Chemical Kinetics
Chapter 13
An automotive catalytic muffler.
15.1. The rate of a reaction is the change in reactant or product concentrations with time
1
Rate of reaction -
13.1 Five factors affect reaction rates
2
A
B
time
D[A]
rate = Dt
D[B]
rate =
Dt
15.1. The rate of a reaction is the change in reactant or product concentrations with time
3
13.1
Factors Affecting Reaction Rate
1. Chemical nature
•
•
Bond strengths
General reactivity
2. Ability to establish contact with
one another
•
•
•
•
Physical state
Surface area for liquids, solids, and
heterogeneous mixtures
Amount of Mixing
Particle shape/size
13.1 Five factors affect reaction rates
4
Factors (Cont.)
3. Concentration of reactants



Molarity for solutions
Pressure effects for gases
Volume effects for gases
4. Temperature
5. Catalysts
13.1 Five factors affect reaction rates
5
Your Turn!
Which of the following would speed a reaction?
A. stirring it
B. dissolving the reactants in water, if ionic
C. adding a catalyst
D. grinding any solids
E. all of these
13.1 Five factors affect reaction rates
6
Measuring Rates
 instantaneous rate (text uses this unless
specified)
 average rate
 initial rate
13.2 Rates of reaction are measured by monitoring change in concentration over time
7
2Br- (aq) + 2H+ (aq) + CO2 (g)
Br2 (aq) + HCOOH (aq)
time
393 nm
light
Detector
393 nm
Br2 (aq)
D[Br2] a DAbsorption
15.1. The rate of a reaction is the change in reactant or product concentrations with time
8
13.1
Fig. 13.5
15.1. The rate of a reaction is the change in reactant or product concentrations with time
9
Br2 (aq) + HCOOH (aq)
2Br- (aq) + 2H+ (aq) + CO2 (g)
slope of
tangent
slope of
tangent
slope of
tangent
[Br2]final – [Br2]initial
D[Br2]
average rate = =Dt
tfinal - tinitial
instantaneous
rate = rate for specific instance in time
15.1. The rate of a reaction is the change in reactant or product concentrations with time
10 13.1
15.1. The rate of a reaction is the change in reactant or product concentrations with time
11
Fig. 13.6
15.1. The rate of a reaction is the change in reactant or product concentrations with time
12
rate a [Br2]
rate = k [Br2] = rate law
rate
= rate constant
k=
[Br2]
= 3.50 x 10-3 s-1
15.1. The rate of a reaction is the change in reactant or product concentrations with time
13 13.1
Your Turn!
Concentration
of B (M)
What is the average rate
of B between 10 and
40 s?
A. -0.006 M/s
B. +0.006 M/s
C. -0.002 M/s
D. +0.002 M/s
E. can’t tell form the
information
0.4
0.3
0.2
0.1
0.0
10
20
30
40
Time Elapsed in Reaction Progress
(s)
13.2 Rates of reaction are measured by monitoring change in concentration over time
14
Rates And Stoichiometry
• Rates based on each substance are related to one
another by the stoichiometric coefficients of the
reaction
• Examine the reaction: aA + bB →dD
 the stoichiometric relationship between substances A and
B is given as a mole A: b mole B
 RateA×(b/a)=RateB
mol A b mol B
mol B


