KINETICS

1. KINETICS The speed of a reaction

2. Kinetics • The study of reaction rates. • Spontaneous reactions are reactions that will happen - but we can’t tell how fast. • Diamond will spontaneously turn to graphite – eventually. • Reaction mechanism- the steps by which a reaction takes place.

3. Reaction Rate • Rate = Conc. of A at t2 -Conc. of A at t1t2- t1 • Rate =D[A]Dt • Change in concentration per unit time • For this reaction • N2 + 3H2 2NH3

4. As the reaction progresses the concentration of H2 goes down Concentration [H2] Time

5. As the reaction progresses the concentration of N2 goes down 1/3 as fast Concentration [N2] [H2] Time

6. As the reaction progresses the concentration of NH3 goes up. Concentration [N2] [H2] [NH3] Time

7. Calculating Rates • Average rates are taken over long intervals • Instantaneous rates are determined by finding the slope of a line tangent to the curve at any given point because the rate can change over time • Derivative.

8. Average slope method Concentration D[H2] Dt Time

9. Instantaneous slope method. Concentration D[H2] D t Time

10. Defining Rate • We can define rate in terms of the disappearance of the reactant or in terms of the rate of appearance of the product. • In our example: N2 + 3H2 2NH3 • -D [N2] = -3 D[H2] = 2 D[NH3] DtDtDt

11. Rate Laws • Reactions are reversible. • As products accumulate they can begin to turn back into reactants. • Early on the rate will depend on only the amount of reactants present. • We want to measure the reactants as soon as they are mixed. • This is called the Initial rate method and time = 0.

12. Rate Laws • Two key points • The concentration of the products do not appear in the rate law because this is an initial rate. • The order must be determined experimentally because it can’t be obtained from the equation

13. 2 NO2 2NO + O2 • You will find that the rate will only depend on the concentration of the reactants. • Rate = k[NO2]n • This is called a rate law expression. • k is called the rate constant. • n is the order of the reactant - usually a positive integer.

14. 2 NO2 2NO + O2 • The rate of appearance of O2 can be said to be. • Rate' = D[O2] = k'[NO2]2Dt • Because there are 2 NO2 for each O2 • Rate = 2 x Rate' • So k[NO2]n= 2 x k'[NO2]n • So k = 2 x k'

15. Types of Rate Laws • Differential Rate law - describes how rate depends on concentration. • Integrated Rate Law - Describes how concentration depends on time. • For each type of differential rate law there is an integrated rate law and vice versa. • Rate laws can help us better understand reaction mechanisms.

16. Determining Rate Laws • The first step is to determine the form of the rate law (especially its order). • Must be determined from experimental data which is usually given. • For this reaction 2 N2O5 (aq) 4NO2 (aq) + O2(g) • The reverse reaction won’t play a role

17. [N2O5] (mol/L) Time (s) 1.00 0 0.88 200 0.78 400 0.69 600 0.61 800 0.54 1000 0.48 1200 0.43 1400 0.38 1600 0.34 1800 0.30 2000 Now graph the data

18. To find rate we have to find the slope at two points • We will use the tangent method.

19. At .90 M the rate is (.98 - .76) = 0.22 =- 5.5x 10 -4 (0-400) -400

20. At .40 M the rate is (.52 - .31) = 0.22 =- 2.7 x 10 -4 (1000-1800) -800

21. Since the rate at twice the concentration is twice as fast the rate law must be.. • Rate = -D[N2O5] = k[N2O5]1 = k[N2O5] Dt • We say this reaction is first order in N2O5 • The only way to determine order is to run the experiment. • So the Rate Law is Rate = k[N2O5]

22. The Method of Initial Rates • This method requires that a reaction be run several times. • The initial concentrations of the reactants are varied. • The reaction rate is measured just after the reactants are mixed. • Eliminates the effect of the reverse reaction. • In our problems, this isn’t a concern.

23. An Example of a Rate Law • For the reaction BrO3- + 5 Br- + 6H+ 3Br2 + 3 H2O • The general form of the Rate Law is: • Rate = k[BrO3-]n[Br-]m[H+]p • We use experimental data to determine the values of n, m, and p

24. Initial concentrations (M) Rate (M/s) Now we have to see how the rate changes with concentration Br- BrO3- H+ 0.10 0.10 0.10 8.0 x 10-4 0.20 0.10 0.10 1.6 x 10-3 0.20 0.20 0.10 3.2 x 10-3 0.10 0.10 0.20 3.2 x 10-3

25. Remember our Formula ! - Δ Concentration order = Δ Rate In words, the change in concentration raised to the order of the exponent = the change in the rate. - Fortunately, most of the time, these can be solved on inspection. Eg. If the concentration is tripled and the rate is tripled, then 3x = 3 so x = 1. HOWEVER…

26. Sometimes more drastic measures are needed. • Namely the law of logarithms. • Δ Concentration order = Δ Rate becomes Order x (Log (conc.)) = Log (rate) • It is simple and works every time. • 23 = 8 3 log 2 = log 8 3 x .301 = .903

27. Integrated Rate Law • Expresses the reaction concentration as a function of time. • Form of the equation depends on the order of the rate law (differential). • Changes Rate = D[A]nDt • We will only work with n=0, 1, and 2

28. First Order • For the reaction 2N2O5 4NO2 + O2 • We found the Rate = k[N2O5]1 • If concentration doubles rate doubles. • If we integrate this equation with respect to time we get the Integrated Rate Law • ln[N2O5] = - kt + ln[N2O5]0 • ln is the natural log • [N2O5]0 is the initial concentration.

