Chapter 12: Kinetics; Outline 1. Introduction 

1. Chapter 12: Kinetics; Outline • 1. Introduction • 2. macroscopic determination of rate (experimental) • define rate  • define rate law, rate constant, reaction order  • rate determination via expt: initial rate  • integrated rate laws  • first order; half-lives  • second order; half-lives  • rate & temperature: the Arrhenius equation Chapter 12

2. Arrhenius equation: • from observation, reaction rates and rate constants increase with temperature • examples: food decays faster at higher temperature; cooking; fireflies; • from observation, a graph of log(k) vs. 1/T gives a straight line • the slope of the log(k) vs. 1/T graph is related to the activation energy Chapter 12

3. where k is rate constant, EA is the activation energy, R is the gas constant in J K-1mol-1, T is temperature in Kelvin, and A is the “steric factor” A graph of ln(k) vs. 1/T gives a straight line with a slope of -EA/R and an intercept of ln(A) Chapter 12

4. Example: The rate constant for a certain reaction is measured at four temperatures (see the data below). What is the activation energy for the reaction? What is the value of the rate constant at 400°C? Chapter 12

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6. activation energy = slope ·2.303·(-R) = +1.13x105 J mol-1 Chapter 12

7. 3. molecular view of kinetics • mechanisms • relationship to rate laws • Arrhenius equation • 4. Catalysis, Factors affecting rates • 3. Molecular View of Kinetics Chapter 12

8. Mechanisms • A mechanism is a series of elementary reactions, or steps, that describe what happens as a reaction proceeds. • Elementary reactions are not overall reactions: overall reactions summarize the products and reactants and give the stoichiometry. • Elementary reactions may have intermediates: short-lived (<1 second) species that are formed and then react away as the reaction proceeds. • An elementary reaction often involves a collisionbetweentwospecies (a bimolecular step or reaction). Chapter 12

9. example: NO2+CONO+CO2 rate=k[NO2]2 [2nd order] possible mechanism: NO2+NO2 NO3+NO NO3+CO NO2+CO2 Chapter 12

10. A few comments on the mechanism and its relation to the rate law: • NO and NO3 are intermediates. They don’t appear as reactants or products and they are very reactive (unstable). • Each of these steps is bimolecular: involves 2 molecules. • The individual reactions add up to give the overall reaction with the correct stoichiometry. • The order and the rate equation of an elementary reaction is determined by its stoichiometry • step 1: rate(1)=k1[NO2]2 bimolecular • step 2: rate(2)=k2[NO][NO3] bimolecular Chapter 12

11. If one step is much slower than the others, the rate of that slow step is the rate of the overall reaction • step 1: slow (forms two unstable intermediates) • step 2: FAST (two unstable, reactive intermediates react) • overall rate predicted by the mechanism: k1[NO2]2 • rate determined by experiment: k[NO2]2 Therefore, we say that the proposed mechanism is REASONABLE. Chapter 12

12. example: devise a plausible mechanism consistent with the overall reaction and the overall reaction rates for each of the following Co(CN)5H2O-2(aq)+I-1(aq) Co(CN)5I-3(aq)+H2O(l) rate=k[Co(CN)5H2O-2]1(aq) slow Co(CN)5H2O-2 Co(CN)5-2+H2O k[Co(CN)5H2O-2] Co(CN)5-2+I1- Co(CN)5I-3 k[Co(CN)5-2][I1-] fast Chapter 12

13. 2NO2(g)+F2(g)2NO2F(g) rate=k[NO2][F] [HINT: consider a slow step and a fast step.] Chapter 12

14. Collision Theory From observation, we know • 1. reaction rates and rate constants increase with temperature • 2. a graph of ln(k) versus 1/T gives a straight line with a negative slope • 3. rate constants are relatively slow considering the HUGE number of collisions that occur at room temperature (around 1025 in a cm3 at 1 atm and 298 K) Develop a theory that accounts for these observations Chapter 12

15. reactions occurs as the result of a collision • only collisions above some minimum energy (the ACTIVATION ENERGY)will result in product formation • only collisions of the correct geometry (orientation) will result in product formation Chapter 12

16. So, we can write an equation based on theory that gives the reaction rate; this equation is based on molecular parameters. rate=(collision rate) x (fraction molecules with EA) x (fraction molecules with correct geometry) collision rate=Z[A][B] where Z depends on temperature and [A], [B] are concentrations fraction molecules with EA=f fraction molecules with correct geometry=P Chapter 12

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18. fraction of molecules with enough energy to react: Activation Energy Chapter 12

19. activation energy lower temperature fraction of particles with energy >EA more particles have energy>EA at higher T higher temperature

20. from before we have combining line form of Arrhenius equation rearranging Chapter 12

21. Catalysis • 1. definition: a catalyst is a chemical substance that increases the rate of a chemical reaction but is not consumed in the reaction (does not appear as a reactant or product). • catalysts work by • 2. providing an alternate, lower energy reaction pathway to product formation • or • 3. stabilizing the activated complex (transition state) and thus lowering the activation energy Chapter 12

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23. 3 examples 1. HOMOGENEOUS CATALYSIS: ozone depletion Cl· catalyzes the depletion reaction through a series of reactions: Cl· acts as a catalyst in the second two steps Chapter 12

24. 2. HETEROGENEOUS CATALYSIS catalytic converter CO(g)+1/2O2(g)CO2(g) reactant molecules adsorb (by intermolecular forces or by chemical bonding) to the metal surface in the converter bonds in reactants weaken  activated complex energy is reduced  reaction goes faster Chapter 12

25. 3. enzymes: large molecules that act as catalysts in biological reactions • enzymes are specific: they work with only 1 substrate • reaction rates are increased by factors of 108 to 1020 • the “turnover number” of number of reaction events per second is large: • 103 to 107 s-1 link to www: http://wizard.pharm.wayne.edu/biochem/enz.html Chapter 12