Kinetics of Complex Reactions Chemistry 232 Kinetics of Complex Reactions

The Pre-Equilibrium Approximation Examine the following process

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!

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

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

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*]

Is That Your ‘Final Answer’? Substituting and rearranging

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

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

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.

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

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

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

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!!

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.

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 .

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

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.

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

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”).

The Lock and Key (II)

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

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]?

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

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

The Final Equation Substituting into the rate law vp.

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.

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.

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

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

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

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

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

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

Hydrogenation of Ethane The Rice-Herzfeld Mechanism Mechanism

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

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.

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

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

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

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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!!!

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)