CHM 1046: General Chemistry and
Qualitative Analysis
Unit 15
Chemical Kinetics
Dr. Jorge L. Alonso
Miami-Dade College –
Kendall Campus
Miami, FL
Textbook Reference:
•Chapter # 16
Chemical
•Module # 4
Kinetics
Thermodynamics vs Kinetics
{Kinetics: paper, Fe, C}
Rusting of Iron:
2Fe (s) + O2 (g) + 2H2O (l) → 2Fe(OH)2 (s)
(with limited O2, magnetite Fe3O4 is formed: FeO·Fe2O3)
Horxn = -884.6 kJ
{Thermite.Rxn}
Thermite Reaction:
Fe2O3 (s) + 2 Al (s)
Mg ignition
Al2O3 (s) + 2 Fe (l)
Horxn = -847.6 kJ
Chemical
Kinetics
{FSH1}
{FSH2}
Kinetics
• Studies the rate (speed) at which a chemical
process occurs.
• Kinetics also sheds light on the reaction
mechanism (exactly how the reaction occurs).
Factors That Affect Reaction Rates:
•
•
•
•
Physical State of the Reactants
Concentration of Reactants
Temperature
Presence of a Catalyst
Chemical
Kinetics
Factors That Affect
Reaction Rates
Which will react faster?
1. Physical State of the
Reactants (surface area)
 In order to react, molecules must
come in contact with each other:
•
•
Gases, liquids or solutions react
faster than solids. (Higher pressure
and concentration also affects rate.)
Finely ground substances have
more surface areas and react faster
than chunk pieces.
(1) Gases, Liquids,
Solutions (High P & Conc.)
{RxRate.LicopodiumPowder}
 The more homogeneous the
mixture of reactants, the faster the
molecules can react.
Chemical
Kinetics
(2) Solids
Factors That Affect Reaction Rates
2. Concentration of Reactants
 As the concentration of
reactants increases, so does
the likelihood that reactant
molecules will collide.
{*Rxn.withConcOxy}
0.3 M
6M
Chemical
{*RxRate&Conc.Mg+HCl}
Kinetics
{RxRate&Conc.Mg+HClGraph}
Reaction
Rates
determined by monitoring
the change in
concentration of either
reactants or products as
a function of time.
A
B
[A]
[A]& [B]
Rate =
-[A]
=
t
[B]
[B]
t
{RxRateIntro}
Chemical
Kinetics
Spectrometer
Reaction Rates
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
butanol
butyl chloride
t
-[A]
t
-[A]
Rate =
-[A]
t
= [B]
t
Chemical
Kinetics
Reaction Rates
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
The average rate of the reaction over each interval
is the change in concentration divided by the
-[C4H9Cl]
change in time:
Ave. rate =
t
• Note that the average
rate decreases as the
reaction proceeds.
• This is because as the
reaction goes forward,
there are fewer collisions
between reactant
molecules.
Chemical
Kinetics
Reaction Rates
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
• All reactions slow down
over time.
• Therefore, the best
indicator of the rate of
a reaction is the
instantaneous rate
near the beginning.
• The slope of a line
tangent to the curve at
any point is the
instantaneous rate at
that time.
Concentration vs. Time Graph
Chemical
Kinetics
Reaction Rates and Stoichiometry
C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq)
• In this reaction, the ratio of
C4H9Cl to C4H9OH is 1:1
• Thus, the rate of
disappearance of C4H9Cl is
the same as the rate of
appearance of C4H9OH.
Rate =
-[C4H9Cl]
=
t
[C4H9OH]
t
Chemical
Kinetics
Reaction Rates and Stoichiometry
• What if the ratio is not 1:1?
2 HI(g)  H2(g) + I2(g)
How do rates
Rate1 = − [HI] ≠ Rate2 = [I2]
compare?
t
t
Rate = − 1 [HI] = [I2]
Rate = − [HI] = 2 [I2]
2 t
t
t
t
• To generalize, then, for the reaction
aA+bB
Rate  -
1  A 
a
t
-
1  B 
b t
cC+dD