Ls
a mol A
Ls
13.2 Rates of reaction are measured by monitoring change in concentration over time
15
Consider the combustion of propane:
C 3 H 8 ( g )  5O 2 ( g )  3CO 2 ( g )  4 H 2 O ( g )
• Compared to the rate with respect to propane:
 Rate with respect to oxygen is five times faster
 Rate with respect to carbon dioxide is three times faster
 Rate with respect to water is four times faster
• Since the rates are all related any may be monitored to determine the
reaction rate
15.1. The rate of a reaction is the change in reactant or product concentrations with time
16
Learning Check
• In the reaction: 2A + 3B →5D We measured the
rate of disappearance of substance A to be
3.5×10-5M/s. What is the rate of appearance of
D?
• In the reaction 3A + 2B →C, we measured the
rate of B. How does the rate of C relate?
8.75×10-5 M/s
RC=1/2 RB
13.2 Rates of reaction are measured by monitoring change in concentration over time
17
3A + 2B + C  Products
Rate = k [A]2[B][C]3
The exponents in the rate law are generally unrelated to the
chemical equation’s coefficients
 Never simply assume the exponents and coefficients are the same
 The exponents must be determined from the results of experiments
The exponent in a rate law is called the order of reaction with
respect to the corresponding reactant
15.1. The rate of a reaction is the change in reactant or product concentrations with time
18
Your Turn!
In the reaction 2CO(g) + O2(g) →2CO2(g), the rate of
the reaction of CO is measured to be 2.0 M/s.
What would be the rate of the reaction of O2?
A. the same
B. twice as great
C. half as large
D. you cannot tell from the given information
13.2 Rates of reaction are measured by monitoring change in concentration over time
19
Learning Check
The rate law for the reaction 2A +B→3C is
rate= 0.045M-1s-1 [A][B]
if the concentration of A is 0.2M and that of B is
0.3M, what will be the reaction rate?
rate=0.045 M-1 s-1 [0.2][0.3]
rate=0.0027 M/s
13.3 Rate laws give reaction rate as a function of reactant concentrations
20
Table 13.2 from Page 529
A  B  products
rate  k [ A ] [ B ]
m
n
Inital Conc.
[ A]
Expt
[B]
-1
Initial Rate
-1
-1
-1
(mol L ) (mol L ) (mol L s )
1
0.10
0.10
0.20
2
0.20
0.10
0.40
3
0.30
0.10
0.60
4
0.30
0.20
2.40
5
0.30
0.30
5.40
Determine the rate law
15.1. The rate of a reaction is the change in reactant or product concentrations with time
21
The initial rate for the reaction of nitrogen monoxide and oxygen was measured
at 25 ºC for various concentrations shown in the table below. Determine the
rate equation for the reaction, the value of the rate constant with proper units,
and the initial rate if [NO]=[O2]=0.010 M
Exp#
1
2
3
4
5
[NO]
mol/L
0.020
0.020
0.020
0.040
0.010
[O2]
mol/L
0.010
0.020
0.040
0.020
0.020
initial rate
mol/Ls
0.028
0.057
0.114
0.227
0.014
15.1. The rate of a reaction is the change in reactant or product concentrations with time
22
Concentration rate data for reaction A + B + C  Products
Initial Conc.mol/L
Initial Rate mol/Ls
[A]
[B]
[C]
Rate
0.10
0.10
0.10
0.20
0.20
0.10
0.10
0.40
0.30
0.10
0.30
0.60
0.30
0.20
0.30
2.40
0.30
0.30
0.60
5.40
Determine the rate law for this reaction
Determine the rate constant for the reaction
Determine the overall reaction order for the reaction
Determine the rate of reaction when [A]=[B]=0.50 mol/L
15.1. The rate of a reaction is the change in reactant or product concentrations with time
23
A certain reaction follows the equation 2A + B  3C + D.
Experimental results yielded the following data. Determine the rate
law, reaction order for A and B, the overall reaction order, the
value for the rate constant k, and the rate of reaction when [A] =
[B] = 1.0 mol/L
Concentration rate data for reaction A + B  C + D
Initial Concentration mol/L
[A]
[B]
Rate
0.40 0.30
1.0e-4
0.80 0.30
4.0e-4
0.80 0.60
1.6e-3
15.1. The rate of a reaction is the change in reactant or product concentrations with time
24
Your Turn!
For the following data, determine the order of NO2 in the
reaction at 25° 2 NO2(g) + F2(g)→ 2 NO2F(g):
Exp. [NO2] [F2]
Rate NO2 disappearance (M/s)
0.005 2 (10-4)
1
0.001
2
3
0.002 0.005 4 (10-4)
0.006 0.002 4.8 (10-4)
A.
B.
C.
D.
E.
0
1
2
3
not enough information given
13.3 Rate laws give reaction rate as a function of reactant concentrations
25
Your Turn!
Chlorine Dioxide, ClO2, is a reddish-yellow gas that
is soluble in water. In basic solution it gives ClO3and ClO2- ions. 2ClO2(aq) + 2OH-(aq)→ 6ClO3- (aq)
+ ClO2- (aq) + H2O(l)
The rate law is Rate=k[ClO2]2[OH-], what is the value
of the rate constant given that when
[ClO2]=0.060M, [OH-] = 0.030, the reaction rate
is 0.0248 M/s
A. 0.02 M-1 /s
B. 0.02 M/s
C. 0.02 sD. None of these
2.3(102) M-2 s-1
13.3 Rate laws give reaction rate as a function of reactant concentrations
26
Zero-Order Reactions
• Rate=k [A]0 = k
• Plot of [reactant ] vs. time will be linear
• The equation of the line will be
[A]=[A0]-kt
 A= amount remaining after elapsed time, t.
 Ao=original amount
•
•
Diffusion controlled - usually are fast reactions in viscous media
Rate is independent of concentrations of reactants, but the reaction still
requires reactants
13.4 Integrated rate laws give concentration as a function of time
27
Learning Check
The rate law for the reaction of A→B is zero order
in A and has a rate constant of 0.02 M/s. If the
reaction starts with 1.50 M A, how much is
present 15 seconds after the reaction begins?
•[A]=[A0]-kt
•[A]=1.2M
13.4 Integrated rate laws give concentration as a function of time
28
Learning Check
The rate law for the reaction of A→2B is zero order
in A and has a rate constant of 0.12 M/s. If the
reaction starts with 1.50 M A, after what time
will the concentration of A be 0.90M?
•[A]=[A0]-kt
•t=5 s
13.4 Integrated rate laws give concentration as a function of time
29
Your Turn!
Which of the following is the correct set of units for
the rate constant for a zero order reaction?
A.
B.
C.
D.
M/s
M-1/s
M-2/s
Can’t tell from the given data
13.4 Integrated rate laws give concentration as a function of time
30
First Order Reactions:
• Rate=k[A]1
• Typically these reactions are decomposition type,
or radioactive decay
• If the rate law is specified as d[A]/dt=k[A] or
Integrating the equation gives us:
ln(
A
)   kt
A0
13.4 Integrated rate laws give concentration as a function of time
31
Learning Check
The radioactive decay
of a new atom occurs
so that after 21 days,
the original amount is
reduced to 33%.
What is the rate
constant for the
reaction in s-?
k = 6.11×10-7 s-1
13.4 Integrated rate laws give concentration as a function of time
32
Consider the first order decomposition reaction
N2O5  N2O4 + O2
For which rate = k[N2O5]. At 45C the rate constant
is 6.22e-4 s-1.
If the initial concentration of dinitrogen pentoxide is
0.100 M, how long will it take for the
concentration to drop to 0.0100 M?
15.1. The rate of a reaction is the change in reactant or product concentrations with time
33
i-Clicker Classroom Participation
15.1. The rate of a reaction is the change in reactant or product concentrations with time
34
i-Clicker Classroom Participation
15.1. The rate of a reaction is the change in reactant or product concentrations with time
35
Consider the first order decomposition reaction
N2O5  N2O4 + O2 for which rate = k[N2O5]. At 45C
the rate constant is 6.22e-4 s-1.
If at 100C the concentration falls from 0.800 to
0.100 M in 45.0 minutes, what is the rate constant at
100C?
15.1. The rate of a reaction is the change in reactant or product concentrations with time
36
Fig. 13.12
15.1. The rate of a reaction is the change in reactant or product concentrations with time
37
Derive the equation for half-life
ln(
A
)   kt
Ao
t 1 is time when A 
2
0.693
k
1
2
Ao
 t1 / 2
13.4 Integrated rate laws give concentration as a function of time
38
Learning Check
The half-life of I-132 is 2.295h. What percentage
remains after 24 hours?
ln( 2)
k
 t1
ln(
2
Ao
)  kt
A
0.302 h-1 = k
A = .0711 %
13.4 Integrated rate laws give concentration as a function of time
39
Your Turn!
What is the half-life of a new element,
Barclium-146, if, after 2.2 h, 1.3% remains?
A. 2.0 h
B. 0.35 h
C. 0.51 h
D. None of these
13.4 Integrated rate laws give concentration as a function of time
40
i-Clicker Classroom Participation
15.1. The rate of a reaction is the change in reactant or product concentrations with time
41
Hydrogen peroxide decomposes in dilute sodium
hydroxide at 20 ºC in a first-order reaction where the rate
constant is 1.06e-3 min-1
2 H2O2 (aq)  2 H2O (l ) + O2 (g)
If the initial concentration of H2O2 is 0.202 mol/L what is
the concentration after exactly 100 minutes?
What fraction of the original hydrogen peroxide is
remaining after 100 minutes?
What is the rate of reaction after 100 minutes?
What is the half-life of this reaction at 20 ºC
15.1. The rate of a reaction is the change in reactant or product concentrations with time
42
Second Order Reaction
2
• Are of several types: Rate=k[A] ,
Rate=k[A]1[B]1 and Rate=k[A]2[B]0, etc…
1
[A]

