Transcript 幻灯片 1 - Shandong University

§9.5 Temperature-dependence of reaction rate
-- Arrhenius equation
Extensive reading: Levine, pp. 554-559 Section 17.8
Teaching design:
BOPPPS: a best way for micro-teaching
Bridging:
Objective
Pre-assessment
Participating
Post-assessment
Summary
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
k increases exponentially with T.
This kind of curve can be
observed in most of the reactions.
T
Problem: why do we use k other than r?
k
Type II
This kind of k~T relation was observed
in
thermal explosions. At ignition
temperature, the rate constant makes a
sharp increase.
T
k
Type III
usually
encountered
in
the
catalytic reaction that has an
optimum temperature.
T
k
Type IV:
observed in oxidation of carbon and
gaseous oxidation of hydrocarbons.
k
T
Type V:
The only example is 2NO +
O2 = 2NO2
T
5.2 Empirical rules
(1) vant’ Hoff’s 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.
kT 10
2~3
kT
d ln k A
 2 B
dT
T
in which A and B are experimental / empirical constants.
(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!]
Arrhenius extended the ideas of vant’ Hoff and suggested a similar
empirical equation.
d ln k
A
 2 B
dT
T
Ea
d ln k

dT
RT 2
Arrhenius
equation
  ln K Θ 
r H mΘ

 
RT 2
 T  p
Dimension analysis
Is the simplification reasonable?
Defined the activation energy (Ea)
 d ln k 
E a  RT 2 

 dT 
The first definition of activation energy: experimental activation energy
If Ea is independent on temperature, integration of the equation
Ea
d ln k

dT
RT 2
yields
Ea
ln k  
 ln A
RT
 Ea 
k  A exp 

 RT 
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.
5. 3 Experimental measurement activation energy
(1) Experimental measurement:
Ea
ln k  
 ln A
RT
(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
ClCOOCH3 + H2O  CO2 + CH3OH + H+ + Cl
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
ln k (/s-1)
T/K
1
ln k  8515 .9  21 .06
T
-5
-6
R = 0.99992
-7
Ea
ln k  
 ln A
RT
-8
-9
-10
-11
3.0x10-3
3.2x10-3
3.4x10-3
3.6x10-3
3.8x10-3
1 / T (/K)
Ea = 70.80 kJmol-1,
A =1.32  109
A is very large
(2) Calculation method:
Ea
ln k1  
 ln A
RT1
Constant
Ea
ln k2  
 ln A
RT2
Ea
k1
ln

k2
R
1 1
  
 T1 T2 
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
5. 4 Tolman’s definition of Ea
The minimum energy that the molecules must absorb before the
reaction can take place is known as the activation energy.
Ea  E*  E
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
Ea  E *  E
5.5 Ea and energy change of reaction
Ea,   U a  U R
Ea,   U a  U P
Ea,  Ea,  U P U R  U
the difference in thermodynamic
energy
reactant, product, activated state,
reaction path. 22
U  Ea,  Ea,
When Ea,->Ea,+, U < 0, the reaction is exothermic.
U  Ea,   Ea, 
When Ea,-< Ea,+, U > 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
Potential curve
5.6 Activation energy of a overall reaction?
Ea ,3
Ea , 4
Ea ,1
Ea , 2
Ea ,6
Ea ,5
Only the activation energy of elementary reaction has definite physical
meaning.
The activation energies of some overall reactions can be taken as a
combination of the activation energy of elementary reactions
composing of the overall reaction. The activation energy of some
overall reactions, usually named as apparent activation energy, may be
meaningless physically.
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.
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)
5. 8 Ea on reaction rate
Half-life of first-order reaction with different activation energy
Ea / kJmol-1
t1/2
40
60
210-5 s 0.066 s
80
100
120
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.
5. 9 Temperature on reaction rate
T2 > T1
T1
T2
What about the fraction of activated
molecule increases?
Ea,2 Ea,1
Can your find another way to increase the fraction of
activated molecules?
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:
 Ec 
k  AT exp 

 RT 
m
Ea  mRT  Ec
This equation suggests that, Ea
depends on temperature.
Problem:
Discussion the relationship between this
equation and vant’ Hoff empirical equation
d ln k
A
 2 B
dT
T
Ea  mRT  Ec
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.
To measure activation energy of the reaction over a large span of
temperature would result in exceptional difficulties.
Ea
ln k  
 ln A
RT
When T , A = k. Is this correct?
How can we measure the activation energy of a reaction?
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.
T. T. Ching, S. C. Kwong and S. C. Kim, JACS, 2012, 134: 11388-11391