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Chapter 13 Chemical Kinetics

Chapter 13 Chemical Kinetics. The study of reaction rate is called chemical kinetics. Reaction rate is measured by the change of concentration (molarity) of reactants or products per unit time. Molarity of A: [A], e.g. [NO 2 ]: molarity of NO 2. −. −. reactants  products,.

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Chapter 13 Chemical Kinetics

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  1. Chapter 13 Chemical Kinetics

  2. The study of reaction rate is called chemical kinetics. Reaction rate is measured by the change of concentration (molarity) of reactants or products per unit time.

  3. Molarity of A: [A], e.g. [NO2]: molarity of NO2 − − reactants  products, [reactant]↓ and [product]↑ Unit: mol·L−1·s−1 ≡ M·s−1

  4. 2NO2 (g)  2NO (g) + O2 (g) − = r(NO2) rate is a function of time 0 s → 50 s: 50 s → 100 s:

  5. 2NO2 (g)  2NO (g) + O2 (g) − = r(NO2) − rate is a function of time 50 s → 100 s: 50 s → 100 s:

  6. 2NO2(g)  2NO(g) + O2(g)

  7. a A + b B  c C + d D r = r does not depend upon the choice of species

  8. 2N2O5(g)  4NO2(g) + O2(g) r(N2O5) = 4.2 x 10−7 M·s−1 What are the rates of appearance of NO2 and O2 ?

  9. Example 13.1. page 567 • Consider the following balanced chemical equation: • H2O2(aq) + 3 I–(aq) + 2 H+(aq)  I3–(aq) + 2 H2O(l) • In the first 10.0 seconds of the reaction, the concentration of I– dropped from 1.000 M to 0.868 M. • Calculate the average rate of this reaction in this time interval. • (b) Predict the rate of change in the concentration of • H+ (that is, [H+]/t) during this time interval.

  10. Consider the general reaction aA + bB cC and the following average rate data over some time period Δt: Determine a set of possible coefficients to balance this general reaction.

  11. − = r(NO2) − All the rates in this table are average rates.

  12. 2:00 pm 2:16 pm 3:16 pm Δt 0 mile Barnesville 16 miles Griffin 56 miles Atlanta Δl Average Speed from B to G = 16 miles ÷ 16 min = 1.0 mile/min Average Speed from G to A = 40 miles ÷ 60 min = 0.7 mile/min Instantaneous speed at green spot Instantaneous speed contains more information

  13. l Atlanta 56 miles Δl Griffin 20 miles Δt Barnesville 0 mile t 16 min 0 min 76 min Instantaneous speed at the red point = slope of the red solid line =

  14. Reaction rate is a function of time

  15. Factors that affect reaction rates State of the reactants Concentrations of the reactants Temperature Catalyst

  16. a A + b B  c C + d D r = k [A]m [B]n Differential rate law: how r depends on concentrations m, n: reaction order, mth order for A, nth order for B (m+n): overall reaction order k: rate constant: depends on temperature, but not concentrations m and n must be measured from experiments. They can be different from the stoichiometry.

  17. (1) 2N2O5(g)  4NO2(g) + O2(g) r = k[N2O5] (2) CHCl3(g) + Cl2(g)  CCl4(g) + HCl(g) r = k[CHCl3][Cl2]1/2 (3) H2(g) + I2(g)  2HI(g) r = k[H2][I2]

  18. aA + bB  cC +dD r = k [A]m [B]n Units overall reaction order (m+n)⇌ unit of k

  19. (1) 2N2O5(g)  4NO2(g) + O2(g) r = k[N2O5] (2) CHCl3(g) + Cl2(g)  CCl4(g) + HCl(g) r = k[CHCl3][Cl2]1/2 (3) H2(g) + I2(g)  2HI(g) r = k[H2][I2]

  20. How to find the rate law by experiment: method of initial rates NH4+ (aq) + NO2− (aq)  N2(g) + 2H2O(l) r = k [NH4+]m [NO2−]n

  21. A very common method to investigate how each factor affects the whole system: Change one thing at a time while keep the others constant. z = f (x,y) How does the change of x affect z? How does the change of y affect z?

