Physical Chemistry II
Phenomenological Chemical Kinetics
(empirical/classical)
1,Reaction Rate & Rate Equation
2,Theoretical Consideration – SCT & TST
3,Microscopic Mechanism
与讲过的热力学大不相同,
热力学 动力学过程的可能性过程的自发性过程的可逆性过程的快慢过程的步骤过程的机制方向和程度 速率概念理解 推导
Three characteristics of a chemical
reaction
1) Stoichiometric characteristics,
balance of the equation
2) Thermodynamic characteristics,
Spontaneity and equilibrium
3) Kinetic characteristics,
Rate and mechanism
开放系统
Food
Air
Heat
Work
Electronic
work
Work
Expansion
Heat
How fast? Why different? Kinetics
The factor concerned by thermodynamics
is the inherent tendency or the possibility
of the reaction but not reality and rate.
C (diamond)? C (graphite)
is spontaneous,but it is so slow that
it is not detectable.
Chemical kinetics:
the area of chemistry that concerns
reaction rate.
Main concerns of chemical kinetics:
1) Reaction rate:
the factors that determines the rate of
reaction and rate law,
2) Reaction mechanism:
the series of steps by which a reaction
takes place.
3) structure-dependence of reactivity.
The correlation between molecular
structure and reaction ability.
the detailed way by which the
reactants are converted into
products,or the series of steps by
which a reaction takes place.
Reaction mechanism and elementary
reaction
Reaction mechanism / reaction pathway
H2 + I2 = 2 HI
Kinetic experiments suggest that this
reaction occurring as follows:
1) I2 = 2I
2) 2I + H2 = 2HI
并不是相当然的,
也不是表面的东西
H2 + Br2 = 2 HBr
1) Br2 = 2 Br
2) Br + H2 = HBr + H
3) H + Br2 = HBr + Br
4) H + HBr = H2 + Br
5) 2 Br = Br2
More complicate!
The species as H and Br,formed in
one step and consumed in a subsequent
step and never seen as a product is
called an intermediate.
The reaction that completes in one act
is called elementary reaction.
基元反应 (步骤 )
中间体
The sum of the elementary reactions
and their series is called the
mechanism of the overall reaction
总包反应反应机理
Classification of reactions
1) elementary reactions
According to the number of molecules
involved in the reaction,elementary
reactions can be divided into three kinds:
unimolecular reaction
bimolecular reaction
termolecular reaction.
单分子反应双分子反应三分子反应
unimolecular reaction:
I2 = 2I
bimolecular reaction:
Br + H2 = HBr + H
termolecular reaction:
2I + H2 = 2HI
Because the probability of three
molecules colliding simultaneously is
very small,termolecular reaction are
quite rare.
三体碰撞的几率很小
According to the number of
elementary reactions involved,the
overall reaction can be classified into:
simple reaction
complex reaction
2) overall reactions
简单反应复杂反应
Reaction rates and rate equation
1,Expression of reaction rate
The reaction rate (r) of a chemical
reaction is defined as the change in
concentration of a reactant or product
per unit time.
There are two kinds of reaction rates,
one is the average rate
t
A
r
][
平均速率
The other is the instantaneous rate
defined as:
dt
Ad
r
][
反应速率
N2 + 3H2? 2NH3
dt
dC
r
H
H
2
2
dt
dC
r
N
N
2
2
dt
dC
r
NH
NH
3
3
322 2
1
3
1
NHHN rrr
It is apparent that
When expressed using different species,the
rate of the reaction may attain different
values,which is not convenient and
sometimes may even cause some confusion.
