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9.5 Temperature-dependence of reaction rate
-- Arrhenius equation
Its the time for you to compose your course
thesis!
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From the middle 19 century, people began to
study the effect of temperature on the reaction
rate. Many empirical relations have been founded.
5.1 Types of rate-temperature curves
Type I k increases exponentially with T. This
kind of curve can be observed in most of the
reactions.
Problem why do we use k other than r?
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Type II This kind of kT relation was observed
in thermal explosions. At ignition temperature,
the rate constant makes a sharp increase.
Type III usually encountered in the catalytic
reaction that has an optimum temperature.
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Type IV observed in oxidation of carbon and
gaseous oxidation of hydrocarbons.
Type V The only example is 2NO O2 2NO2
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5.2 Empirical rules
(1) vant Hoffs Law
It was found that for homogeneous reaction, an
important generalization is that reaction rate
double or triple for every 10 degree increase in
temperature.
in which A and B are experimental / empirical
constants.
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(2) Arrhenius equation
In 1889, Arrhenius made detailed theoretical
consideration on the hydrolysis of sucrose.
C12H22O11 H2O ? C6H12O6 C6H12O6
in which sucrose molecules were surrounded by
water, if all sucrose molecules could react
directly with water, the reaction should
completed instantly. However, this is not the
case.
Arrhenius postulated that only a small part of
sucrose molecules with higher energy (activated
molecules) can react with water and, therefore,
the reaction can only proceed at a low rate. By
taking enough energy, the common sucrose
molecules can change into activated molecules.
The energy needed for this conversion was called
activation energy. A very important concept!
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Arrhenius extended the ideas of vant Hoff and
suggested a similar empirical equation.
Arrhenius equation
Dimension analysis
Is the simplification reasonable?
Defined the activation energy (Ea)
The first definition of activation energy
experimental activation energy
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If Ea is independent on temperature,
integration of the equation
Arrhenius equation
yields
A is the pre-exponential factor which has the
same unit as the rate constant.
In those five r T relation types, only Type I
obeys Arrhenius equation. Type I is usually named
as Arrhenius type.
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5. 3 Experimental measurement activation energy
(1) Experimental measurement

1. Graphic method
2. Calculation method

Graphic method to plot lnk against 1/T
Arrhenius plot, for the reaction of Arrhenius
type, a straight line may be obtained, the slope
of which equals Ea/R
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ClCOOCH3 H2O ? CO2 CH3OH H Cl?
T / K 273.72 278.18 283.18 288.14
104 k / s-1 0.4209 0.7016 1.229 2.087
T / K 198.18 308.16 318.29
104 k / s-1 5.642 14.05 32.65
R 0.99992
Ea 70.80 kJ?mol-1, A 1.32 ? 109
A is very large
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(2) calculation method
Constant
T / K 273.72 278.18 283.18 288.14
104 k / s-1 0.4209 0.7016 1.229 2.087
T / K 198.18 308.16 318.29
104 k / s-1 5.642 14.05 32.65
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5. 4 Tolmans definition of Ea
The minimum energy that the molecules must
absorb before the reaction can take place is
known as the activation energy.
According to Tolman, the activation energy of
elementary reaction is the difference between the
average energy of the activated molecules and the
average energy of total molecules
Boltzmann distribution
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5.5 Ea and energy change of reaction
the difference in thermodynamic energy
reactant, product, activated state, reaction
path. 22
When Ea,-gtEa,, ?U lt 0, the reaction is
exothermic.
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When Ea,-lt Ea,, ?U gt 0, the reaction is a
endothermic one.
For a strong endothermic reaction, the
activation energy for backward reaction is very
small. What about Ea, ?
principle of micro-reversibility
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5.6 Activation energy of a overall reaction?
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5. 7 Theoretical evaluation of Ea
The activation energy can be related to the
energy change of the reaction. The energy change
can be calculated using dissociation energy of
chemical bond. To do this, some empirical
rules may be used

1. Dissociation reaction

Cl-Cl ? 2 Cl
Ea will not be less than and need not be larger
than the dissociation energy of the bond, i.e.,
Ea DCl-Cl
Dissociation energy of the bond is different
from energy of bond.
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2) Combination reaction of radicals
2CH3 ? CH3?CH3
Ea 0
3) Radicals react with molecules
A? B?C ? A?B C?
If the reaction is a exothermal one, Ea ? 5 DB-C
4) Molecules react with molecules
A?B C?D ? A?C B?D
If the reaction is exothermal, Ea 30 (DAB
DCD)
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5. 8 Ea on reaction rate
Half-life of first-order reaction with different
activation energy
Ea / kJ?mol-1 40 60 80 100 120
t1/2 2?10-5 s 0.066 s 5.6 h 11.6 d 68.7 y
Ea ranges between 40 400 kJ mol-1. For
first-order reaction, when Ea increases by 4
kJ mol-1, k decreases by 80. The effect of Ea on
reaction rate is significant. Reaction with
Ea less than 80 kJ mol-1 belongs to fast
reactions. To study their kinetics, special
methods have to be used. For reaction with
Ea larger than 100 kJ mol-1 , it is too slow to
study.
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5. 9 Temperature on reaction rate
T2 gt T1
What about the fraction of activated molecule
increases?
Can your find another way to increase the
fraction of activated molecules?
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5. 10 temperature-dependence of Ea
The Arrhenius plots for some reactions are
curved, which suggests that the activation energy
of these reactions is a function of temperature.
At this situation, the temperature dependence of
k can be usually expressed as
This equation suggests that, Ea depends on
temperature.
Problem Discussion the relationship between
this equation and vant Hoff empirical equation
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The value of m, usually be 0, 1, 2, 1/2,
etc., is not very large. Therefore, mRT is not
very large with comparison to Ea. In a
relatively small temperature range, Ea seems
independent on temperature.
However, for some reaction such as
CCl3COOH ? CHCl3 CO2, m -10.7 CH3Br
H2O ? CH3OH H Br?, m -34.3 The effect of
temperature on the activation energy of these
reactions is too large to ignore.
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To measure activation energy of the reaction
over a large span of temperature would result in
exceptional difficulties.
When T ??, A k. Is this correct?
How can we measure the activation energy of a
reaction?
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5.11 A on reaction rate
Type of reaction Unimolecular reaction Bimolecular reaction Termolecular reaction
A 1013 s 1011 mol-1?dm3?s-1 109 mol-2?dm6?s-1
5.12 Application of Arrhenius equation
1) make explanation for some experimental
results
2) calculate the reaction rate at different
temperature
3) determine the optimum temperature for reaction.
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T. T. Ching, S. C. Kwong and S. C. Kim, JACS,
2012, 134 11388-11391