1
 kt
[A 0 ]
13.4 Integrated rate laws give concentration as a function of time
43
Learning Check
The rate constant for the
second order reaction
2A→B is 5.3×10-5 M1s-1. What is the
original amount
present if, after 2
hours, there is 0.35M
available?
A0=0.40 M
13.4 Integrated rate laws give concentration as a function of time
44
Second Order Half-Life
• Depends on the amount present at the start of the
time period
• What is the relationship between k and t1/2 for this
reaction type?
1
k [A0 ]
 t1/2
13.4 Integrated rate laws give concentration as a function of time
45
Learning Check
The rate constant for
a second order
reaction is 4.5×10-4
M-1s-1. What is the
half-life if we start
with a reactant
concentration of
5.0 M?
t1/2 =440 s
=7.4 min
1
k [A0 ]
13.4 Integrated rate laws give concentration as a function of time
 t1/2
46
i-Clicker Classroom Participation
15.1. The rate of a reaction is the change in reactant or product concentrations with time
47
The gas-phase decomposition of hydrogen
iodide is second order with a rate constant of
30. L/mol min at 443 ºC. How much time
does it take for the concentration to fall from
0.010 mol/L to 0.0050 mol/L at this
temperature?
What will be the HI concentration after just
12 minutes?
HI (g)  1/2 H2 (g) + 1/2 I2 (g)
15.1. The rate of a reaction is the change in reactant or product concentrations with time
48
a) If k=0.020 L/mol s for the second order reaction
NOCl  NO + Cl2 what will the concentration be
after 30 minutes if the initial concentration is
0.0500 M
b) How long will it take for the concentration of
NOCl to fall from 0.0500 to 0.001 M at the same
temperature?
15.1. The rate of a reaction is the change in reactant or product concentrations with time
49
Your Turn!
Which order has a half-life that is independent of the
original amount?
A. Zero
B. First
C. Second
D. None depend on the original quantity
13.4 Integrated rate laws give concentration as a function of time
50
Your Turn!
A 0.10M solution of moxium, a new antidepressant
is bottled. The drug decays to fortium, a toxic
chemical as a second order process. The rate
constant is 2.3×10-3 M-1h-1. What quantity of
moxium is present after 90. days?
A. 0.098M
B. 5.5(10-5)M
C. 0.067M
D. None of the above
13.4 Integrated rate laws give concentration as a function of time
51
Graphical methods can be used to determine the
first-order rate constant, note
ln
[ A ]0
 kt
[ A ]t
ln[ A ] 0  ln[ A ] t  kt
ln[ A ] t  ln[ A ] 0   kt
ln[ A ] t   kt  ln[ A ] 0



