Chapter 13 Chemical Kinetics

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Chapter 13Chemical Kinetics
Read Study Chapter 13 View the videos in the
Science Learning Center (SLC), N-604. One is
entitled, Catalysis Technology for a Clean
Environment and the other is Reaction Rates.
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Chapter Overview
1. Introduction - Background and Key
Definitions 2. Factors Influencing the Rates of
Reactions 3. Rate Laws 4. Activation
Energies 5. Reaction Mechanisms - The
Paragraphs of the Chemical Language 6.
Effects of Catalysts
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Introduction
1. Chemical Kinetics - The study of how fast
chemi- cal reactions take place a study of the
RATE of a reaction. 2. Chemical Reaction Rate
- A change in the amount or concentration of a
reactant or product in a given period of
time. Rate - DReactant
DProduct D time D time
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3. Kinetics vs. thermodynamics - Factors to be
con- sidered when predicting whether or not a
change will take place 1) Energy (Enthalpy)
Change 2) The Change in disorder (Entropy) 3)
The RATE of the change
Thermodynamics
Kinetics
4. Reaction Mechanism - A detailed molecular-,
atomic-, or ionic-level picture or model of
how a reaction takes place.
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How does NO (g) react with O2 (g) in the
atmosphere to form NO2 (g), a major contributor
to smog?
2 NO (g) O2 (g) 2 NO2 (g)
R1
Step 1 NO (g) O2 (g) NO3 (g)
Fast
R2
Step 2 NO3 (g) NO (g) O2 (g)
Fast
R3
Step 3 NO3 (g) NO (g) NO2 (g)
Slow
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By measuring the rates of reactions under
various conditions, rate laws can be deduced.
The chemist, then, designs reaction mechanisms to
explain the observed rate laws.
5. Factors affecting the rates of reactions -
1) The Nature of the Reactants 2) The
Reactants Concentrations 3) The Reactants
Total Surface Area 4) The Temperature 5) The
presence or absence of catalysts
Memorize!!
Memorize!!
Memorize!!
Memorize!!
Memorize!!
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FACTORS AFFECTING REACTION RATES

• 1) The Nature of the Reactants -
• Ions in solution tend to react very quickly.
• Covalent molecules tend to react more slowly.
• Large covalent molecules tend to react more
• slowly than small covalent molecules.
• Molecules with strong covalent bonds tend to
• react more slowly than those with weak bonds.

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• 2) The Concentrations of the Reactants -
• For a reaction to occur, three things must happen
  -
• The reacting molecules, atoms, or ions, must
• collide.
• They must be properly oriented with respect to
  one
• another.
• The must have sufficient energy.
• The probability of these three factors being
  present is
• increased as the concentration of the reactants
  is
• increased.

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Proper Orientation is Necessary
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Suffcient Energy is Necessary
Bounces Off!
Reacts!
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Homogeneous Reactions - Reactions that take
place in a single solution (phase). Cu2 4
NH3 (aq) Cu(NH3)42
NaOH (aq) HCl (aq) NaCl (aq) H2O (l)
3) The Reactants State of Subdivision
- Heterogeneous Reactions - Reactions in which
reactants are in different phases. The
reactions take place at the interface between the
phases. The larger the surface area of the
interface, the higher the rate of reaction.
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V 1 m3 A 6 m2
V 1 m3 A 8 m2
V 1 m3 A 12 m2
V 1 m3 A 36 m2
V 1 m3 A 20 m2
V 1 m3 A ?? m2
Powder
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http//blog.wired.com/wiredscience/2008/03/top-10-
amazing.html
http//pubs.acs.org/cen/government/86/8608gov1.htm
l
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Examples of Heterogenous Reactions - C (s)
O2 (g) CO2 (g) Zn (s) 2 HCl (aq) ZnCl2
(aq) H2 (g) AgCl (s) 2 NH3
(aq) Ag(NH3)2 Cl -
4) The Temperature - Reaction rates are
increased by increases in temperature. Rule of
Thumb A 10oC rise in temperature will double
the rate of the reaction.
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Practice Exercise The temperature at which a
reaction is run is raised from 0oC to 40oC. How
much is the rate of the reaction
increased? toC Rate 0 R1 10 2R1 20 4R1 30
8R1 40 16R1 R2
R2 2(t2 - t1)/10R1
If you want to slow down the reaction that causes
your milk to sour, you put the milk in the
refrigerator to lower its temperature.
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What about the Thermite Reaction and temperature?
http//blog.wired.com/wiredscience/2008/03/top-10-
amazing.html
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5) Catalysis - How can a catalyst change the
rate of a reaction and yet NOT be
consumed? Thermodynamic Answer By changing the
energy pathway.
Activation Energy
Reactants
Energy
Products
With a catalyst, the energy hump is lowered
-- the energy pathway is changed.
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Kinetic Answer The catalyst is a reactant in
one step of the reaction mechanism and a product
in a subsequent step.
Homogeneous Catalysis - Reactions wherein the
catalyst is present in the same phase as the
reactants. 2 SO2 (g) O2 (g) 2 SO3 (g)
NO (g)
Catalyst
Heterogeneous Catalysis - Reactions wherein the
cat- alyst is present in a separate phase from
the reactants.
Pt (s)
2 H2 (g) O2 (g) 2 H2O (g)
Catalyst
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Heterogeneous Catalysis
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Hydrogen reacts very exothermically with oxygen.
Even so, they can be held in the same container
together for years without reacting unless a
catalyst or source of energy, such as a spark,
are introduced into the mixture.
Rate Laws
Rate Law - A mathematical equation that shows how
the rate of a reaction is affected by the
concentration of re- actants or products in a
reaction.
Measuring the Rate of a Reaction - Follow the
disap- pearance of a reactant or the appearance
of a product.
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2 N2O5 (g) ? 2 N2O4 (g) O2 (g)
Rate DO2/Dt (1/2)(DN2O4/Dt)
- (1/2)(DN2O5/Dt)
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Decomposition of N2O5 (g)
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Reaction of Ethylene w/ O3 (g)
Another Case!
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Measuring the Rate of a Reaction