29. First Order • General form Rate = D[A] / Dt = k[A] • ln[A] = - kt + ln[A]0 • In the form y = mx + b • y = ln[A] m = - k • x = t b = ln[A]0 • A graph of ln[A] vs time is a straight line.

30. First Order Rates • By getting the straight line you can prove it is first order. • Often expressed in a ratio.

31. First Order • By getting the straight line you can prove it is first order. • Often expressed in a ratio

32. Half Life • The time required to reach half the original concentration. • If the reaction is first order • [A] = [A]0/2 when t = t1/2

33. Half Life • The time required to reach half the original concentration. • If the reaction is first order • [A] = [A]0/2 when t = t1/2 • ln(2) = kt1/2

34. Half Life • t1/2 = 0.693/k • The time to reach half the original concentration does not depend on the starting concentration. • An easy way to find k.

35. Second Order • Rate = -D[A] / Dt = k[A]2 • integrated rate law • 1/[A] = kt + 1/[A]0 • y= 1/[A] m = k • x= t b = 1/[A]0 • A straight line if 1/[A] vs t is graphed • Knowing k and [A]0 you can calculate [A] at any time time.

36. Second Order Half Life • [A] = [A]0 /2 at t = t1/2

37. Zero Order Rate Law • Rate = k[A]0 = k • Rate does not change with concentration. • Integrated [A] = -kt + [A]0 • When [A] = [A]0 /2 t = t1/2 • t1/2 = [A]0 / 2k

38. Zero Order Rate Law • Most often when reaction happens on a surface because the surface area stays constant. • Also applies to enzyme chemistry. • The material is said to be at the zeroeth order.

39. Concentration Time

40. Concentration k = D[A]/Dt D[A] Dt Time

41. More Complicated Reactions • BrO3- + 5 Br - + 6H+ 3Br2 + 3 H2O • For this reaction we found the rate law to be: • Rate = k[BrO3-][Br-][H+]2 • To investigate this reaction rate we need to control the conditions.

42. Rate = k[BrO3-][Br-][H+]2 • We set up the experiment so that two of the reactants are in large excess. • [BrO3-]0= 1.0 x 10-3 M • [Br-]0 = 1.0 M • [H+]0 = 1.0 M • As the reaction proceeds [BrO3-] changes noticably • [Br-] and [H+] don’t

43. Rate = k[BrO3-][Br-][H+]2 • This rate law can be rewritten • Rate = k[BrO3-][Br-]0[H+]02 • Rate = k[Br-]0[H+]02[BrO3-] • Rate = k’[BrO3-] • This is called a pseudo first order rate law. • k = k’ [Br-]0[H+]02

44. Summary of Rate Laws • Know your integrated rate laws. • Know how to find the order for the reaction • Know how to find k after you determine the orders. • As always, read the question carefully to make sure you are using all the given information.

45. Reaction Mechanisms • The series of steps that actually occur in a chemical reaction. • Kinetics can tell us something about the mechanism. • A balanced equation does not tell us how the reactants become products. • We will always want to find the rate determining step, which will usually be the slowest step in the mechanism.

46. Reaction Mechanisms • 2NO2 + F2 2NO2F • Rate = k[NO2][F2] • The proposed mechanism is • NO2 + F2 NO2F + F (slow) • F + NO2 NO2F (fast) • F is called an intermediate It is formed then consumed in the reaction, so it isn’t present in the given equation.

47. Reaction Mechanisms • Each of the two reactions is called an elementary step . • The rate for a reaction can be written from its molecularity . • Molecularity is the number of pieces that must come together.

48. Molecularity • Unimolecular step requires one molecule so the rate is first order. • Bimolecular step - requires two molecules so the rate is second order. • Termolecular step - requires three molecules so the rate is third order. • Termolecular steps are almost never heard of because the chances of three molecules coming into contact at the same time are miniscule.

49. A Products Rate = k[A] • A + A Products Rate= k[A]2 • 2A Products Rate= k[A]2 • A + B Products Rate= k[A][B] • A + A + B Products Rate= k[A]2[B] • 2A + B Products Rate= k[A]2[B] • A + B + C Products Rate= k[A][B][C]

50. How to get rid of intermediates • Use the reactions that form them • If the reactions are fast and irreversible - the concentration of the intermediate is based on stoichiometry. • If it is formed by a reversible reaction set the rates equal to each other. • A picture is worth 1,000 words here, so let’s check out the next slide.