Chemistry 232

1. 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. 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 = -136.98 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 • 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 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 I  2 R• Or M + R•  M1 • • Propagation 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