• Method of Initial Rates A method that involves
  running
• A reaction several times starting with different
  initial
• Concentrations of reactants.
• Hold the temperature constant.
• If Present, keep the solvent constant.
• Vary (change) only one concentration at a
• time.

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Method of Initial Rates
2 NO (g) 2 H2 (g) ? N2 (g) 2 H2O (g)
866oC
Run Reactant Rate of Number Concentration de
crease in NO H2 NO
1 0.10 0.010 0.062 2 0.10 0.040 0.24
6 3 0.30 0.010 0.558
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Method of Initial Rates
Effect of H2 on the Rate 0.040 M 0.246
M/s 0.010 M 0.062 M/s
4.0
4.0
As the H2 is raised by a factor of 4.0, the
rate of decrease in NO (the rate of the
reaction) is raised by a factor of 4.0. ? Rate
? H2
Effect of NO on the Rate 0.30 M 0.558
M/s 0.10 M 0.062 M/s
? Rate ? NO2
3.0
9.0
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Method of Initial Rates
Rate ? H2NO2 Rate k H2NO2 This is
the RATE LAW!
where k is called the Reaction Rate
Constant! k is independent of reactant
concentrations but IS dependent on temperature.
The Rate Law exponents are usually NOT the same
as the coefficients in the balanced chemical
equation. Therefore, the rate law cannot be
predicted. It MUST be experimentally determined.
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k
aA bB ? cC dD
Rate k AmBn
Run Reactant Initial Number Concentration R
ate A B 1 0.030 0.010 1.7
x 10-8 2 0.060 0.010 6.8 x 10-8
3 0.030 0.020 4.9 x 10-8
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rate 1 k(0.030)m(0.010)n 1.7 x 10-8 M/s rate
2 k(0.060)m(0.010)n 6.8 x 10-8 M/s
rate 1 1.7 x 10-8 (0.030)m
0.030 m rate 2 6.8 x 10-8 (0.060)m
0.060



0.25 (0.50)m Log (0.25) Log (0.50)m
m Log (0.50) Log (0.25) m 2.0 Log (0.50)
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rate 1 k(0.030)m(0.010)n 1.7 x 10-8 M/s rate
3 k(0.030)m(0.020)n 4.9 x 10-8 M/s
rate 1 1.7 x 10-8 (0.010)n
0.010 n rate 3 4.9 x 10-8 (0.020)n
0.020



0.35 (0.50)m Log (0.35) Log (0.50)n
n Log (0.50) Log (0.35) n 1.5 Log (0.50)
Rate k A2B3/2
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2 I- S2O82- I2 (aq) 2 SO42-
Run I- S2O82- Initial Rate
1 0.15 0.45 2.6 x 10 - 4
2 0.15 0.25 1.4 x 10 - 4
3 0.50 0.45 8.6 x 10 - 4
Find the Rate Law Rate k I-mS2O82- n
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rate 1 k(0.15)m(0.45)n 2.6 x 10 -4 M/s rate
3 k(0.50)m(0.45)n 8.6 x 10 -4 M/s
rate 1 2.6 x 10-4 (0.15)m 0.15
m rate 3 8.6 x 10-4 (0.50)m 0.50



0.30
0.30 (0.30)m Log (0.30) Log (0.30)m
m Log (0.30) Log (0.30) m 1.0 Log (0.30)
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rate 1 k(0.15)m(0.45)n 2.6 x 10 -4 M/s rate
2 k(0.15)m(0.25)n 1.4 x 10 -4 M/s
rate 1 2.6 x 10-4 (0.45)n 0.45
n rate 2 1.4 x 10-4 (0.25)n 0.25



