Chemical Kinetics

1. Chemical Kinetics

2. A2(g) + B2(g) 2 AB(g) • Fundamental questions: • Will it take place? Thermodynamics • If it does, how long will it take to reach completion or equilibrium? • Chemical kinetics: is the study of the speeds, or rates, of chemical reactions

3. Outline • Why study kinetics? • Factors affecting rates • Measuring rates • reactant concentration • temperature • action of catalysts • surface area. • Concentration vs. Rate (Rate Laws) • Concentration vs. Time (Integrated Rate Laws) • Theories about Rxn Rates • Activation Energy • Mechanisms • Catalysts

4. D[AB] Rate of appearance of AB = Dt -D[A2] Rate of disappearance of A2 = Dt mol/liter Unit: = mol / L  s = mol dm-3 s-1 S The rate of the reaction is a measure of how fast the changes are taking place.

5. The nature of the reactants • 2 NO+ O2 2 NO2 fast reaction at 25°C • 2 CO + O2 2 CO2 very slow at 25°C Rate constant -D[A2] = k [A] mol dm-3 s-1 Dt (in the simplest case: A products) Factors affecting reaction rates 2. The concentration of reactants Rate equation or rate law The rate of reaction is proportional to the rate of disappearance of reactants:

6. Rate Laws: Basic Assumptions • aA + bB  cC + dD • Simple rate laws depend only on the concentrations of the reactants, not the products. • Rate = k[A]x[B]y • k = rate constant, units depend on the values of x and y. • x and y = the orders of A and B respectively • x + y = overall order of the rxn • 3 unknowns (x, y, k)  3 experiments

7. Slope (Rate) Changes w/ Time • Rate is a function of concentration. • When the concentration is high, the rate is large. • Concentration is a function of time. • When the reaction starts the concentration changes the most. 2HI  H2 + I2

8. Zero order reaction: 2 N2O+ O2 2 N2 + O2 rate = k Au First order reaction: 2 N2O5 4 NO2 + O2 rate = k [A] Factors affecting reaction rates rate = k [N2O5]

9. Second order reaction: 2 A products A+B products rate = k [A]2 rate = k [A] [B] Third order reaction: 3 A products rate = k [A]3 rate = k [A] [B] [C] A + B + C products rate = k [A]2 [B] 2 A + B products

10. The order of a reaction is given by the sum of the exponents of the conc. terms in the rate equation. rate = k [A]m [B]n [C]p …. order = m + n + p + …

11. Temperature and Rate Constants (k) • Since the rate law has no temperature term in it, the rate constant must depend on temperature. • The size of k depends on T. • Greater T gives a larger k • Consider the reaction H2(g) + I2(g)  2HI(g).

12. effective collisions most probable energy at t1 t2 No of molecules t2 t1 Minimum energy required for reaction Ea 3. The temperature of the reaction. Collision theory of reaction rates

13. -Ea/RT n = n0e -Ea/RT k = Ae Ea ln k = lnA - RT Ea log k = log A - 2.303 RT Maxwell-Boltzmann distribution law Arrhenius equation Ea = activation energy A = frequency factor K = rate constant

14. Arrhenius Equation • K = rate constant • A = frequency factor • Ea = activation energy • T = temperature • R = 8.314 J/mol K

15. Frequency Factor • Solve for A Effective collisions / 6.02 x 1023

16. Temperature Increases Rate • Most reactions speed up as temperature increases. (E.g. food spoils when not refrigerated.) • When two light sticks are placed in water: one at room temperature and one in ice, the one at room temperature is brighter than the one in ice. • The chemical reaction responsible for chemi-luminescence is dependent on temperature: the higher the temperature, the faster the reaction and the brighter the light.

17. Half-Life • Half-lives are typically reported for radioactive materials, medications, toxins…etc. • 238U has a t½ = 5 x 109 y • 234P has a t½ = 7 h • Amount of time required for half of the compound to react. • Half life equations are found from the integrated rate laws. • Find the time required for the concentration to be one half the initial concentration.

18. The Collision Model • Observations: rates of reactions are affected by concentration and temperature. • Concentration terms already accounted for in rate laws • R = k[A]x • Goal: develop a model that explains why rates of reactions increase as temperature increases. Low T Collision High T Collision

19. The Rules of Reaction Mechanisms • Elementary step: any process that occurs in a single step. • Molecularity: the number of molecules present in an elementary step. • Unimolecular: one molecule in the elementary step, • Bimolecular: two molecules in the elementary step, and • Termolecular: three molecules in the elementary step. • It is not common to see termolecular processes (statistically improbable).

