Chapter 14 Chemical Kinetics

1. Chapter 14Chemical Kinetics CHEM 160September 13, 2006

2. Factors that Affect Reaction Rates • Kinetics is the study of how fast chemical reactions occur. • There are 4 important factors which affect rates of reactions: • reactant concentration, • temperature, • action of catalysts, and • surface area. • Goal: to understand chemical reactions at the molecular level.

3. Reaction Rates • Speed of a reaction is measured by the change in concentration with time. • For a reaction A  B • Suppose A reacts to form B. Let us begin with 1.00 mol A.

4. Reaction Rates

5. Reaction Rates • At t = 0 (time zero) there is 1.00 mol A (100 red spheres) and no B present. • At t = 20 min, there is 0.54 mol A and 0.46 mol B. • At t = 40 min, there is 0.30 mol A and 0.70 mol B. • Calculating,

6. Reaction Rates • For the reaction A  B there are two ways of measuring rate: • the speed at which the products appear (i.e. change in moles of B per unit time), or • the speed at which the reactants disappear (i.e. the change in moles of A per unit time).

7. Reaction Rates • Change of Rate with Time • For the reaction A  B there are two ways of • Most useful units for rates are to look at molarity. Since volume is constant, molarity and moles are directly proportional. • Consider: • C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)

9. Reaction Rates • Change of Rate with Time • C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) • We can calculate the average rate in terms of the disappearance of C4H9Cl. • The units for average rate are mol/L·s or M/s. • The average rate decreases with time. • We plot [C4H9Cl] versus time. • The rate at any instant in time (instantaneous rate) is the slope of the tangent to the curve. • Instantaneous rate is different from average rate. • We usually call the instantaneous rate the rate.

11. Reaction Rates • Reaction Rate and Stoichiometry • For the reaction • C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) • we know • In general for • aA + bB cC + dD

12. Concentration and Rate • In general rates increase as concentrations increase. • NH4+(aq) + NO2-(aq)  N2(g) + 2H2O(l)

13. Concentration and Rate • For the reaction • NH4+(aq) + NO2-(aq)  N2(g) + 2H2O(l) • we note • as [NH4+] doubles with [NO2-] constant the rate doubles, • as [NO2-] doubles with [NH4+] constant, the rate doubles, • We conclude rate  [NH4+][NO2-]. • Rate law: • The constant k is the rate constant.

14. Concentration and Rate • Exponents in the Rate Law • For a general reaction with rate law • we say the reaction is mth order in reactant 1 and nth order in reactant 2. • The overall order of reaction is m + n + …. • A reaction can be zeroth order if m, n, … are zero. • Note the values of the exponents (orders) have to be determined experimentally. They are not simply related to stoichiometry.

15. Concentration and Rate • Using Initial Rates to Determines Rate Laws • A reaction is zero order in a reactant if the change in concentration of that reactant produces no effect. • A reaction is first order if doubling the concentration causes the rate to double. • A reacting is nth order if doubling the concentration causes an 2n increase in rate. • Note that the rate constant does not depend on concentration.

16. The Change of Concentration with Time • First Order Reactions • Goal: convert rate law into a convenient equation to give concentrations as a function of time. • For a first order reaction, the rate doubles as the concentration of a reactant doubles.

17. The Change of Concentration with Time • First Order Reactions • A plot of ln[A]t versus t is a straight line with slope -k and intercept ln[A]0. • In the above we use the natural logarithm, ln, which is log to the base e.

18. The Change of Concentration with Time • First Order Reactions

19. The Change of Concentration with Time • Second Order Reactions • For a second order reaction with just one reactant • A plot of 1/[A]t versus t is a straight line with slope k and intercept 1/[A]0 • For a second order reaction, a plot of ln[A]tvs. t is not linear.

20. The Change of Concentration with Time Second Order Reactions

21. The Change of Concentration with Time • Half-Life • Half-life is the time taken for the concentration of a reactant to drop to half its original value. • For a first order process, half life, t½ is the time taken for [A]0 to reach ½[A]0. • Mathematically,

23. The Change of Concentration with Time • Half-Life • For a second order reaction, half-life depends in the initial concentration:

24. Temperature and Rate • The Collision Model • 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 chemiluminescence is dependent on temperature: the higher the temperature, the faster the reaction and the brighter the light.

25. Temperature and Rate • The Collision Model • As temperature increases, the rate increases.

26. Temperature and Rate • The Collision Model • Since the rate law has no temperature term in it, the rate constant must depend on temperature. • Consider the first order reaction CH3NC  CH3CN. • As temperature increases from 190 C to 250 C the rate constant increases from 2.52  10-5 s-1 to 3.16  10-3 s-1. • The temperature effect is quite dramatic. Why? • Observations: rates of reactions are affected by concentration and temperature.