1  C 
c t

1  D 
d
t
Chemical
Kinetics
Practice
Problems
Rate  -
1   NO 2 
a
t

Rate  -
1  O 2 
b
Rate 
t
1  A 
3 t

1  0 . 0035   O 2 
-5
 1 . 8 x 10


2  100 s 
t
1  B 
2 t
Chemical
Kinetics
ave .rate 
 A 
t

. 022
 2 . 2 x 10 mol / sec
-3
10 s
( 0 . 124 - 0 . 073 )  0 . 051
Chemical
Kinetics
How does Concentration affect Rate?
NH4+(aq) + NO2−(aq)
N2(g) + 2 H2O(l)
• The data demonstrates:
Rate  [NH4+]
Data shows the relationship between the
reaction rate and the conc. of reactants.
Rate  [NO2−]
Rate  [NH4+] [NO2−]
or
Chemical
This equation is the rate law, andKinetics
k is
Rate = k [NH4+] [NO2−]
the rate constant @ particular temp.
Generalized Rate Laws
-
1  A 
a
t
aA+bB
1  B 
1  C 
-
b t

c t
cC

x
Rate = k [A] [B]
y
• The exponents, x and y, express the order of reaction and bear no
necessary relationship to the coefficients of the balanced equation* – they
must be determined experimentally!
• This reaction is: x - order in [A]
y - order in [B]
Overall rate = x + y
• The overall reaction order can be found by adding the exponents on the
reactants in the rate law.
The previous reaction is second-order overall.
* Only if reaction occurs in one step mechanism will x and y equal
coefficients of balanced equation.
Chemical
Kinetics
Determination of Rate Law from
Reaction Rate Data
What are the possible
values for x and y?
x
y
Rate = k [A] [B]
*
Possibilities for x and y:
Zero order = no effect
1st order = linear effect
2nd order = exponential
If rate not affected by [A], then order with respect to [A] is x = 0
[2A]  rate= k, [3A]  rate= k
etc…. the same applies to [B]
If the rate affected by [A] in linear fashion, then order [A] is x = 1,
[2A]1  rate= 2x, [3A]1  rate= 3x,etc…. the same applies to [B]
If rate affected by [A] in exponential fashion, order [A] is x = 2,
[2A]2  rate =4x, [3A]2  rate =9x,
etc…. the same applies to [B]
Experiment
Number
[A] (M)
[B] (M)
Initial Rate
(M/s)
1
0.100
0.100
4.0 x 10-5
2
0.100
0.200
4.0 x 10-5
3
0.200
0.100
16.0 x 10-5
Rate = k [A]2 [B]0 = kChemical
[A]2
Kinetics
Integrated Rate Laws
Products
For reaction: a A
Rate =
-[A]
t
= k [A]
x
Reaction rate can be defined in two mathematical ways: (1) empirically, as
change in conc. over time, or (2) as a function of concentration (rate law).
Using calculus we can integrate the rate law equation to gives us a
mathematical relationship that shows us how the concentration varies over a
period of time. Rate expressions are then rearranged into linear equations.
For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)
-[A]
-[A]
-[A]
0
1
= k [A] = k
= k [A]
= k [A]2
t
t
t
Integrate
Integrate
Integrate


1
1
Chemical

ln [A]t = − kt + ln [A]0 [A]t = kt +
Kinetics
[A]t = − kt + [A]0
[A]0
y
= mx + b
y
= mx + b
y
= mx +
b
Integrated Rate Laws
For zero order rxn (x=0) For first order rxn (x=1) For second order rxn (x=2)
-[A]
-[A]
-[A]
0
1
= k [A] = k
= k [A]
= k [A]2
t
t
t
Integrate
Integrate
Integrate
1
1
ln [A]t = − kt + ln [A]0 [A]t = kt +
[A]t = − kt + [A]0
[A]0
y
= mx + b
[A]
[A]
ln[A]
[A]
ln[A]
1
[A]
Chemical
Kinetics
How many moles of X were initially in the
flask?
X(g)  2 Y(g) + Z (g)
1
[X ]
 [X ]
-1
How many molecules of Y were produced in
the first 20 minutes of the reaction?
What is the order of this reaction with respect
to X? Justify your answer.
Write the rate law for this reaction.
Chemical
Kinetics
X(g)  2 Y(g) + Z (g)
Calculate the specific rate constant for this
reaction. Specify units.
ln [A]t = − kt + ln [A]0
Calculate the concentration of X in the flask
after a total of 150 minutes of
reaction.
Chemical
Kinetics
Practice Problems
1
[ A ]t
 kt 
1
1
[ A ]0
[ A ]t
-
1
[ A ]0
 kt
1
[ 0 . 0065 ] t
-
1
[ 0 . 0100 ] 0
 k (100 s )
154 - 100
k
100
Chemical
Kinetics
Half-Life
•
{1stOrder&½Life} *
Half-life is defined as the time required for one-half of a reactant to react.
For a zero-order
process,
[A]0
t1/2 =
[A]½
[A]0 
2k
For a first-order
process,
t1/2
0.693

