Understanding Chemical Kinetics: Rates of Reactions

1. Chapter 15: Chemical KineticsRates of Reactions How does a reaction take place? Consider: NO + O3 NO2 + O2 product molecules separate Molecules collide Bonds are formed and break

2. So, what controls the rate of a reaction? • Number of collisions • How often they collide in a shape that allows new bonds to form • The energy of the colliding reactant molecules

3. Collision Theory For a reaction to take place: • Molecules must collide • They must do so in the correct orientation • They must collide with an energy greater than the “activation” energy

4. Concentration Dependence • It makes sense that as concentration increases, the number of collisions per second will increase • Therefore, in general, as concentration increases, rate increases • But, it depends on which collisions control the rate • So, you can’t predict concentration dependence- it must be measured experimentally

5. But, what do we mean by “rate?” • In real life, rate = distance/time • This is change in position over time • In chemistry, generally change in concentration over time

6. Types of measured rates: • Rate over time: • Instantaneous rate: • Initial rate:

7. Example of rate measurement:

8. Rate Laws (also called Rate Equations) For the reaction: 2 N2O5 4 NO + O2 Rate = k[N2O5] For the reaction: NO2  NO + ½ O2 Rate = k[NO2]2 For the reaction: CO + NO2  CO2 + NO Rate = k[CO][NO2]

9. Rate Laws (also called Rate Equations) For the reaction: 2 N2O5 4 NO + O2 Rate = k[N2O5] first order reaction For the reaction: NO2  NO + ½ O2 Rate = k[NO2]2 second order reaction For the reaction: CO + NO2  CO2 + NO Rate = k[CO][NO2] first order in CO and in NO2; second order overall

10. Determining a Rate Law • Remember– it must be done by experiment; the reaction equation does not tell you the rate law • Two methods: Initial Rates Graphical Method

11. Determining a Rate Law: Initial Rate Method • Measure the rate of the reaction right at the start. • Vary the starting concentrations • Compare initial rates to initial concentrations

12. Determining a Rate Law: Initial Rate Method • Useful rules: Vary only one concentration at a time • If concentration doubles and: • Rate does not change, then zero order • Rate doubles, then first order • Rate quadruples, then second order • General Rule:

13. Initial Rate Method: Example 1 When concentration is doubled, rate increases by: Therefore reaction is second order: Rate = k[NH4NCO]2 Now, use one of the experiments to find the rate constant, k:

14. Initial Rate Method: Example 2

15. Initial Rate Method: Example 2 NOTICE: When [O2] is doubled without changing [NO], the rate doubles. Therefore the reaction is first order in [O2].

16. Initial Rate Method: Example 2 NOTICE: When [NO] is doubled without changing [O2], the rate quadruples. Therefore the reaction is second order in [NO].

17. Initial Rate Method: Example 2 The reaction is first order in [O2] and second order in [NO]. Rate = k[O2][NO]2 Now we find the value of k.

18. Concentration-Time Relationships

19. Concentration-Time Relationships

20. Graphical Method for Determining Rate Laws

21. Graphical Method for Determining Rate Laws A plot of 1/[R] vs. Time will be linear. A plot of concentration vs. Time will be linear. A plot of ln[R] vs. Time will be linear.

22. Graphical Method for Determining Rate Laws How it works: 1. Collect [R] over an interval of times. 2. Make plots of [R] vs. time ln[R] vs. time 1/R vs. time Only one will be linear. That tells you the reaction order. The slope of the linear plot is the rate constant.

23. Graphical Method for Determining Rate Laws • Example: 2 H2O2 2 H2O + O2 • Time(min) [H2O2](mol/L) • 0 0.0200 • 200 0.0160 • 400 0.0131 • 600 0.0106 • 800 0.0086 • 1000 0.0069

24. Graphical Method for Determining Rate Laws • Example: 2 H2O2 2 H2O + O2 • Time(min) [H2O2](mol/L) • 0 0.0200 • 200 0.0160 • 400 0.0131 • 600 0.0106 • 800 0.0086 • 1000 0.0069

25. Graphical Method for Determining Rate Laws time concentration

26. Graphical Method for Determining Rate Laws ln(conc)

27. Graphical Method for Determining Rate Laws Rate = k[H2O2] k = 0.0011 min-1 ln(conc)

28. Graphical Method for Determining Rate Laws 1/concentration Check the second order plot to be sure it doesn’t also look linear.

29. Half-Life • Half-Life = the time it takes for half the reactant concentration to drop to half of its original value

30. First Order Reaction:2 H2O2 2 H2O + O2Rate = k[H2O2]; k = 1.05 x 10-3/min

31. First Order Reaction:2 H2O2 2 H2O + O2Rate = k[H2O2]; k = 1.05 x 10-3/min

32. First Order Reaction:2 H2O2 2 H2O + O2Rate = k[H2O2]; k = 1.05 x 10-3/min

33. First Order Reaction:2 H2O2 2 H2O + O2Rate = k[H2O2]; k = 1.05 x 10-3/min

34. First Order Reaction:2 H2O2 2 H2O + O2Rate = k[H2O2]; k = 1.05 x 10-3/min

35. Calculations involving Half-Life For a first order reaction: At the half-life, one half is gone, so [R]t = ½ [R]o and

36. Radioactive Decay Radioisotopes decay via first order reactions. Instead of concentrations, amounts are used. Measured as radioactive activity, in counts per minute (cpm) using a detector.

37. Radioactive Decay: Example 1 Radioactive gold-198 is used in the diagnosis of liver problems. The half-life of this isotope is 2.7 days. If you begin with a 5.6-mg sample of the isotope, how much of this sample remains after 1.0 day?

38. Radioactive Decay: Carbon Dating C-14 In living thing Sunlight + Nitrogen Atmospheric C-14 C-14 Dead thing Sunlight + Nitrogen Atmospheric C-14

39. Radioactive Decay: Example 2 The Carbon-14 activity of an artifact in a burial site is found to be 8.6 counts per minute per gram. Living material has an activity of 12.3 counts per minute per gram. How long ago did the artifact die? t1/2 = 5730 years