1.86
1.86 (1.80)n Log (1.86) Log (1.80)n n
Log (1.80) Log (1.86) n 1.0 Log (1.80)
? Rate k I-S2O82-
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Rate Laws
The Order of a Reaction The sum of the
exponents in the Rate Law for the reaction
866oC 2 NO (g) 2 H2 (g) ? N2 (g) 2 H2O
(g) k1
Rate k1 H2NO2
Determined by Experiment
First Order with respect to H2 Second Order
with respect to NO Third order OVERALL
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Rate Laws
a A b B ? c C d D k2
Determined by Experiment
Rate k2 A2B3/2
Second Order with respect to A 1.5 Order with
respect to B 3.5 order OVERALL
2 I- S2O82- ? I2 (aq) 2 SO42-
Rate k I-S2O82-
First Order with respect to both I- and
S2O82- and second order OVERALL
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Rate Laws
a A b B c C ? d D e E k4
Rate k4 AmBn
Subtances involved in a reaction that have NO
concentration effect on the rate of the reaction
are said to have a zeroth order effect. The
reaction above is zeroth order with respect to
C.
REMEMBER The rate law for a reaction CANNOT
be predicted from the chemical equation! It MUST
be experimentally determined!
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Rate Laws
Class Exercise The following reaction is second
order with respect to acetaldehyde. Write the
Rate Law for this reaction.
CH3-C H (g) ? CH4 (g) CO (g)
k O
Rate k CH3-C H2 O
Rate Constants The value of the rate constant,
k, for a given reaction depends on the NATURE of
the reactants and the TEMPERATURE, but NOT on the
concentration of reactants.
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Rate Constants
Class Exercise A 2 B ? C Rate k B
0.012 molL-1s-1
When B0 0.60 M and A0 0.020 M, Find k.
k rate/B0 (0.012 molL-1s-1)/(0.60
molL-1) 0.020 s-1

Find the rate of the reaction when A0 B0
0.010 M
rate k B (0.020 s-1)(0.010 M) 2.0 x
10-4 Ms-1
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Rate Law Characteristics
Zero Order Reactions Reactions with rates that
are not dependent on the concentration of
reactants.
Reactant
Reaction Rate
Time
Time
The rate of metabolism of alcohol in the body is
indepen- dent of alcohol. The RATE is constant!
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Rate Law Characteristics
First Order Reactions 2 N2O5 (g) ? 4 NO (g)
O2 (g) Rate kN2O5
In General Rate kA
A
ln A
Time
Time
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Rate Law Characteristics
A Ao e-kt Integrated Rate Law (1st
Order)
ln A ln Ao (-kt) ln A - kt
ln Ao y mx b
Half-Life The time required for one-half of a
reactant to disappear in a reaction. For FIRST
ORDER reactions, The half-life is INDEPENDENT of
reactant concentration.
O.K. Lets Prove That!
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Rate Law Characteristics
ln A ln Ao (-kt)
A Ao
ln
-kt
ButA ½ Ao at time t1/2
Ao 2Ao
ln
ln (1/2)
-kt1/2
kt1/2 - ln (1/2) ln 2 0.693 t1/2
0.693/k CONSTANT
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The Half-Life (t1/2) of a First Order process is
inversely proportional to the rate constant, k,
and is independent of the reactant concentration.
2nd Order Reactions Rate kA2
Simplest Type Rate kAB Also 2nd Order
k 2 NO2 (g) ? 2 NO (g) O2 (g)
Rate kNO22
Integrated Rate Law (2nd Order)
1/A kt 1/Ao y mx b
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At time t1/2, A 1/2Ao . Therefore
2/Ao kt1/2 1/Ao 2/Ao - 1/Ao
kt1/2
1 Ao
kt1/2 ? t1/2 1/kAo
How can you tell 1st order reactions from 2nd
order?
1st Order
2nd Order
ln A
1/A
time
time
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Temperature Effects on Reaction Rates
k Ae-Ea/RT
Arrhenius Plot
Take log of both sides ln k ln A ln e
-Ea/RT ln k ln A - Ea/RT ln k
-(Ea/R)(1/T) ln A
y mx b
Slope - Ea/R Ea -R(Slope)
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Temperature Effects on Reaction Rates
If you know the k at one temperature, you can
find k for a different temperature with the
Arrhenius Equation.
ln k1 -(Ea/R)(1/T1) ln A ln k2
-(Ea/R)(1/T2) ln A ln k1 Ea/RT1 ln
A ln k2 Ea/RT2 ln A ln k1 Ea/RT1
ln k2 Ea/RT2
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Temperature Effects on Reaction Rates
ln k1 Ea/RT1 ln k2 Ea/RT2 ln k1 - ln k2
Ea/R(1/T2)-(1/T1) ln (k1/k2)
Class Exercise Ea 18.7 kJ/mol k1 0.0400
s-1 T1 273 K T2 298 K k2
??
ln k2 ln k1 - Ea/R(1/T2)-(1/T1) ln k2
-2.538 k2 0.0798 s-1
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Activation Energy The minimum energy
necessary for a reaction to occur.
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Temperature Effects on Reaction Rates
Arrhenius Plot
k Ae-Ea/RT
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Reaction Mechanisms
Reaction Mechanism A series of consecutive
molecular- level events or steps that lead from
reactants to products. They can be disproven but
never proven.
For a mechanism to be valid, it must account for
every- thing that is known about the reaction,
including the rate law for the reaction and its
stoichiometry.
Elementary Process A single reaction step in a
reaction mechanism.