Presentation on theme: "Kinetics of Complex Reactions"— Presentation transcript:
1 Kinetics of Complex Reactions Chemistry 232Kinetics 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.MechanismRate 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 CaseLow Pressure Case
9 The Pressure Dependence of k’ In the Lindemann-Hinshelwoood Mechanism, the rate constant is pressure dependent.
10 CatalystsSo 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 reactionsA+B ® C rate constant kA+B ® C rate constant with catalyst is kcatNOTE: RATE WITH CATALYST > RATE WITHOUT CATALYST
13 Types of CatalystWe will briefly discuss three types of catalysts. The type of catalyst depends on the phase of the catalyst and the reacting species.HomogeneousHeterogeneousEnzyme
14 Homogeneous Catalysis The catalyst and the reactants are in the same phasee.g. Oxidation of SO2 (g) to SO3 (g)2 SO2(g) + O2(g) ® 2 SO3 (g) SLOWPresence 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 phasesadsorption the binding of molecules on a surface.Adsorption on the surface occurs on active sitesPlaces 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 favourablerxnH = 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 surfacethe 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 productE + S ® ESES ® P + Erate = 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 primarilyLiving 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”).
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 IntermediateApply the SSA to the equation for d[ES]/dt = 0
27 Working Out the Details Let [E]o = [E] + [ES]Complex concentrationInitial enzyme concentrationFree enzyme concentrationNote that [E] = [E]o - [ES]
28 The Final EquationSubstituting into the rate law vp.
29 The Michaelis Constant and the Turnover Number The Michaelis Constant is defined asThe 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.
34 The H2 + Br2 ReactionThe overall rate for the reaction was established in 1906 by Bodenstein and Lind
35 The MechanismThe mechanism was proposed independently by Christiansen and Herzfeld and by Michael Polyani.Rate LawsMechanism
36 Using the SSAUsing the SSA on the rates of formation of Br• and H•
37 Hydrogenation of Ethane The Rice-Herzfeld MechanismMechanism
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 explosionschain 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 PhotosensitizationTransfer of excitation energy from one molecule (the photosensitizer) to another nonabsorbing species during a collision..
43 Polymerization Kinetics Chain polymerizationActivated monomer attacks another monomer, chemically bonds to the monomer, and then the whole unit proceeds to attack another monomer.Stepwise polymerizationA reaction in which a small molecule (e.g., H2O) is eliminated in each step.
44 Chain PolymerizationThe overall polymerization rate is first order in monomer and ½ order in initiator.The kinetic chain length, kclMeasure 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 chainsDefine = 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 + H2OAfter many stepsH-(NH-(CH2)6-NHOC-(CH2)4CO)n-OH
49 The Reaction Rate LawConsider the condensation of a generic hydroxyacidOH-M-COOHExpect 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 monomern = number of polymers of mass MnMJ = molar mass of polymer of length nJ
58 Definitions of <M>w <M>w is defined as followsNote - 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 polymerizationNote – as the polymerization proceeds, the ratio of <M>w/<M>n approaches 2!!!
61 Mass Distributions in Polymer Samples For a random polymer sample0911131517192123252729313335373941Monodisperse SamplePolydisperse SamplePnMolar mass / (10000 g/mole)