Reaction
The overall rate for the reaction was established in 1906 by Bodenstein and Lind

35. The Mechanism
The mechanism was proposed independently by Christiansen and Herzfeld and by Michael Polyani.
Rate Laws
Mechanism

36. Using the SSA
Using the SSA on the rates of formation of Br• and H•

37. Hydrogenation of Ethane
The Rice-Herzfeld Mechanism
Mechanism

38. Rate Laws for the Rice-Herzfeld Mechanism
The rate laws for the elementary reactions are as follows.

39. Explosions Thermal explosions Chain branching explosions
Rapid increase in the reactions rate with temperature.
Chain branching explosions
chain branching steps in the mechanism lead to a rapid (exponential) increase in the number of chain carriers in the system.

40. Photochemical Reactions
Many reactions are initiated by the absorption of light.
Stark-Einstein Law – one photon is absorbed by each molecule responsible for the primary photochemical process.
I = Intensity of the absorbed radiation

41. Primary Quantum Yield Define the overall quantum yield, 
Define the primary quantum yield, 
Define the overall quantum yield, 

42. Photosensitization
Transfer of excitation energy from one molecule (the photosensitizer) to another nonabsorbing species during a collision..

43. Polymerization Kinetics
Chain polymerization
Activated monomer attacks another monomer, chemically bonds to the monomer, and then the whole unit proceeds to attack another monomer.
Stepwise polymerization
A reaction in which a small molecule (e.g., H2O) is eliminated in each step.

44. Chain Polymerization
The overall polymerization rate is first order in monomer and ½ order in initiator.
The kinetic chain length, kcl
Measure of the efficiency of the chain propagation reaction.

45. Mechanism Initiation Rate Laws Propagation I  2 R• Or M + R•  M1 •
M + M1•  M2 •
M + M2•  M3 •
M + M3•  M4 •
Etc.
Rate Laws

46. Mechanism (Cont’d) Termination M + M3•  M4 •
Note – Not all the initiator molecules produce chains
Define  = fraction of initiator molecules that produce chains

47. Return to Kinetic Chain Length
We can express the kinetic chain length in terms of kt and kp

48. Stepwise Polymerization
A classic example of a stepwise polymerization – nylon production.
NH2-(CH2)6-NH2 + HOOC-(CH2)4COOH 
NH2-(CH2)6-NHOC-(CH2)4COOH + H2O
After many steps
H-(NH-(CH2)6-NHOC-(CH2)4CO)n-OH

49. The Reaction Rate Law
Consider the condensation of a generic hydroxyacid
OH-M-COOH
Expect the following rate law

50. The Reaction Rate Law (Cont’d)
Let [A] = [-COOH]
A can be taken as any generic end group for the polymer undergoing condensation.
Note 1 –OH for each –COOH

51. The Reaction Rate Law (Cont’d)
If the rate constant is independent of the molar mass of the polymer

52. The Fraction of Polymerization
Denote p = the fraction of end groups that have polymerized

53. Statistics of Polymerization
Define Pn = total probability that a polymer is composed of n-monomers

54. The Degree of Polymerization
Define <n> as the average number of monomers in the chain

55. Degree of Polymerization (cont’d)
The average polymer length in a stepwise polymerization increases as time increases.

56. Molar Masses of Polymers
The average molar mass of the polymer also increases with time.
Two types of molar mass distributions.
<M>n = the number averaged molar mass of the polymer.
<M>w = the mass averaged molar mass of the polymer.

57. Definitions of <M>n
Two definitions!
Mo = molar mass of monomer
n = number of polymers of mass Mn
MJ = molar mass of polymer of length nJ

58. Definitions of <M>w
<M>w is defined as follows
Note - xn the number of monomer units in a polymer molecule

59. The Dispersity of a Polymer Mixture
Polymers consists of many molecules of varying sizes.
Define the dispersity index () of the mass distribution.
Note – monodisperse sample ideally has <M>w=<M>n

60. The Dispersity Index in a Stepwise Polymerization
The dispersity index varies as follows in a condensation polymerization
Note – as the polymerization proceeds, the ratio of <M>w/<M>n approaches 2!!!

61. Mass Distributions in Polymer Samples
For a random polymer sample 09 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Monodisperse Sample
Polydisperse Sample Pn
Molar mass / (10000 g/mole)