Unit 3: Chemical Kinetics
 Reaction Rates
 Rate Laws
 Zero Order Reactions
 First Order Reactions
 Second Order Reactions
 Reaction Energy Diagrams
 Arrhenius Equation
Reaction Rates
 Questions to consider:
 What makes “superglue” bond instantly
while Elmer’s glue does not?
 What factors determine how quickly food
spoils?
 Why do “glow sticks” last longer when
stored in the freezer?
 How do catalytic converters remove
various pollutants from car exhaust?
Reaction Rates
 These types of questions can be answered
using chemical kinetics.
 The study of the speed or rate at which
chemical reactions occur
 The rate of a chemical reaction is affected
by many factors, including:
 Physical state of the reactants:
 In order to react, molecules must come in
contact with each other.
 Molecules react faster under homogeneous
conditions.
Reaction Rates
 The rate of a chemical reaction is affected
by many factors, including (cont):
 concentration of reactants
 As concentration of reactants increases
the rate of reaction generally increases
 Greater chance of molecules colliding
 reaction temperature
 As temperature increases, reaction rate
generally increases.
 Molecules have more kinetic energy and
collide more frequently with enough
energy for a reaction to occur.
Reaction Rates
 The rate of a chemical reaction is affected
by many factors (cont):
 presence of a catalyst
 a substance that increases the rate of a
reaction without being consumed in the
reaction
 Enzymes
 biological catalysts
 proteins that increase the rate of
biochemical reactions
Reaction Rates
 The speed of an object or event is the
change that occurs in a given time interval.
 Speed of a car = change in distance
= Dd
Dt
time interval
Remember, “ change” refers to final value minus
initial value.
Reaction Rates
 The speed or rate of a reaction can be defined
in a similar manner.
 Average reaction rate:
 a positive value that describes the change in
either the product or reactant concentration
as a function of time
 Common units:
M/s, M/min, or M/hr
Reaction Rates
 For a general reaction with 1:1 stoichiometry:
A  B
Negative sign needed
to give a positive
value
Avg rate = D [Product] = - D [Reactant]
Dt
Dt
where [ ] is used to indicate the molarity of the
material shown within the square brackets
Reaction Rates
Consider the chemical reaction:
A
Time = 0.
1.0 M A
B
t = 20. min
0.50 M A
[B] = ?
t = 40. min
0.20 M A
[B] = ?
Reaction Rates
For the reaction A  B, the following data can
be used to determine the average reaction rate
for a particular time interval:
Time
(min)
A
(M)
0.0
20.0
40.0
1.00
0.50
0.20
B
(M)
0.0
Rate
(M/min)
Reaction Rates
 Why are the reaction rates different for
each of the time intervals in the previous
example???
Reaction Rates
Example: Given the following data, what is the
average rate of the following reaction over the
time interval from 54.0 min to 215.0 min?
CH3OH (aq) + HCl (aq)  CH3Cl (aq) + H2O (l)
Time (min)
0.0
54.0
107.0
215.0
[HCl] (M)
1.85
1.58
1.36
1.02
Reaction Rates
Example: Calculate the average rate of reaction
during the first 200.0 s of the reaction.
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
Time (s)
[C4H9OH]
0.0
50.0
100.0
150.0
200.0
300.0
0.1000 M
0.0095
0.0180
0.0259
0.0329
0.0451
Reaction Rates
 On the exam, you will be expected to find
the average rate of reaction for a specific
time interval when given the concentration
(or number of moles) of either a reactant or
a product as a function of time.
A Momentary Diversion – A Return to
Chem I
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
Time (s)
[C4H9Cl]
[C4H9OH]
0.0
100.0
200.0
300.0
0.1000 M
0.0820
0.0671
0.0549
0.0000 M
How would you
calculate the
[C4H9OH] for this
reaction at each
time interval?
(Note: This is
NOT a kinetics
question!!)
You should expect a similar question on your exam!!!
Reaction Rates
 So far, all reactions have had a one-to-one
stoichiometry.
 What happens when the coefficients are not
all 1?
2 A  3B
Reaction Rates
Consider the following reaction:
2 HI (g)  H2 (g) + I2 (g)
Time
(min)
mol
HI
mol
H2
mol
I2
0.0
10.0
20.0
30.0
2.00
1.50
1.00
0.75
0.0
0.25
0.50
0.0
0.25
0.50
0.625
0.625
Reaction Rates
Calculate the change in HI and H2 as a function
of time (this is NOT the rate) for the first
20.0 minutes of reaction:
2 HI (g)  H2 (g) + I2 (g)
Time
(min)
mol
HI
0.0
10.0
20.0
30.0
2.00
1.50
1.00
0.75
mol
H2
mol
I2
0.0
0.25
0.50
0.625
0.0
0.25
0.50
0.625
DHI
DH2
Dt
Dt
(mol/min)
Reaction Rates
 The average reaction rate must be numerically
the same, regardless of whether you express it
as the rate of appearance of a product or the
rate of disappearance of a reactant.
 HI disappears twice as fast as H2 appears. To
make the rates equal:
Rate = - 1 D [HI] = D [H2]
2 Dt
D t
Reaction Rates
 In general, for any reaction:
a A + b B  c C + d D
the rate of the reaction can be found by:
Rate = - 1 D[A] = - 1 D[B] = 1 D[C] = 1 D[D]
a Dt
b Dt
c Dt
d Dt
Reaction Rates
 You should be able to use this equation on
your exam to find the relationship between
the rate of change of one reactant or
product and any other reactant or product.
