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Chemical Kinetics

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  1. Chemical Kinetics Chapter 12

  2. Reaction Rates 01 • Reaction Rate: The change in the concentration of a reactant or a product with time (M/s). • change in concentration divided by the change in time Reactant  Products A  B 2 HI(g) H2(g) + I2(g) Chapter 12

  3. 1 2 [HI] t Rate = − = [I2] t Reaction Rates and Stoichiometry • What is the general rate of the following reaction ? 2 HI(g) H2(g) + I2(g) Chapter 12

  4. aA + bB cC + dD = = Rate* = − = − 1 d 1 c 1 a 1 b [C] t [D] t [A] t [B] t Reaction Rates and Stoichiometry • To generalize, for the reaction *: General rate of reaction Chapter 12

  5. Which of the expressions below, corresponding to the reaction of bromine with formic acid, is incorrect?

  6. Which of the expressions below, corresponding to the reaction of bromine with formic acid, is incorrect?

  7. How Do we study Rate of a reaction? • Consider the decomposition of N2O5 to give NO2 and O2: 2 N2O5(g) 4 NO2(g) + O2(g) Brown Colorless Chapter 12

  8. 2 N2O5(g) 4 NO2(g) + O2(g) Reaction Rates: concentration versus time curve 03 Average Rate = Rate between two points in time The slope of each triangle Between two points Chapter 12

  9. 2N2O5(g) 4NO2(g) + O2(g) Reaction Rates

  10. Rate for specific instance in time Instantaneous rate: Slope of the tangent to a concentration versus time curve Initial Rate Chapter 12

  11. Br2(aq) + HCOOH (aq) 2Br-(aq) + 2H+(aq) + CO2(g) time Br2(aq) 393 nm 393 nm Detector light D[Br2] aDAbsorption Chapter 12

  12. Br2(aq) + HCOOH (aq) 2Br-(aq) + 2H+(aq) + CO2(g) slope of tangent slope of tangent slope of tangent [Br2]final – [Br2]initial D[Br2] average rate = - = - Dt tfinal - tinitial instantaneous rate = rate for specific instance in time The slope of a line tangent to the curve at any point is the instantaneous rate at that time Chapter 12

  13. slope of tangent slope of tangent Chapter 12

  14. rate k = [Br2] rate a [Br2] rate = k [Br2] = rate constant The Rate Law; rate = 3.50 x 10-3 s-1 [Br2] Chapter 12

  15. k = 3.50 x 10-3 s-1 Chapter 12

  16. aA + bB cC + dD The Rate Law and Reaction Order The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some powers. Rate = k [A]x[B]y reaction is xth order in A reaction is yth order in B reaction is (x +y)th order overall Chapter 12

  17. The Rate Law and Reaction Order are Experimentally Determined Chapter 12

  18. Determine the reaction order for: F2(g) + 2ClO2(g) 2FClO2(g) ---- rate = k [F2]x[ClO2]y 1 vs 3 Double [F2] with [ClO2] constant Rate doubles x = 1 1 vs 2 rate = k [F2][ClO2] Quadruple [ClO2] with [F2] constant Rate quadruples y = 1 The instantaneous rate at the beginning of a reaction is called initial rate Chapter 12

  19. F2(g) + 2ClO2(g) 2FClO2(g) 1 Rate Laws • Rate laws are always determined experimentally. • Reaction order is always defined in terms of reactant (not product) concentrations. • The order of a reactant is not related to the stoichiometric coefficient of the reactant in the balanced chemical equation. rate = k [F2][ClO2] Chapter 12

  20. Determine the rate law and calculate the rate constant for the following reaction from the following data: S2O82-(aq) + 3I-(aq) 2SO42-(aq) + I3-(aq) rate k = 2.2 x 10-4 M/s = [S2O82-][I-] (0.08 M)(0.034 M) rate = k [S2O82-]x[I-]y y = 1 x = 1 rate = k [S2O82-][I-] Double [I-], rate doubles (experiment 1 & 2) Double [S2O82-], rate doubles (experiment 2 & 3) = 0.08/M•s Chapter 12

  21. N2(g) + 2 H2O(l) NH4+(aq) + NO2−(aq) Determine the Rate Law and Reaction Order Comparing Experiments 1 and 2, when [NH4+] doubles, the initial rate doubles. Chapter 12

  22. N2(g) + 2 H2O(l) NH4+(aq) + NO2−(aq) Likewise, comparing Experiments 5 and 6, when [NO2−] doubles, the initial rate doubles. Chapter 12

  23. This means Rate  [NH4+] Rate  [NO2−] Rate  [NH+] [NO2−] or Rate = k [NH4+] [NO2−] • This equation is called the rate law, and k is the rate constant. Chapter 12

  24. Rate Laws • The exponents tell the order of the reaction with respect to each reactant. • This reaction is First-order in [NH4+] First-order in [NO2−] Chapter 12

  25. E x p e ri m e n t [ NO ] [ H ] I n iti a l Ra t e (M/ s ) 2 – 3 – 3 – 5 1 5 . 0 x 1 0 2 . 0 x 1 0 1 . 3 x 1 0 – 3 – 3 – 5 2 1 0 . 0 x 1 0 2 . 0 x 1 0 5 . 0 x 1 0 – 3 – 3 – 5 3 1 0 . 0 x 1 0 4 . 0 x 1 0 1 0 . 0 x 1 0 Rate Law & Reaction Order • The reaction of nitric oxide with hydrogen at 1280°C is: 2 NO(g) + 2 H2(g) N2(g) + 2 H2O(g) • From the following data determine the rate law and rate constant. Second order in NO, First order in H2 k = 1/3(250+250+260) = 250 M-2.s-1 Chapter 12