20. Biomolecular reaction A + B products 2A products Termolecular reaction A + B + C products 2A + B products 3A products Unimolecular reaction A products A unimoleculare reaction is first order They are not common!

21. Energy of Collision • Chemical rxns usually occur with bonds breaking and bonds forming. • Collision energy supplies the energy needed to break the bonds. • With increased temperature, collision energy increases and the rate of rxn increases.

22. Effective Collisions • The right molecules must collide. • The collision must be energetic enough. • The molecules must collide in the proper orientation. • All of the above conditions must be met for a rxn to occur! • There are far more collisions between the wrong molecules or in the wrong orientation or with the wrong energy! • Some estimate that only 1 in 1018 collisions are effective.

23. Molecular Orientation • If H2 and I2 collide, they can collide along any possible trajectory. • However, only one trajectory leads to a rxn.

24. H H I I Top of the Peak ‡ • At the top of the peak, we have… • Maximum potential energy • Transition state • Point where reactants change to products • Bonds breaking and bonds forming • Intermediate structures • The [activated complex]‡ 2 HI Potential Energy H2 + I2 Progress of Rxn

25. Activation Energy • In order to form products, bonds must be broken in the reactants. • Bond breakage requires energy • Arrhenius: molecules must posses a minimum amount of energy to react.. • Ea is the minimum energy required to initiate a chemical reaction.

26. Energy of Collision Activation Energy Ea Potential Energy Energy of Rxn Enthalpy DH Progress of Rxn Progress of Reaction Diagrams • Relates the PE of the rxn to time. • For example, an exothermic rxn between A + B is shown on the right. Reactants Note: DH and Ea are unrelated! 100% of Ea is returned! Products

27. Energy of Collision Activation Energy Ea Potential Energy Energy of Rxn Enthalpy DH Progress of Rxn Endothermic System is Reversed • Products are higher in PE than reactants. Products Note: Less than 100% of Ea is returned. Reactants

28. Reaction Mechanisms Rate Laws of Multistep Mechanisms • Rate-determining step: is the slowest of the elementary steps. • Therefore, the rate-determining step governs the overall rate law for the reaction. Mechanisms with an Initial Fast Step • It is possible for an intermediate to be a reactant. • … 2NO2Cl(g) Cl2(g) + 2NO2(g)

29. E1 E2 Reaction mechanisms: The rate equation for a reaction must be determined by experimentation Two step mechanism Rate-determining step (intermediate)

30. Uncatalysed reaction Catalysed reaction reactants products 5. The catalysis A catalyst is a substance that increases the rate of a chemical reaction without being used up in the reaction 4. The surface area of a solid Increasing the surface area of a solid reactant will increase the rate of reaction (explosion of flour dust)

31. Catalysis • A catalyst changes the rate of a chemical reaction. • There are two types of catalyst: • homogeneous, and • heterogeneous. • Chlorine atoms are catalysts for the destruction of ozone. • Homogeneous Catalysis • The catalyst and reaction is in one phase. • Hydrogen peroxide decomposes very slowly: • 2H2O2(aq)  2H2O(l) + O2(g).

32. Promoters catalytic poisons homogeneous Catalyst heterogeneous positive (accelerate…) negative or inhibitor (retard…)

33. Catalysis • Homogeneous Catalysis • 2H2O2(aq)  2H2O(l) + O2(g). • In the presence of the bromide ion, the decomposition occurs rapidly: • 2Br –(aq) + H2O2(aq) + 2H+(aq)  Br2(aq) + 2H2O(l). • Br2(aq) is brown. • Br2(aq) + H2O2(aq)  2Br –(aq) + 2H+(aq) + O2(g). • Br – is a catalyst because it can be recovered at the end of the reaction. • Generally, catalysts operate by lowering the activation energy for a reaction.

34. Catalysis • Homogeneous Catalysis

35. Catalysis • Heterogeneous Catalysis

36. Catalysis • Enzymes • Enzymes are biological catalysts. • Most enzymes are protein molecules with large molecular masses (10,000 to 106 amu). • Enzymes have very specific shapes. • Most enzymes catalyze very specific reactions. • Substrates undergo reaction at the active site of an enzyme. • A substrate locks into an enzyme and a fast reaction occurs.

37. 1. S + E ES Enzyme-substrate complex Substrate (reactant) Enzyme 2. ES E + P Product Natural catalysts = enzymes (very specific) Michaelis – Menten mechanism:

38. First order Zero order Reaction rate Concentration of substrate At low concentrate: Rate of disappearence of S = k [S] At high concentrate:Rate of disappearence of S = k’ [S]0 = k’ The enzyme is saturated!

39. Catalysis • Enzymes