1. Chapter 15: Chemical Kinetics Rates 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 concentration
vs. Time will be linear.
A plot of ln[R]
vs. Time will be linear.
A plot of 1/[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)

24. Graphical Method for Determining Rate Laws
Example: 2 H2O2  2 H2O + O2
Time(min) [H2O2](mol/L)

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 = 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 + O2 Rate = k[H2O2]; k = 1
First Order Reaction: 2 H2O2  2 H2O + O2 Rate = k[H2O2]; k = 1.05 x 10-3/min

31. First Order Reaction: 2 H2O2  2 H2O + O2 Rate = k[H2O2]; k = 1
First Order Reaction: 2 H2O2  2 H2O + O2 Rate = k[H2O2]; k = 1.05 x 10-3/min

32. First Order Reaction: 2 H2O2  2 H2O + O2 Rate = k[H2O2]; k = 1
First Order Reaction: 2 H2O2  2 H2O + O2 Rate = k[H2O2]; k = 1.05 x 10-3/min

33. First Order Reaction: 2 H2O2  2 H2O + O2 Rate = k[H2O2]; k = 1
First Order Reaction: 2 H2O2  2 H2O + O2 Rate = k[H2O2]; k = 1.05 x 10-3/min

34. First Order Reaction: 2 H2O2  2 H2O + O2 Rate = k[H2O2]; k = 1
First Order Reaction: 2 H2O2  2 H2O + O2 Rate = 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
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