Presentation on theme: "Kinetics of Complex Reactions"— Presentation transcript:
1Kinetics of Complex Reactions Chemistry 232Kinetics of Complex Reactions
2The Pre-Equilibrium Approximation Examine the following process
3Pre-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!
4Pre-Equilibrium (III) We now have a simple expression for the [B]; hence
5Lindemann-Hinshelwood Mechanism An early attempt to explain the kinetics of complex reactions.MechanismRate Laws
6The ‘Activated’ Intermediate Formation of the product depends directly on the [A*].Apply the SSA to the net rate of formation of the intermediate [A*]
7Is That Your ‘Final Answer’? Substituting and rearranging
8The ‘Apparent Rate Constant’ Depends on Pressure The rate laws for the Lindemann-Hinshelwood Mechanism are pressure dependent.High Pressure CaseLow Pressure Case
9The Pressure Dependence of k’ In the Lindemann-Hinshelwoood Mechanism, the rate constant is pressure dependent.
10CatalystsSo 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.
11A+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
13Types 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
14Homogeneous 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
15SO3 (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!!
16Heterogeneous 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.
17The 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 .
18There 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
20Simplified 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.
21Enzyme 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
22The 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”).
24The Michaelis-Menten Mechanism Enzyme kinetics – use the SSA to examine the kinetics of this mechanism.ES – the enzyme-substrate complex.
25Applying 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]?
26ES – The IntermediateApply the SSA to the equation for d[ES]/dt = 0
27Working Out the Details Let [E]o = [E] + [ES]Complex concentrationInitial enzyme concentrationFree enzyme concentrationNote that [E] = [E]o - [ES]
28The Final EquationSubstituting into the rate law vp.
29The 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.
30The 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.
31Lineweaver-Burk Equation Plot the inverse of the reaction rate vs. the inverse of the initial substrate concentration.
34The H2 + Br2 ReactionThe overall rate for the reaction was established in 1906 by Bodenstein and Lind
35The MechanismThe mechanism was proposed independently by Christiansen and Herzfeld and by Michael Polyani.Rate LawsMechanism
36Using the SSAUsing the SSA on the rates of formation of Br• and H•
37Hydrogenation of Ethane The Rice-Herzfeld MechanismMechanism
38Rate Laws for the Rice-Herzfeld Mechanism The rate laws for the elementary reactions are as follows.
39Explosions 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.
40Photochemical 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
41Primary Quantum Yield Define the overall quantum yield, Define the primary quantum yield, Define the overall quantum yield,
42PhotosensitizationTransfer of excitation energy from one molecule (the photosensitizer) to another nonabsorbing species during a collision..
43Polymerization 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.
44Chain 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.
45Mechanism Initiation Rate Laws Propagation I 2 R• Or M + R• M1 • M + M1• M2 •M + M2• M3 •M + M3• M4 •Etc.Rate Laws
46Mechanism (Cont’d) Termination M + M3• M4 • Note – Not all the initiator molecules produce chainsDefine = fraction of initiator molecules that produce chains
47Return to Kinetic Chain Length We can express the kinetic chain length in terms of kt and kp
48Stepwise 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
49The Reaction Rate LawConsider the condensation of a generic hydroxyacidOH-M-COOHExpect the following rate law
50The 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
51The Reaction Rate Law (Cont’d) If the rate constant is independent of the molar mass of the polymer
52The Fraction of Polymerization Denote p = the fraction of end groups that have polymerized
53Statistics of Polymerization Define Pn = total probability that a polymer is composed of n-monomers
54The Degree of Polymerization Define <n> as the average number of monomers in the chain
55Degree of Polymerization (cont’d) The average polymer length in a stepwise polymerization increases as time increases.
56Molar 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.
57Definitions of <M>n Two definitions!Mo = molar mass of monomern = number of polymers of mass MnMJ = molar mass of polymer of length nJ
58Definitions of <M>w <M>w is defined as followsNote - xn the number of monomer units in a polymer molecule
59The 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
60The 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!!!
61Mass Distributions in Polymer Samples For a random polymer sample0911131517192123252729313335373941Monodisperse SamplePolydisperse SamplePnMolar mass / (10000 g/mole)