Definition,extent of reaction or the
advancement (?)
i
ii nn
0,?
where?i is the stoichiometric coefficient
of the reaction,
Definition,
The true rate of the reaction (J):
dt
d
J
For general reaction:
aA + bB? gG + hH
When the extent of reaction is d?
h
dn
g
dn
b
dn
a
dn
d HGBA
dt
dn
hdt
dn
gdt
dn
bdt
dn
adt
d
J HGBA
1111
When the reaction takes place in a
container with constant volume
Definition,
V
J
r?
dt
dn
hdt
dn
gdt
dn
bdt
dn
adt
d
J HGBA
1111
dt
Hd
hdt
Gd
gdt
Bd
bdt
Ad
a
r
][1][1][1][1
dt
Cd
r i
i
][1
Unit,mol m-3 s-1
molecule cm-3 s-1
mol L-1 S-1
2,Measurement of reaction rate
i
r
1
Physical meaning:
slope of the C ~ t curve
dt
Cd i ][
C ~ t curve is
usually called
kinetic curve
The rate at a particular time can be obtained by
computing the slope of a line tangent to the curve at
that time point.
动力学曲线
0?
tdt
dC
r
ttdt
dC
r
Initial rate
The key subject of kinetic study is to
measure the concentration of any species
after arbitrary time intervals.
The concentration of the species can be
measured using either chemical methods
or physical ones,
CH3COOC2H5 + NaOH?
CH3COONa + C2H5OH
The reaction can be stopped by removing of
CH3COOC2H5,and the consumption of
NaOH can be determined by chemical
titration.
For example
CH3COOC2H5 + NaOH?
CH3COONa + C2H5OH
the rate of which can be monitored
using pH meter or conductometer.
t = 0 t = t1 t = t
2
The change in physical properties
usually chosen as indicator of progress
of the reaction.
比方说,颜色变化
N2O4? 2NO2
红棕色无色与压缩的速度有关系吗?
The first successful example for measuring
concentration of reactant physically was
made by Wilhelmy in 1850,He determined
the residual concentration of sucrose by
measuring the change of the rotation angle
of a beam of plane-polarized light passing
through the hydrolysis solution.
偏振光方法蔗糖的水解
Polarimeter,旋光光度计
C12H22O11 + H2O?
C6H12O6 (R) + C6H12O6 (L)sucrose
glucose fructose
Substance sucrose glucose fructose
[?]D25 +66.5 o +52 o - 92 o
The rotation angle of the 1:1 mixture of
glucose and fructose is –20 o
N2O5 = N2O4 + 0.5 O2
When this reaction takes place in a
container with constant volume,the rate of
the reaction can be monitored by measuring
the pressure change,And when this reaction
takes place under constant pressure,the
advance of the reaction can be monitored by
measuring the volume increase.
Stretch of
epoxy group
FTIR spectroscopy.
Analyzing methods:
1) Real time analysis
2) Quenching
3) Flow method
The physical parameters usually
used for monitoring reaction process
includes volume,pressure,electric
conductance,pH,refractive index,
thermal conductivity,polarimetry,
spectrometry,chromatography,etc.
Flow method
t = L / V
3,The law of mass action and rate
equation
The concentration-dependence of rate:
r = r(Ci) = r(CA,CB,CC… )
where Ci represents concentration of
individual specie present in rate equation,
质量作用定律
In many instances,the rate of a reaction is
proportional to the concentrations of the
reactants raised to some power.
CBAA CCkC
dt
dC
For example,H2 + I2 = 2 HI
1
2
1
2 ][][ IHkr?
H2 + Cl2 = 2 HCl
5.0
2
1
2 ][][ ClHkr?
where rate coefficient/constant (k) is a
proportional constant independent of
concentration,
The exponent shows the effect of
concentration on the reaction rate,in 1895,
Noyes defined them as partial order of the
reactant.
CBAA CCkC
dt
dC
r
速率常数
,? is the partial order of the
reaction with respect to A or B,
respectively.
5.0
2
1
2 ][][ ClHkr?
This implies that the reaction obeying rate
law is first-order in H2 and 0.5-order in Cl2.
the sum of the partial order n =? +?
+? +… is the overall order of the
reaction,or more simply,the reaction
order.
5.0
2
1
2 ][][ ClHkr?
The overall order is 1.5.