27. Temperature and Rate • The Collision Model • Goal: develop a model that explains why rates of reactions increase as concentration and temperature increases. • The collision model: in order for molecules to react they must collide. • The greater the number of collisions the faster the rate. • The more molecules present, the greater the probability of collision and the faster the rate.

28. Temperature and Rate • The Collision Model • The higher the temperature, the more energy available to the molecules and the faster the rate. • Complication: not all collisions lead to products. In fact, only a small fraction of collisions lead to product. • The Orientation Factor • In order for reaction to occur the reactant molecules must collide in the correct orientation and with enough energy to form products.

29. Temperature and Rate • The Orientation Factor • Consider: • Cl + NOCl  NO + Cl2 • There are two possible ways that Cl atoms and NOCl molecules can collide; one is effective and one is not.

30. Temperature and Rate The Orientation Factor

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

32. Temperature and Rate • Activation Energy • Consider the rearrangement of methyl isonitrile: • In H3C-NC, the C-NC bond bends until the C-N bond breaks and the NC portion is perpendicular to the H3C portion. This structure is called the activated complex or transition state. • The energy required for the above twist and break is the activation energy, Ea. • Once the C-N bond is broken, the NC portion can continue to rotate forming a C-CN bond.

34. Temperature and Rate • Activation Energy • The change in energy for the reaction is the difference in energy between CH3NC and CH3CN. • The activation energy is the difference in energy between reactants, CH3NC and transition state. • The rate depends on Ea. • Notice that if a forward reaction is exothermic (CH3NC  CH3CN), then the reverse reaction is endothermic (CH3CN  CH3NC).

35. Temperature and Rate • Activation Energy • How does a methyl isonitrile molecule gain enough energy to overcome the activation energy barrier? • From kinetic molecular theory, we know that as temperature increases, the total kinetic energy increases. • We can show the fraction of molecules, f, with energy equal to or greater than Ea is • where R is the gas constant (8.314 J/mol·K).

36. Temperature and Rate Activation Energy

37. Temperature and Rate • The Arrhenius Equation • Arrhenius discovered most reaction-rate data obeyed the Arrhenius equation: • k is the rate constant, Eais the activation energy, R is the gas constant (8.314 J/K-mol) and T is the temperature in K. • A is called the frequency factor. • A is a measure of the probability of a favorable collision. • Both A and Ea are specific to a given reaction.

38. Temperature and Rate • Determining the Activation Energy • If we have a lot of data, we can determine Ea and A graphically by rearranging the Arrhenius equation: • From the above equation, a plot of ln k versus 1/T will have slope of –Ea/R and intercept of ln A.

39. Temperature and Rate

40. Temperature and Rate • Determining the Activation Energy • If we do not have a lot of data, then we recognize

41. Reaction Mechanisms • The balanced chemical equation provides information about the beginning and end of reaction. • The reaction mechanism gives the path of the reaction. • Mechanisms provide a very detailed picture of which bonds are broken and formed during the course of a reaction. • Elementary Steps • Elementary step: any process that occurs in a single step.

42. Reaction Mechanisms • Elementary Steps • 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).

43. Reaction Mechanisms • Multistep Mechanisms • Some reaction proceed through more than one step: • NO2(g) + NO2(g)  NO3(g) + NO(g) • NO3(g) + CO(g)  NO2(g) + CO2(g) • Notice that if we add the above steps, we get the overall reaction: • NO2(g) + CO(g)  NO(g) + CO2(g)

44. Reaction Mechanisms • Multistep Mechanisms • If a reaction proceeds via several elementary steps, then the elementary steps must add to give the balanced chemical equation. • Intermediate: a species which appears in an elementary step which is not a reactant or product.

45. Reaction Mechanisms • Rate Laws for Elementary Steps • The rate law of an elementary step is determined by its molecularity: • Unimolecular processes are first order, • Bimolecular processes are second order, and • Termolecular processes are third order.

46. Reaction Mechanisms Rate Laws for Elementary Steps

47. Reaction Mechanisms • Rate Laws for 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. • Consider • 2NO(g) + Br2(g)  2NOBr(g)

48. Reaction Mechanisms • Mechanisms with an Initial Fast Step • 2NO(g) + Br2(g)  2NOBr(g) • The experimentally determined rate law is • Rate = k[NO]2[Br2] • Consider the following mechanism

49. Reaction Mechanisms • Mechanisms with an Initial Fast Step • The rate law is (based on Step 2): • Rate = k2[NOBr2][NO] • The rate law should not depend on the concentration of an intermediate (intermediates are usually unstable). • Assume NOBr2 is unstable, so we express the concentration of NOBr2 in terms of NOBr and Br2 assuming there is an equilibrium in step 1 we have

50. Reaction Mechanisms • Mechanisms with an Initial Fast Step • By definition of equilibrium: • Therefore, the overall rate law becomes • Note the final rate law is consistent with the experimentally observed rate law.