Chemical Kinetics

1. Chemical Kinetics The Study of Reaction Rates

2. Chemical Kinetics Kinetics involves the study of several factors that affect the rates of chemical reactions. The final goal is to use all of the data to develop a step-by-step reaction mechanism. The mechanism is a possible path by which reactants become products.

3. Factors Affecting Reaction Rates Scientists typically examine how each of the following factors affect the rate of a particular reaction. • Concentration of Reactants • Temperature • Solvent (if applicable) • Catalysts (if applicable)

4. Reaction Rates The rate of reaction is typically expressed in the rate of disappearance of reactants, or the rate of formation of products. Since the stoichiometry of the reaction is known, the concentration of only one component of the reaction needs to be measured.

5. Reaction Rates Note that the concentration of NO increases by the same amount that [NO2] decreases.

6. Reaction Rates [O2] = ½[NO] So only one component of the reaction need be measured.

7. Reaction Rates For the reaction: 2NO2(g)  2NO(g) + O2(g) rate of loss of NO2 = rate of formation of NO = 2 (rate of formation of O2)

8. Reaction Rates For the reaction: 2NO2(g)  2NO(g) + O2(g) rate of loss of NO2 = rate of formation of NO = 2 (rate of formation of O2) -Δ[NO2] = Δ[NO] = 2(Δ[O2]) Δt Δt Δt Note the negative sign for the rate of loss of reactant.

9. Reaction Rates -Δ[NO2] = Δ[NO] = 2(Δ[O2]) Δt Δt Δt This relationship can also be seen in a graphical presentation of concentration versus time.

10. 2NO2(g)  2NO(g) + O2(g) Note that the rate of reaction varies as the reaction proceeds.

11. Reaction Rates: 2NO2(g)  2NO(g) +O2(g) The rate of reaction of NO2 is most rapid at the beginning of the reaction. It slows considerably as the reaction proceeds.

12. Reaction Rates Reaction rates vary with time, and also depend upon the temperature and stoichiometry of the reaction. As a result, we must be very specific in what we mean by a reaction rate. Initial rates are often used. This is the rate of reaction just after the reaction begins. The tangent to the curve during the initial moments of the reaction provides the rate.

13. Reaction Rates This graph for the decomposition of N2O5 to form NO2 and O2 shows an initial rate of 5.4 x 10-4 mol/L-s

14. Reaction Rates The convention for dealing with the stoichiometry of the reaction is that for a general reaction: aA + bB  cC + dD Rate = - 1 Δ[A] = - 1 Δ[B] = 1 (Δ[C]) = 1(Δ[D]) a Δt b Δt c Δt d Δt

15. Rate Laws One of the goals of kinetics is to determine the rate law for a reaction. The rate law is the mathematical relationship that shows how the reaction rate depends upon the concentration of reactants. Rate = k[A]x[B]y k is the rate constant, and is highly temperature dependent

16. Rate Laws Rate = k[A]x[B]y x and y are called the order of the reaction with respect to reactant A and B respectively. They will usually have the value of 0, 1 or 2, though other values are possible. Rate laws must be determined experimentally.

17. Rate Laws The rate law of a reaction, along with information about temperature effects and solvent effects can be used to develop a possible reaction mechanism. The reaction mechanism is the step-by-step process by which reactants become products.

18. Determination of Rate Laws All rate laws are experimentally determined. There are two basic methods used: 1. The Method of Initial Rates 2. Graphical Techniques using the Integrated Rate Law

19. The Method of Initial Rates The reaction rate is measured for several different experiments. In each trial, on reactant concentration is changed (usually doubled) while the others are held constant. The change in rate will depend only upon the reactant with the changed concentration.

20. The Method of Initial Rates

21. The Method of Initial Rates O [NO2-] doubles

22. The Method of Initial Rates O [NO2-] doubles Rate doubles

23. The Method of Initial Rates O [NO2-] doubles Rate doubles Rate α [NO2-] 1

24. The Method of Initial Rates O [NH4+] doubles Rate doubles Rate α [NH4+] 1

25. The Method of Initial Rates rate α [NH4+][NO2-] or rate = k [NH4+][NO2-] The reaction is first-order in ammonium ion, first-order in nitrite ion, and second-order overall.