反应级数
2SO2 + O2? 2SO2
2
1
32
3 ]][[2][
SOSOk
dt
SOd
r
is first-order in SO2,-0.5-order in SO3
and 0.5 order overall,
n,?,?,?,etc.,different from the
stoichiometric coefficient,may be
integers,decimals,of plus or
minus values.
For elementary reaction,?=a,?=b,etc.
CBAA CCkC
dt
dC
r
cCbBaAA CCkC
dt
dC
r
Partial order = stoichiometric coefficient
reaction order = number of molecules
involved in the reaction
For example:
2I + H2 = 2HI
][][
][
2
1
2
2 HIk
dt
Id
r
Law of mass action valid only for
elementary reaction
质量作用定律
The overall reaction:
the first-order reaction
the second-order reaction
It was found that reactions with same
reaction order are usually of same
kinetic characteristics,therefore,
reactions are usually classified on the
basis of reaction order.
一级反应二级反应
1
2
1
2 ][][ IHkr?
H2 + I2 = 2 HI
H2 + Cl2 = 2 HCl
5.0
2
1
2 ][][ ClHkr?
H2 + Br2 = 2 HBr
][
][
'1
]][[
2
5.0
22
Br
H B r
k
BrH
kr
Overall
reactions
Reaction with
definite order
Reaction without
definite order
Reaction with
simple order
The purposes of the rate law:
1) Given the composition of the reaction
mixture,the rate law can predict the
reaction rate.
2) Gives clues to the mechanism and testify
the proposed mechanism.
3) To classify reactions on the reaction order.
4,The rate equation of reaction
with simple order
The reaction whose rate only
depends on the concentration of
reactants,and both the partial order
and the reaction order is zero or plus
integer is called reaction with simple
order.
Kinds of reaction with simple order
r = k Cn
n kinds
0 zeroth-order reaction
1 first-order reaction
2 second-order reaction
3 third-order reaction
4.1 the first-order reaction:
Reaction,A? P
C0
C
Differential rate
equation:
Ck
dt
dC
1
can be rearranged into:
Ck
dt
dC
1
dtk
C
dC
1
Which can be integrated directly.
tk
C
C
1
0ln?
The integration rate equation
)ex p ( 10 tkCC
0 1000 2000 3000 4000 5000
0.0
0.2
0.4
0.6
0.8
1.0
C
/
mol
dm
-3
t / s
C~t curve of first-order reaction
)ex p ( 10 tkCC
tkCC 10lnln
The slope of the lnC ~ t curve is
the k1
tk
C
C
1
0ln?
0 1000 2000 3000 4000 5000
-5
-4
-3
-2
-1
0
ln(
C
/m
ol
dm
-3
)
t / s
lnC ~ t curve of the first-order reaction
tkCC 10lnln
tk
C
C
1
0ln?
112
1
6 9 3 2.02ln
kk
t
Half-life
2
0CC?
半衰期
Characteristics of the first-order
reaction
1) Unit of k is s-1
2) lnC is in linear proportion to t
3) Half-life does not depend on C0
Example:
1)Decay of isotopes
2) Decomposition
HeRnRa 422268622688
24252 2
1 OONON
3) Isomerization
1960 Noble Prize
USA
1908/12/17 ~
1980/09/08
Application of 14C for
age determinations
(radiocarbon dating)
Willard F,Libby
4.2 Second-order reaction
2A P
pure second-order reaction
A + B P
mixed second-order reaction
A + B P
a b
CA= a-x CB =b-x
BA
A CCk
dt
dC
2
Differential rate equation:
(a? b)
))((2 xbxak
dt
dx
dtk
xbxa
dx
2))((
tx
dtk
xbxa
dx
0 20 ))((
tx
dtk
xbxa
dx
0 20 ))((
txx
dtk
xaba
dx
xbba
dx
0 200 ))(())((
tk
ba
a
ba
xa
ba
b
ba
xb
2)(
ln
)(
)ln (
)(
ln
)(
)ln (
tk
xba
xab
ba 2)(
)(
ln
)(
1
2
2 Ckdt
dC
When a = b
dtk
C
dCC
C 220
tk
CC
2
0
11
0
20 1
C
C
k C t
2
0
11
kt
CC
0 1000 2000 3000 4000 5000
0.0
0.2
0.4
0.6
0.8
1.0
C / mo
l
dm
-3
t / s
C~t curve of second-order reaction
0
20 1
C
C
k C t
0 1000 2000 3000 4000 5000
0
10
20
30
40
50
1/
C
/ mol dm
-3
t / s
1/C ~ t curve of second-order reaction
2
0
11
kt
CC
tk
CC
2
0
11
02
2/1
1
Ck
t?
