Why do some reactions happen
and others don’t?
Are the products more stable than the reactants? Thermodynamics
Does the reaction go at a reasonable rate?
Kinetics
Chapter 14: Chemical Kinetics
Rates of Reactions
Control of Reactivity
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
Consider: NO + O3  NO2 + O2
Molecules collide
Bonds are
formed and
break
product molecules
separate
What would control how fast a
reaction happens?
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
We’ll consider dependence on:
1. Concentration
a. Rate laws
b. Concentration vs. time relationships
2. Temperature and activation energy
3. Mechanism
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
Types of measured rates:
• Rate over time:
• Instantaneous rate:
• Initial rate:
 concentration
rate =
 time
Example of rate measurement:
Rate Laws (also called Rate Equations)
first order reaction
For the reaction: 2 N2O5  4 NO + O2
Rate = k[N2O5]
second order reaction
For the reaction: NO2  NO + ½ O2
Rate = k[NO2]2
first order in CO and in NO2; second order overall
For the reaction: CO + NO2  CO2 + NO
Rate = k[CO][NO2]
Determining a Rate Law
Determining the rate law must be done by experiment; the reaction
equation does not tell you the rate law
Two methods: Initial Rates and the Graphical Method
Method of Initial Rates
• Measure the rate of the reaction right at the start.
• Vary the starting concentrations
• Compare initial rates to initial concentrations
Determining a Rate Law: Initial Rate Method
• Isolation of variables: Vary only one concentration at a time and
keep temperature constant
• If concentration doubles and:
– Rate does not change, then zero order
– Rate doubles, then first order
– Rate quadruples, then second order
• General Rule:
Initial Rate Method: Example 1
What is the rate law?
Initial Rate Method: Example 2
Concentration-Time Relationships
[R]t = [R]o e-kt
Example 1
[R]t = [R]o e-kt
Example 2
The decomposition of nitrous oxide at 565 oC,
2 N2O  2 N2 + O2
is second order in N2O. If the reaction is initiated with [N2O] equal to 0.108 M,
and drops to 0.940 M after 1250 s have elapsed, what is the rate constant?
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.
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.
Graphical Method for Determining
Rate Laws
Example: 2 H2O2  2 H2O + O2
Time(min)
0
200
400
600
800
1000
[H2O2](mol/L)
0.0200
0.0160
0.0131
0.0106
0.0086
0.0069
Graphical Method for Determining Rate Laws: Order
Example: 2 H2O2  2 H2O + O2
Time(min)
0
200
400
600
800
1000
[H2O2](mol/L)
0.0200
0.0160
0.0131
0.0106
0.0086
0.0069
Graphical Method for Determining Rate Laws: k
Half-Life: t1/2
the time it takes for half the reactant concentration to drop
to half of its original value
First Order Reaction: 2 H2O2  2 H2O + O2
Rate = k[H2O2]; k = 1.05 x 10-3/min
Cool things about half-life:
Calculations involving Half-Life
For a first order reaction:
 R t
ln
 R o
= -kt
 R t
=  R o e kt
What is the relationship between t1/2 and k?
What is the relationship between t1/2 and k for a second order reaction?
Radioactive Decay
All radioisotopes decay via first order reactions. Instead of
concentrations, amounts are used.
Nt
ln
= -kt
No
N t = N o e kt
Measured as radioactive activity, in counts per minute (cpm) using a detector.
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?
Nt
ln
= -kt
No
N t = N o e kt
Radioactive Decay: Carbon Dating
Sunlight + Nitrogen
C-14
In living thing
Atmospheric C-14
Sunlight + Nitrogen
C-14
Dead thing
Atmospheric C-14
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
Nt
ln
= -kt
No
N t = N o e kt