Atkins & de Paula: Elements of Physical Chemistry: 5e

1. Atkins & de Paula: Elements of Physical Chemistry: 5e Chapter 10: Chemical Kinetics: The Rates of Reactions

2. End of chapter 10 assignments Discussion questions: • 2, 3, 4, 5, 7 Exercises: • 1, 2, 4, 5, 7, 9, 12, 13, 19, 20 Use Excel if data needs to be graphed

3. Homework assignments • Did you: • Read the chapter? • Work through the example problems? • Connect to the publisher’s website & access the “Living Graphs”? • Examine the “Checklist of Key Ideas”? • Work assigned end-of-chapter exercises? • Review terms and concepts that you should recall from previous courses

4. Empirical chemical kinetics In order to investigate the rate and mechanism of a reaction: • Determine the overall stoichiometry of the rxn and any side rxns • Determine how the concentrations of reactants and products change over time • Spectrophotometry, conductivity, pH, GC/MS, NMR, polarimetry, etc

5. Io I Spectrophotometry • Beer-Lambert law log =  [J] l • Io = incident light • I = transmitted light • l = length of light path •  = molar absorption coefficient • [J] = molar concentration of J • I = Io 10–[J]l

6. Molar extinction coefficient? • Molar absorption coefficient () was known as the “molar extinction coefficient” • Use of the term “molar extinction coefficient” has been discouraged since the 1960s

7. Preferred terminology of  Molar absorption coefficient (ε)Synonyms: Molar extinction coefficient, molar absorptivity "The recommended term for the absorbance for a molar concentration of a substance with a path length of 1.0 cm determined at a specific wavelength. Its value is obtained from the equation ε = A / cl-- R.C. Denney, Dictionary of Spectroscopy, 2nd ed. (Wiley, 1982), p.119-20.

8. Preferred terminology of  Molar absorption coefficient (ε) “Strictly speaking, in compliance with SI units the path length should be specified in meters, but it is current general practice for centimeters to be used for this purpose.” -- R.C. Denney, Dictionary of Spectroscopy, 2nd ed. (Wiley, 1982), p.119-20.

9. Preferred terminology of  Molar absorption coefficient (ε) “Under defined conditions of solvent, pH, and temperature the molar absorption coefficient for a particular compound is a constant at the specified wavelength." -- R.C. Denney, Dictionary of Spectroscopy, 2nd ed. (Wiley, 1982), p.119-20.

10. A  l Spectrophotometry • Beer’s law: [J] = • Thus, absorbance is directly proportional to the molar concentration • A = [J] l (notice A is dimensionless) • Absorbance a/k/a “optical density” • What is max? • Do we always use max? • Is  specific to a compound? To a?

11. Table 10.1 Kinetic techniques for fast reactions

12. Spectrophotometry Fig 10.1 (231) The intensity of the absorbed light increases exponentially with path length

13. Spectrophotometry Fig 10.2 (231) Two concentrations of two absorbing species can be determined from their  at two different ’s within their joint absorption region

14. Spectrophotometry • Fig 10.3 (232) • An isosbestic point is formed when two unrelated absorbing species are present in the rxn solution • The curves repre-sent different stages of the rxn

15. Applications of Spectrophotometry We can use spectrophotometers to follow the progress of a reaction in “real time”

16. Applications of spectrophotometry • Fig 10.4 (232) • Flow technique • Fig 10.5 (232) • Stopped-flow technique

17. Applications of spectrophotometry • Flash photolysis • Quenching methods • Rapid cooling • Adding a large volume of solvent • Rapid neutralization • Applicable to relatively slow rxns

18. rate = – A B rate = D[A] D[B] Dt Dt Reaction rate Reaction rate is the change in the concentration of a reactant or a product with time (M/s). D[A] = change in concentration of A over time period Dt D[B] = change in concentration of B over time period Dt Because [A] decreases with time, D[A] is negative. Review from Gen Chem

19. 2A B rate = – D[B] D[A] rate = 1 Dt Dt 2 Reaction Rates and Stoichiometry Two moles of A disappear for each mole of B that is formed. Review from Gen Chem

20. 2A B aA + bB cC + dD rate = – = = rate = – = – D[C] D[B] D[B] D[A] D[A] D[D] rate = 1 1 1 1 1 Dt Dt Dt Dt Dt Dt a b 2 c d Reaction Rates and Stoichiometry Two moles of A disappear for each mole of B that is formed. Another generic chemical reaction Review from Gen Chem

21. |[J]| d[J] dt t Definition of reaction rate Notice Atkins/de Paula use the absolute value • Rate = • More precisely, Rate = • Partial pressures can be used instead of molar concentrations t is infinitesimally small