 If you know the rate of change of one
reactant or product, you should be able to
calculate the rate of change of another
reactant of product.
 Simply using molar ratios is actually easier
for this type of problem, however!
Reaction Rates
Example: Write a mathematical expression
(equation) that shows how the rate of
disappearance of N2O5 is related to the rate
of appearance of NO2 in the following
reaction?
2 N2O5 (g)  4 NO2 (g) + O2 (g)
Reaction Rates
Example: If the rate of decomposition of
N2O5 in the previous example at a particular
instant is 4.2 x 10-7M /s, what is the rate of
appearance of NO2?
2 N2O5 (g)  4 NO2 (g) + O2 (g)
Reaction Rates
 Recall that the average reaction rate
changes during the course of the reaction.
 Until now, we have calculated average
reaction rates.
 The reaction rate at a particular time (not
time interval) is called the instantaneous
reaction rate.
Reaction Rate
 The instantaneous reaction rate is found by
determining the slope of a line tangent to the
curve at the particular time of interest.
 Fortunately (for
you), you won’t
have to do this
on the exam or
HW!
Rate Laws
 The average reaction rate decreases with
time.
 The reaction slows down as the
concentration of reactants decreases.
CH3OH (aq) + HCl (aq)  CH3Cl (aq) + H2O (l)
Time (min)
0.0
54.0
107.0
215.0
[HCl] (M)
1.85
1.58
1.36
1.02
Avg. Rate (M /min)
0.0050
0.0042
0.0031
Rate Laws
 In general, the rate of any reaction depends
on the concentration of reactants.
 The way in which the reaction rate varies
with the concentration of the reactants can
be expressed mathematically using a rate
law.
 An equation that shows how the reaction
rate depends on the concentration of the
reactants
Rate Laws
 For a generalized chemical reaction:
w A + x B  y C + z D
the general form of the rate law is:
Rate = k[A]m [B]n
where k = rate constant
m, n = reaction order
Rate Laws
 Rate Constant (k)
 a proportionality constant that relates the
concentration of reactants to the reaction
rate
 Reaction Order
 the power to which the concentration of a
reactant is raised in a rate law
 Overall reaction order
 The sum of all individual reaction orders
Rate Laws
 Rate laws must be determined experimentally.
 Measure the instantaneous reaction rate at
the start of the reaction (i.e. at t = 0) for
various concentrations of reactants.
 You CANNOT determine the value of “m” or
“n” by looking at the coefficients in the
balanced chemical equation for the overall
reaction!
Rate Laws
 First Order Reaction
 Overall reaction order = 1
 Rate = k[A]
Expt
[A] (M)
Rate (M/s)
1
0.50
1.00
2
1.00
2.00
3
2.00
4.00
When [A] doubles,
the rate doubles.
When [A] increases
by a factor of 4
the rate increases
by a factor of 4.
Rate Laws
 Second Order Reaction
 Overall reaction order = 2
 Rate = k[A]2
Expt
[A] (M)
Rate (M/s)
1
0.50
0.50
2
1.00
2.00
3
1.50
4.50
When [A] doubles,
the rate increases
by a factor of 22=4.
When [A] increases
by a factor of 3 the
rate increases by a
factor of 32 = 9.
Rate Laws
 Third Order Reaction
 Overall reaction order = 3
 Rate = k[A]3
Expt
[A] (M)
Rate (M/s)
1
0.50
0.25
2
1.00
2.00
3
1.50
6.75
When [A] doubles,
the rate increases
by a factor of 23=8.
When [A] increases
by a factor of 3 the
rate increases by a
factor of 33 = 27.
Rate Laws
 Zero Order Reaction
 Overall reaction order = 0
 Rate = k[A]0 so Rate = k
Expt
[A] (M)
Rate (M/s)
1
0.50
2.00
2
1.00
2.00
3
1.50
2.00
When [A] doubles, the
rate stays constant.
When [A] increases by
a factor of 3, the rate
stays constant.
Rate Laws
REMEMBER
 Rate laws must be determined experimentally.
 Determine the instantaneous reaction rate at
the start of the reaction (i.e. at t = 0) for
various concentrations of reactants.
 You CANNOT determine the value of “m” or “n”
by looking at the coefficients in the balanced
chemical equation!
Rate Laws
 To determine the rate law from experimental
data,
 identify two experiments in which the
concentration of one reactant has been
changed while the concentration of the
other reactant(s) has been held constant
 determine how the reaction rate changed in
response to the change in the
concentration of that reactant.
Rate Laws
 To determine the rate law from experimental
data (cont)
 Repeat this process using another set of
data in which the concentration of the
first reactant is held constant while the
concentration of the other one is changed.
Rate Laws
Example: The initial reaction rate of the
reaction A + B  C was measured for several
different starting concentration of A and B.
The following results were obtained. Determine
the rate law for the reaction.
Expt #
1
2
3
[A] (M)
0.150
0.150
0.450
[B] (M)
0.100
0.200
0.100
Initial rate (M /s)
4.0 x 10-5
8.0 x 10-5
3.6 x 10-4
Rate Laws