=
k
For a secondorder process,
•
Because [A] at t1/2 is one-half of the original [A],
[A]t = 0.5 [A]0.
t1/2
1 
= k[A]
0
Chemical
Kinetics
Half-Life
For a first-order process,
For a second-order process,
1
[A]t
ln [A]t = − kt + ln [A]0
ln 0.5[A]0 = − kt1/2 + ln [A]0
ln
0.5 [A]0
[A]0
= kt +
1
0.5 [A]0
= −kt1/2
2
[A]0
ln 0.5 = −kt1/2
1
[A]0
= kt1/2 +
1
[A]0
= kt1/2 +
1
[A]0
−0.693 = −kt1/2
0.693
= t1/2
k
NOTE: For a first-order
process, the half-life does not
depend on [A]0.
2
[A]0
-
1
[A]0
= kt1/2
1
k[A]0 = t1/2
Chemical
Kinetics
0 . 600
Practice
Problems
 0 . 300
2
0 . 300
0.150
 0 . 150
2
54 min
2
 18 min
k  0 . 0385
3
ln [A]t = − kt + ln [A]0
 0 . 075
0.693
= t1/2
k
ln 0.5[A]0 = − kt½ + ln [A]0
For each of the following rate expression, determine the units of the rate constant, k.
-[A]
= k [A]
t
= k [M]
t
M
s
 M s
1
= k [A]
t
-[M]
k 
-[A]
0
-1
0
-[M]
t
k 
= k [M]
1
s
 s
-[A]
= k [A]2
t
1
-[M]
t
= k [M]2
-1
k
1
Ms
Chemical
-1 -1
 Kinetics
M s
Kinetics
Factors That Affect Reaction Rates:
1. Physical State of the Reactants
2. Concentration of Reactants
Rate
(s)  (l ) (g)
Rate =
-[A]
t
= k [A]x
3. Temperature
•
Activation Energy (Transition State Theory)
•
Reaction Mechanisms
4. Presence of a Catalyst
Chemical
Kinetics
Factors That Affect Reaction Rates
3. Temperature
At higher temperatures,
reactant molecules have more
kinetic energy, move faster,
and collide more often and
with greater energy.
ln [A]t = − kt + ln [A]0
• Generally, as temperature
increases, so does the reaction
rate.
• This is because k is temperature
dependent.
• k is also dependent on activation
energy.
{RxRate&Temp}
Chemical
Kinetics
Activation Energy:
The Collision Model
• In a chemical reaction, bonds are broken and new bonds are formed.
• Molecules can only react if they collide with each other with sufficient
(activation) energy (Ea).
O3
+ NO
O2
Reactants
+
Activated Complex
(
+
NO2
Products
)
Furthermore, molecules must collide with the
correct orientation and with enough energy to
cause bond breakage and formation.
+
{Ea.CollisionEnergy}
{Ea.Orientation}
Chemical
Kinetics
{Ea.Ener+Orient}
Transition State Theory
Reactants
Activated Complex
(
+
Products
)
Energy Reaction Coordinate Diagrams:
*
+
- H
Transition state
(Energy Level))
X3-YZ Activated Complex (the molecule)
Ea = Activation Energy
Potential
Energy
Reactants
- H
Products
Reaction Coordinate
Chemical
Kinetics
{Ea&TransS tate}
Maxwell–Boltzmann Distributions
• Temperature is defined as a measure of the average kinetic energy of the
molecules in a sample.
• At any temperature there is a
wide distribution of kinetic
energies.
• As the temperature
increases, the curve flattens
and broadens.
• Thus at higher
temperatures, a larger
population of molecules has
higher energy.
• If the dotted line represents the activation energy, as the temperature
increases, so does the fraction of molecules that can overcome the
Chemical
activation energy barrier.
• As a result, the reaction rate increases.
Kinetics
Maxwell–Boltzmann Distributions
This fraction of molecules can be found through the
expression
where R is the gas constant and T is the Kelvin temperature.
f = e−Ea/RT
Chemical
Kinetics
Arrhenius Equation
Svante Arrhenius developed a
mathematical relationship between
the rate constant k , the
temperature (T) at which the
reaction occurs and the activation
energy Ea:
k = A e−Ea/RT
where A is the frequency factor, a
number that represents the likelihood
that collisions would occur with the
proper orientation for reaction.
ln
k2
k1
Ea  1
1 