  22. How to find the rate law by experiment: method of initial rates NH4+ (aq) + NO2− (aq)  N2(g) + 2H2O(l) r = k [NH4+]m [NO2−]n

  23. 2NO(g) + 2H2(g)  N2(g) + 2H2O(g) • Determine the differential rate law • Calculate the rate constant • Calculate the rate when [NO] = 0.050 M and [H2] = 0.150 M

  24. 2NO(g) + 2H2(g)  N2(g) + 2H2O(g) again • Determine the differential rate law • Calculate the rate constant • Calculate the rate when [NO] = 0.050 M and [H2] = 0.150 M

  25. A + B  C • Determine the differential rate law • Calculate the rate constant • Calculate the rate when [A] = 0.050 M and [B] = 0.100 M

  26. EXAMPLE 13.2 Determining the Order and Rate Constant of a Reaction NO2(g) + CO(g)  NO(g) + CO2(g) From the data, determine: (a) the rate law for the reaction (b) the rate constant (k) for the reaction

  27. Use the data in table to determine 1) The orders for all three reactants 2) The overall reaction order 3) The value of the rate constant

  28. r = k [BrO3−]m [Br−]n [H+]p r1 = k (0.10 M)m (0.10 M)n (0.10 M)p = 8.0 x 10−4 M · s−1 r2 = k (0.20 M)m (0.10 M)n (0.10 M)p = 1.6 x 10−3 M · s−1 r3 = k (0.20 M)m (0.20 M)n (0.10 M)p = 3.2 x 10−3 M · s−1 r4 = k (0.10 M)m (0.10 M)n (0.20 M)p = 3.2 x 10−3 M · s−1

  29. one quiz after lab Relationship among reaction rates as expressed by different species. r = overall reaction order (m+n)⇌ unit of k Method of initial rates: table of experimental data  rate order, k, rate at other concentrations.

  30. a A + b B  c C + d D r = k [A]m [B]n Differential rate law: how r depends on concentrations Differential rate law: differential equation How concentration changes as a function of time  integrated rate law

  31. A  Products First order reaction differential rate law: First order reaction integrated rate law: or integrated rate law: how concentration changes as a function of time.

  32. First order reaction integrated rate law: [A] is the molarity of A at t y = mx + b Plot ln[A] vs. t gives a straight line Slope = −k, intercept = ln[A]0

  33. N2O5(g)  2NO2(g) + ½ O2(g) Use these data, verify that the rate law is first order in N2O5, and calculate the rate constant. k = 6.93 x 10−3 s−1

  34. Read a similar Example 13.3 on page 575

  35. Using the data given in the previous example, calculate [N2O5] at 150 s after the start of the reaction. 0.0354 M

  36. Practice on Example 13.4 on page 576 and check your answer

  37. The half-life of a reaction, t1/2, is the time required for a reactant to reach one-half of its initial concentration.

  38. The half-life for first order reaction: The half-life for first order reaction does NOT depend on concentration.

  39. A Plot of [N2O5] versus Time for the Decomposition Reaction of N2O5

  40. A certain first order reaction has a half-life of 20.0 s. • Calculate the rate constant for this reaction. • How much time is required for this reaction to be 75 % • complete? a) k = 0.0347 s−1 b) k = 40.0 s

  41. Try Example 13.6 and For Practice 13.6 on page 579 and check your answers

  42. A  Products Second order reaction differential rate law: Second order reaction integrated rate law: integrated rate law: how concentration changes as a function of time.

  43. Second order reaction integrated rate law: y = mx + b Plot 1/[A] vs. t gives a straight line Slope = k, intercept = 1/[A]0

  44. The half-life for second order reaction: The half-life for second order reaction depends on initial concentration.

  45. A certain reaction has the following general form: A  B • At a particular temperature [A]0 = 2.80 x 10−3 M, • concentration versus time data were collected for this reaction, • and a plot of 1/[A] versus time resulted in a straight line with a • slope value of 3.60 x 10−2 M−1·s−1 • Determine the (differential) rate law, the integrated rate law, • and the value of the rate constant. • b) Calculate the half-life for this reaction. • c) How much time is required for the concentration of A to • decrease to 7.00 x 10−4 M ?

  46. (show your work, do not copy the question) For first order reaction, show that from the integrated rate law

  47. A  Products Zero order reaction differential rate law: Zero order reaction integrated rate law: integrated rate law: how concentration changes as a function of time.

  48. Zero order reaction integrated rate law: y = mx + b Plot [A] vs. t gives a straight line Slope = −k, intercept = [A]0

  49. The half-life for zero order reaction: The half-life for zero order reaction depends on initial concentration.

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