y
 mx
 b
15.1. The rate of a reaction is the change in reactant or product concentrations with time
52
A plot of ln[A]t versus t gives a straight line with a slope of -k
The decomposition of N2O5. (a) A graph of concentration versus time for the
decomposition at 45oC. (b) A straight line is obtained from a logarithm versus time
plot. The slope is negative the rate constant.
15.1. The rate of a reaction is the change in reactant or product concentrations with time
53
Learning Check
Determine the order of the reactant graphically
2N2O5(g)  4 NO 2(g) + O2(g)
Time (s)
0
100
200
300
400
500
600
[N2 O5 ]
0.02
0.0169
0.0142
0.012
0.0101
0.0086
0.0072
[NO2 ]
0
0.0063
0.0115
0.016
0.0197
0.0229
0.0256
0 order plot
[O2 ]
1st order plot
2nd order plot
0
0.0016
0.0029
0.004
0.0049
0.0057
0.0064
13.4 Integrated rate laws give concentration as a function of time
54
Graphical methods can also be applied to second-order reactions
A plot of 1/[B]t versus t gives a straight line with a slope of k
Second-order
kinetics. A plot
of 1/[HI]
versus time
(using the data
in Table 15.1).
15.1. The rate of a reaction is the change in reactant or product concentrations with time
55
Collision Theory Of Reactions
For a reaction to occur, three conditions must be met:
1. Reactant particles must collide
2. Collision energy must be enough to break bonds/initiate
3. Particles must be oriented so that the new bonds can form
13.5 Reaction rate theories explain experimental rate laws in terms of molecular
collisions
56
Potential Energy Diagrams
• Demonstrate the energy needs and products as a
reaction proceeds
• Tell us whether a reaction is exothermic or
endothermic
• Tell us if a reaction occurs in one step or several
steps
• Show us which step is the slowest
13.5 Reaction rate theories explain experimental rate laws in terms of molecular
collisions
57
Potential Energy Diagrams
What about the reverse reaction?
13.5 Reaction rate theories explain experimental rate laws in terms of molecular
collisions
58
i-Clicker Classroom Participation
Where does Ea come from?
15.1. The rate of a reaction is the change in reactant or product concentrations with time
59
15.1. The rate of a reaction is the change in reactant or product concentrations with time
60
Features of PE Diagrams
Connect to the graph:
Activation Energies
Activated
Complexes
Product
Energy
P.E.
Enthalpy of
reaction
Reactant Energy
Reaction Coordinate
(progress of reaction)
13.5 Reaction rate theories explain experimental rate laws in terms of molecular
collisions
61
Your Turn!
Examine the Potential energy diagram. Which is the
Slowest (Rate Determining) Step?
A. Step 1
B. Step 2
C. Can’t tell from the given information
Potential Energy
Reaction Progress
13.5 Reaction rate theories explain experimental rate laws in terms of molecular
collisions
63
Fig. 13.13
15.1. The rate of a reaction is the change in reactant or product concentrations with time
64
Fig. 13.16
15.1. The rate of a reaction is the change in reactant or product concentrations with time
65
Temperature Effects
Changes in temperature affect the rate constant, k,
according to the Arrhenius equation:






p is the steric factor
Z is the frequency of collisions.
Ea is the activation energy
R is the Ideal Gas Constant (8.314 J/mol K)
T is the temperature (K)
A is the frequency factor
k  pZe
 E a /RT
k  Ae
 E a /RT
13.6 Activation energies are measured by fitting experimental data to the Arrhenius
equation
66
Working With The Arrhenius Equation
Linear Form: To determine the Ea and A value
ln k  ln A 
Ea
RT
Ratio form: Can be used when A isn’t known.
 Ea  1
1 
ln(
)



k1
R T 2 T1
k2
13.6 Activation energies are measured by fitting experimental data to the Arrhenius
equation
67
Learning Check
Given that k at 25°C is 4.61×10-1 M/s and that at
50°C it is 4.64×10-1 M/s, what is the activation
energy for the reaction?
 Ea  1
1
ln( ) 
 

k1
R  T 2 T1
k2
208 J/mol=Ea
13.6 Activation energies are measured by fitting experimental data to the Arrhenius
equation
68
Working With The Arrhenius Equation
Given the following
data, predict k at 75°C
using the graphical
approach
graph
T °C
k (M/s)
0.000886
25
0.000894
50
0.000918
150
0.000908
100
Ea 1
ln k  
  lnA
R T
ln (k) = -0.0278/T-0.1917
k=8.25×10-1
13.6 Activation energies are measured by fitting experimental data to the Arrhenius
equation
69
The reaction CH3I + HI  CH4 + I2 was observed to
have rate constants
k= 3.2 L/(mol s) at 350C and
k=23 L/(mol s) at 400C.
What is the value of Eafor this reaction expressed in
kJ/mol?
What would the rate constant be at 300C?
k  Ae