R  T1 T 2 
Chemical
Kinetics
k=Ae
−Ea/RT
Arrhenius
Equation
Taking the natural logarithm of both sides, the equation becomes
ln k = -Ea
R
y
=
(
m x
1
T
) + ln A 
+ b
Therefore, if k is determined
experimentally at several temperatures, Ea
can be calculated from the slope of a plot
of ln k vs. 1/T.
Problem: Calculate the activation energy (in J/mol) for the reaction in plot above.
R= 8.31 J/mol·K
E 
slope  -  a 
 R 
E a  - slope x R
 ( - 10 . 4 ) - ( - 6 . 7 ) 
E a  -
 x ( 8 . 31 J / mol  K )
0
.
00215
0
.
00195


- 3 .7


4
E a  -
x
(
8
.
31
J
/
mol

K
)

1
.
8
x
10
J / mol

-1
 0 . 0002 K 
Chemical
Kinetics
Reaction Mechanisms
The detailed sequence of events that describes the actual
pathway by which reactants become products.
OH- (aq) + CH3Cl (g)

CH3OH (aq) + Cl- (aq)
Methyl alcohol
Methyl chloride
Transition State
Reactants
Activated Complex
Products
Chemical
Kinetics
{RxMecha.Bimolecular.Intro}
Reaction Mechanisms
*
Consider the following reaction:
NO2 (g) + CO (g)  NO (g) + CO2 (g)
Bimolecular mechanism: conc.
of both reactants affects rate.
{RxMechanism.NO2+CO.Prop1}
Experimental Evidence: reaction rate is second order in [NO2] & does not
depend on [CO] at all, even though CO is required for reaction to occur.
Rate = k [NO2]2
• A proposed mechanism for this reaction is
Step 1: NO2 + NO2  NO3* + NO (slow)
Step 2: NO3* + CO  NO2 + CO2 (fast)
NO3* = intermediate reactant
• The overall reaction cannot occur faster than this
slowest, rate-determining step.
{Movie1}
{Movie 2}
Chemical
Kinetics
Determining Rx Mechanisms
Using radioactive isotope labeling can help us to
experimentally determine the reaction mechanism.
The simplest proposed mechanism is
NO2 (g) + CO (g)  NO (g) + CO2 (g)
½ labeled
• Better proposed mechanism is:
Step 1: NO2 + NO2  NO3 + NO (slow)
Step 2: NO3 + CO  NO2 + CO2 (fast)
{DeterRxMechanismIsotopLabel1.NO2+CO}
{DeterRxMechanismIsotopLabel2.NO2+CO}
Chemical
Kinetics
Factors That Affect Reaction Rates
4. Presence of a Catalyst
 Catalysts speed up reactions.
 Catalysts are not consumed during
the course of the reaction.
2 H2O2 (l)
SO2 + 2 H2S
MnO2
H2O
2 H2O (l) + O2 (g)
{*Catalysis of H2O2 by MnO2}
2 H2O(l) + 3 S(aq)
{Catalyst of
SO2 + H2S}
Chemical
Kinetics
Catalysts
Increase the reaction rate by changing the
mechanism, thus also changing (decreasing) the
activation energy by which the process occurs..
Ea
Add catalyst:
Ea
Chemical
Kinetics
Surface Catalysis
Some Reactions an in Internal Combustion Engine:
2 C8H18 (l) + 25 O2 (g)  16 CO2 (g) + 18 H2O (g)
(+heat)
N2 (g) + O2 (g)  2 NO (g) (causes acid rain & ozone depletion))
{Pt Catalytic Converter: 2 NO(g) Pt O2(g) + N2(g)}
NO
NO
Pt
N2
O2
Pt Surface
Reactant molecules attach to
Catalytic Surface
Bonds of attached
molecules are Broken
Chemical
Atoms recombine
to form
Kinetics
product, which are then
released from surface
Catalytic
Converters
The catalyst (in the form of platinum and palladium) is
coated onto a ceramic honeycomb or ceramic beads that
are housed in a muffler-like package attached to the
exhaust pipe.
The catalyst helps to convert carbon monoxide into
carbon dioxide. It converts the hydrocarbons into carbon
dioxide and water. It also converts the nitrogen oxides
back into nitrogen and oxygen.
Chemical
Kinetics
Catalysis
H2
+
H2C=CH2
Ethylene
Ni
H3C-CH3
Ethane
{Surface.Catalysis.
Hydrogenation}
One way a catalyst can speed up a reaction is by holding the
reactants together and helping bonds to break.
Chemical
Kinetics
Enzymes: biological catalysts
substrate
enzyme
• Lock and Key Theory: the substrate (reactant) fits into
the active site of the enzyme much like a key fits into a
lock.
Chemical
Kinetics
Chemical
Kinetics
Chemical
Kinetics
Additional
Practice
Problems
Where are the
answers?
Chemical
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2000
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c
)
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2004
A
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2004
B
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2005
A
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B
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2006 (A)
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2007 (A)
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