26. The Method of Initial Rates

27. The Method of Initial Rates [BrO3-]doubles ratedoubles rate α [BrO3-]1

28. The Method of Initial Rates rate quadruples [H+] doubles rate α [H+]2

29. The Method of Initial Rates [Br-] doubles rate doubles rate α [Br-]1

30. Method of Initial Rates rate α [BrO3-][Br-][H+]2 The rate law is usually written with the rate constant, k, included: rate =k[BrO3-][Br-][H+]2 The reaction is first order in bromate, first order in bromide, and second order in hydronium ion.

31. Method of Initial Rates rate =k[BrO3-][Br-][H+]2 The data for any reaction trial can be used to calculate the value of k, the rate constant. The reaction rate has the units mol/liter-time, so the units of k depend upon the exponents in the rate law. Usually the value of k for several trials is averaged.

32. Graphical Techniques The Integrated Rate Laws

33. The Integrated Rate Law In general, rate laws will be first or second order. In either case, the rate law can be integrated to provide a linear equation of the form: y=mx + b. This permits graphical presentation of the data and determination of the value of the rate constant.

34. The Integrated Rate Law Once concentration versus time data have been collected, the scientist constructs one or more graphs to determine both the order of the reaction and the value of the rate constant.

35. The Integrated Rate Law We need not measure concentration. Any property that is proportional to concentration (intensity of color, pressure or volume of gases, pH, etc.) may be graphed. HCO2H(aq) + Br2(aq)  2Br1-(aq) + CO2(g)

36. The Integrated Rate Law- First Order Reactions rate = - d[A] = k[A]1 dt Rearranging, we obtain: -d[A] = kdt [A] When this expression is integrated from time =0 to time t, we obtain: ln[A] = -kt + ln[A]o

37. The Integrated Rate Law- First Order Reactions ln[A] = -kt + ln[A]o This is the integrated rate law for first-order reactions. It has the linear form y=mx+b. If the reaction is first-order, a graph of ln[A] versus time will be linear with a slope equal to –k.

38. The Integrated Rate Law- First Order Reactions The linearity indicates that the reaction is first-order with respect to N2O5. The rate constant (- slope) has the units of (time)-1.

39. The Integrated Rate Law- First Order Reactions ln[A] = -kt + ln[A]o If a graph isn’t linear, a second-order plot must be prepared.

40. The Integrated Rate Law- First Order Reactions The curvature of the graph of ln[A] vs time indicates that this reaction is not first order.

41. The Integrated Rate Law – 2nd Order Reactions rate = - d[A] = k[A]2 dt Rearranging, we obtain: - d[A] = kdt [A]2 When this expression is integrated from time =0 to time t, we obtain: 1 = kt + 1_ [A][A]o

42. The Integrated Rate Law – 2nd Order Reactions 1 = kt + 1_ [A][A]o This equation has a linear (y=mx +b) form. If a reaction is second-order, a plot of 1/[A] versus time is linear, with the slope equal to the rate constant. The rate constant has the units (M)-1(time)-1.

43. The Integrated Rate Law – 2nd Order Reactions The linearity of the graph of [A]-1 indicates that the reaction is second-order with respect to NO2.

44. The Integrated Rate Law- 2nd Order Reactions The linearity of the graph of 1/[A] versus time indicates that the reaction is second-order with respect to C4H6.

45. Zero-Order Rate Laws Most reactions involving a single reactant exhibit first or second-order kinetics. Rarely, a reaction will have zero-order kinetics. In this case, Rate = k[A]0 = k(1) = k

46. Zero-Order Rate Laws Rate = k[A]0 = k(1) = k The integrated rate law is: [A] = -kt + [A]o and a graph of [A] versus time is linear.

47. Zero-Order Rate Laws Unlike the rate laws for other reactions, for a zero-order reaction, a graph of [A] versus time is linear. The slope = -k.

48. Graphical Techniques

49. Half-life and 1st Order Reactions The half-life is the time it takes for the concentration of a reactant to halve. It is represented by the symbol t½. The half-life for a 1st-order reaction doesn’t depend upon concentration. First-order reactions have a constant half-life. That is, it takes the same length of time for the concentration to halve throughout the reaction.

50. Half-life and 1st Order Reactions