EA
RT
 k2   E A

ln 

k
R
 1 
 1
1 


T  T 
1 
 2
15.1. The rate of a reaction is the change in reactant or product concentrations with time
70
Your Turn!
In the reaction 2N2O5(g) 4 NO2(g) + O2(g) the
following temperature and rate constant
information is obtained. What is the activation
energy of the reaction?
A. 99.7 kJ
T (K)
k (s-1)
4.87(10-3)
338
B. -99.7 kJ
1.50(10-3)
328
C. 1004 kJ
4.98(10-4)
318
D. -1004 kJ
E. none of these
13.6 Activation energies are measured by fitting experimental data to the Arrhenius
equation
71
The first order reaction 2NO2  2 NO + O2 has an
activation energy of 111 kJ/mol. At 400C, k = 7.8
L/mol s
1. What is the value of k at 430C?
2. If the [NO2] is 1.5e-2M, what is the rate of
reaction at 430 C?
k  Ae

EA
RT
 k2   E A

ln 

R
 k1 
 1
1 



T

 2 T1 
15.1. The rate of a reaction is the change in reactant or product concentrations with time
72
i-Clicker Classroom Participation
15.1. The rate of a reaction is the change in reactant or product concentrations with time
73
Reaction Mechanisms
• The rate determining step is the slowest step of
the reaction that accounts for most of the
reaction time
• Elementary steps sum to the overall reaction
• Catalysts interact with the reactant, they will
appear in the mechanism
• Intermediates are temporary products, formed in
an early step and consumed in a later step
13.7 Experimental rate laws can be used to support or reject proposed mechanisms for a
reaction
74
Learning Check
The reaction mechanism that has been proposed for
the decomposition of H2O2 is
1.
2.
•
•
H2O2 + I- → H2O + IO- (slow)
H2O2 + IO- → H2O + O2 + I- (fast)
Which is the rate determining step?
Are there any intermediates?
13.7 Experimental rate laws can be used to support or reject proposed mechanisms for a
reaction
75
Learning Check
The reaction mechanism that has been proposed for
the decomposition of H2O2 is
1.
2.
H2O2 + I- → H2O + IO- (slow)
H2O2 + IO- → H2O + O2 + I- (fast)
What is the expected rate law?
13.7 Experimental rate laws can be used to support or reject proposed mechanisms for a
reaction
76
Learning Check
The reaction: A + 3 B → D + F was studied
and the following mechanism was finally
determined
1.
2.
3.
A + B→C
(fast)
C + B → D + E
(slow)
E + B→F
(very fast)
What is the expected rate law?
13.7 Experimental rate laws can be used to support or reject proposed mechanisms for a
reaction
77
Catalysts
• Speed a reaction, but are not
consumed by the reaction
• May appear in the rate law
• Lower the Ea for the reaction.
• May be heterogeneous or
homogeneous
13.8 Catalysts change reaction rates by providing alternative paths between reactants and
products
78
CATALYSIS
Catalysis and activation energy
MnO2 catalyzes
decomposition of H2O2
2 H2O2 ---> 2 H2O + O2
Uncatalyzed reaction
Catalyzed reaction
15.1. The rate of a reaction is the change in reactant or product concentrations with time
79
Catalytic Actions
• May serve to weaken bonds through induction
• May serve to change polarity through
amphipathic/surfactant effects
• May reduce geometric orientation effects
• Heterogeneous catalyst: reactant and product
exist in different states.
• Homogeneous catalyst: reactants and catalyst
exist in the same physical state
13.8 Catalysts change reaction rates by providing alternative paths between reactants and
products
81
Heterogeneous catalysts
13.8 Catalysts change reaction rates by providing alternative paths between reactants and
products
82
i-Clicker Classroom Participation
15.1. The rate of a reaction is the change in reactant or product concentrations with time
83
i-Clicker Classroom Participation
15.1. The rate of a reaction is the change in reactant or product concentrations with time
84
For the reaction
C2H6(g)  2CH3(g)
rate = k[C2H6]
If k = 5.50 E–4 s–1 and [C2H6]initial = 0.0200 M, calculate
the rate of reaction after 30 min.
15.1. The rate of a reaction is the change in reactant or product concentrations with time
85