  26. A product D[A] - = k [A] Dt First-Order ReactionsConcentration and Time Equation 01 • First Order: Reaction rate depends on the reactant concentration raised to first power. Rate = k[A] Chapter 12

  27. D[A] - = K Δt rate = [A] M/s M [A] = [A]0exp(-kt) ln = k t [A]0 [A] Concentration and Time Equation For A First-Order Reactions -(ln[A] -ln[A]0) = kt [A] ln[A] = ln[A]0 - kt See next slide for proof of the formula [A] = [A]0exp(-kt) [A] is the concentration of A at any time t [A]0 is the concentration of A at time t = 0 = 1/s or s-1 k = Chapter 12

  28. Integration: Chapter 12

  29. ln[A] = ln[A]0 - kt ln = k t [A]0 [A] First-Order Reactions ln[A] = ln[A]0 - kt [A] is the concentration of A at any time t [A]0 is the concentration of A at time t = 0 Chapter 12

  30. 0.88 M ln The reaction 2A B is first order in A with a rate constant of 2.8 x 10-2 s-1 at 800C. How long will it take for A to decrease from 0.88 M to 0.14 M ? 0.14 M = 2.8 x 10-2 s-1 ln ln = k t k [A]0 [A]0 [A] [A] [A]0 = 0.88 M [A] = 0.14 M t = ? = 66 s t = Chapter 12

  31. [A]0 ln t½ [A]0/2 0.693 = = = k k ln ln2 = k t k [A]0 [A] What is Half- Life ? The half-life, t½, is the time required for the concentration of a reactant to decrease to half of its initial concentration. t½ = t when [A] = [A]0/2 Half Life For the First Order Reaction Chapter 12

  32. Reaction Orders Zeroth Order Reaction: Rate = K [A]0 = K Units of Rate Constants vs Reaction Orders Chapter 12

  33. What is the order of decomposition of N2O5if it decomposes with a rate constant of 5.7 x 10-4s-1? What is the half life of decomposition of N2O5 ? = t½ ln2 0.693 = k 5.7 x 10-4 s-1 2N2O5(g)  4NO2(g) + O2(g) units of k (s-1) Therefore, decomposition is first order? = 1200 s = 20 minutes Chapter 12

  34. Half life of a First Order Reaction Chapter 12

  35. A product # of half-lives [A] [A] = [A]0 x(1/2)n First-order reaction 1 ½ [A]0 2 1/4 [A]0 3 1/8 [A]0 4 1/16 [A]0 Chapter 12

  36. First-Order Reaction 2N2O5(g)  4NO2(g) + O2(g) • Show that the decomposition of N2O5 is first order and calculate the rate constant and Half life. t1/2 = 408 S k = 1.7 x 10-3 s-1 Chapter 12

  37. A product rate = [A]2 M/s D[A] 1 1 - M2 = k [A]2 = + kt Dt [A] [A]0 D[A] rate = - Dt Second-Order Reactions rate = k [A]2 What is Unit of k ? = 1/M•s or M-1 s-1 k = What is Conc. Vs time equation? [A] is the concentration of A at any time t [A]0 is the concentration of A at time t = 0 Chapter 12

  38. [A]0 = [A] t1/2 2 Second-Order Reactions So if a process is second-order in A, a plot of 1/[A] vs. t will yield a straight line, and the slope of that line is k. t = t1/2 Drive the formula for half life of a second order reaction Chapter 12

  39. = kt1/2 + = kt + 2 1 1 1 t1/2 = [A]0 [A]0 [A]0 [A]t [A]0 1 = [A] t1/2 k[A]0 2 Half-life for a second-order reaction t = t1/2 Chapter 12

  40. t1/2 = 1 k[A]0 Second-Order Reactions For a second-order reaction, the half-life is dependent on the initial concentration. Each successive half-life is twice as long as the preceding one. Chapter 12

  41. Is the following reaction first or second order ? • What is the value of k? Example: 2 NO2(g)  2NO(g) + O2(g) Chapter 12

  42. Chapter 12

  43. k = 0.54 M-1 . S-1 Second-Order Reactions Chapter 12

  44. Zero Order Reaction: Rate = k Example of Zeroth Order Reaction: Decomposition of N2O on hot platinum surface:        N2O →  N2  +  1/2 O2        Rate  [N2O]0 =  k[N2O]0 = k        d[N2 O]/dt = k Chapter 12

  45. Reaction Mechanisms 01 • A reaction mechanism is a sequence of molecular events, or reaction steps, that defines the pathway from reactants to products. Chapter 12

  46. Reaction Mechanisms 02 • Single steps in a mechanism are called elementary steps (reactions). • An elementary step describes the behavior of individual molecules. • An overall reaction describes the reaction stoichiometry. Chapter 12

  47. Reaction Mechanisms NO2(g) + CO(g)  NO(g) + CO2(g) • NO2(g) + NO2(g) NO(g) + NO3(g) Elementary • NO3(g) + CO(g) NO2(g) + CO2(g) Elementary • NO2(g) + CO(g)  NO(g) + CO2(g) Overall • The chemical equation for an elementary reaction is a description of an individual molecular event that involves the breaking and/or making of chemical bonds. NO3(g) is called reaction intermediate. Chapter 12

  48. Reaction Mechanisms 04 • Molecularity: is the number of molecules (or atoms) on the reactant side of the chemical equation. • Unimolecular: Single reactant molecule. Chapter 12

  49. Reaction Mechanisms 05 • Bimolecular: Two reactant molecules. • Termolecular: Three reactant molecules. Chapter 12