22. Definition of reaction rate • Fig 10.6 (233) • Concentration of reactant vs time • The rxn rate changes as the rxn proceeds • Slope is the instantaneous rate at that time

23. Rate laws and rate constants • The rate of a rxn is often (usually?) found proportional to the product of the molar concentrations raised to a simple power: Rate = [A]x [B]y • The units of the rate constant are determined by the form of the rate law (p.234)

24. Rate laws and rate constants • The rate law allows us to predict the concentrations of reactants and products at time t • Proposed mechanisms must be consistent with the rate law

25. Classification according to order • The power to which a concentration is raised in the rate law is the order with respect to that species • The overall order of a reaction is the sum of the orders of all the reactants • The order may be a fraction, zero, or indefinite • The rate law is determined empirically and cannot be inferred from the stoichiometry of the chemical eqn

26. Determination of the rate law • The rate law is determined empirically • Two common methods: • The isolation method (as performed in Gen Chem lab; all reactants except one present in great excess, so their concentrations do not change much) • The method of initial rates

27. The method of initial rates • log rate0 = log k’ + a log[A]0 • This equation is of the form: • y = intercept + slope x • So, for a series of initial concentrations, a plot of the log rate0 vs log[A]0 should be a straight line, with the slope = a,the order of the rxn with respect to A • Let’s look at an example

28. Determination of the rate law • Fig 10.7 (237) • The slope of a graph of log(rate0) vs log[A]0 is equal to the order of the reaction

29. The method of initial rates You should work through Example 10.1, pp.237f

30. [A]0 [A] Integrated rate laws • First order rxns: • ln = kt • ln[A] = ln[A]0 – kt OR [A] = [A]0 e–kt • In 1st order rxns, the [reactants] decays exponentially with time

31. Integrated rate laws • Fig 10.10 (239) • The exponen-tial decay of reactant in a 1st order rxn. • The larger the rate constant, the faster the decay

32. Integrated rate laws • Fig 10.11 (240) • Part of Ex 10.2 • You should work through Example 10.2

33. Integrated rate laws • Fig 10.12 (241) • Variation with time of the [reactant] in a 2nd order rxn

34. Integrated rate laws • Fig 10.13 (241) • The determination of the rate constant of a 2nd order rxn • The slope equals the rate constant

35. Table 10.2 Kinetic data for first-order reactions

36. Table 10.3 Kinetic data for second-order reactions

37. Table 10.4 Integrated rate laws

38. Half-lives and time constants • A half-life is a good indicator of the rate of a 1st order rxn • The half-life is the time it takes for [reactant] to drop to ½[reactant]0

39. [A]0 [A] ½[A]0 [A]0 Half-lives and time constants • Useful for 1st order rxns • [A] = ½[A]0 at t½ substitute into next eqn… • ln = kt to get…. • kt½ = – ln = – ln ½ = ln 2 • For 1st order rxn, t½ of a reactant is independent of its concentration

40. Using a half-life • Fig 10.15 (242) • Illustration 10.2

41. Using a half-life • Fig 10.16 (243) • Illustration 10.3

42. Ea 1 R T The Arrhenius parameters In the 1800s Arrhenius noticed that the rates of many different rxns had a similar dependence on temperature • He noticed that a plot of ln k vs 1/T gives a straight line with a slope characteristic of that rxn • ln k = intercept + slope  1/T • ln k = ln A – 

43. Ea RT The Arrhenius parameters • ln k = ln A– • k = Ae • The Arrhenius parameters: • A is the pre-exponential factor • Ea is the activation energy, kJ/mol • When Ea is high, the rxn rate is sensitive to temperature, steep slope • When Ea is low, the rxn rate is less sensitive to temperature, less steep slope Two common forms of the Arrhenius equation –Ea/RT

44. The Arrhenius Parameters Fig 10.17 (244) The general from of an Arrhenius plot

45. The Arrhenius Parameters • Fig 10.18 (244) • ln k vs 1/T • Notice the rxn with a higher Ea has a steeper slope

46. The Arrhenius parameters Tables of Arrhenius parameters have values for A (in sec-1) and for Ea (in kJ mol-1) Want to see some Arrhenius parameters??

47. Table 10.5 Arrhenius parameters – First-order reactions

48. Table 10.5 Arrhenius parameters – Second-order reactions

49. Collision theory • For bimolecular, gas phase rxns • Collisions must have at least a minimum energy in order for products to form • (What is a “bimolecular” rxn?)

50. Collision theory Fig 10.20 (246) A rxn occurs when two molecules collide with sufficient energy (a) insufficient energy (b) sufficient energy