Half-life 半衰期
Characteristics of second-order reaction
1) Unit of k is mol-1 m3 s-1
2) 1/C is in linear proportion to t
3) Half-life
02
1
1
C
t?
Increasing the initial concentration of
the reactant will shorten the reaction
time.
For pure second-order reaction
2
22
1
Ck
dt
dC
tk
CC 20
2
11
02
2/1
2
1
Ck
t?
2A P
Example:
1) Dimerization
2) Decomposition
222 IHHI
3) Recombination
6232 HCCH
4) Esterification
OHHC O O CCH
OHHCC O O HCH
2523
523
5) Hydrolysis
C12H22O11 + H2O?
C6H12O6 (R)+ C6H12O6 (L)
In 1850,the experiment done by Wilhelmy
suggested the rate equation of the reaction is:
][ 112212 OHCkr?
]][[ 2112212 OHOHCkr?
C12H22O11 + H2O?
C6H12O6 (R)+ C6H12O6 (L)
Because the amount of water keeps nearly
unchanged during the reaction,[H2O] keeps
nearly constant,and the rate equation
]][[ 2112212 OHOHCkr?
can be then simplified as
][ 112212 OHCkr?
Pesudo first-order reaction 准一级反应
4.3 Third-order reaction
Three kinds of third-order reaction
3A P
A + B + C P
2A + B P
For 3A P
3
33
1
Ck
dt
dC
Differential rate equation
tk
CC
32
0
2
3
11
2
1
Integrated rate equation
tk
CC
32
0
2
6
11
2
032
1
2
1
Ck
t?
For A + B + C P with same initial
concentration
3
3 Ckdt
dC
Differential rate equation
tk
CC
32
0
2
11
2
1
Integrated rate equation
tk
CC
32
0
2
2
11
2
032
1
2
3
Ck
t?
Examples:
2NO + X2? N2O + X2O; X = H,D
2NO + O2? 2NO2;
2NO + X2? 2NOX; X = Br,Cl
r = k [C6H5CHO]2[CN-]
r = k [C2H4O][H+][Br-]
Hydrolysis of sucrose
]][][[ 2112212 HOHOHCkr
During reaction,both [H2O] and [H+]
keep nearly constant and the reaction
behaves as a first-order reaction.
4.4 Zeroth-order reaction
A P
Differential rate equation:
0k
dt
dC
tC
C
dtkdC
0 00
tkCC 00
0
0
2/1
2 k
C
t?
00C k t C
When C = 0,the reaction completes,
the time need is:
0
0
k
C
t?
The zero-order reaction is the only
reaction that can complete.
0 1000 2000 3000 4000 5000
0,0
0,2
0,4
0,6
0,8
1,0
C
/ m
ol d
m
-3
t / s
C ~ t curve for zero-order reaction
00C k t C
Characteristics of zeroth-order reaction
1) Unit of k is mol dm-3 s-1
2) C is in linear proportion to t
3) When C increases,reaction time
will be prolonged.
Examples:
Decomposition over catalysts:
1) 2N2O? 2N2 + O2 over Pt wire
2) 2NH3? N2 + 3H2 over W wire
Photochemical reaction:
r = k I
I,intensity of radiation
4.5 Nth-order reaction
nkCr?
tk
axan nnn
}
1
)(
1
{
1
1
11
1
0
1
0
1
2/1
)1(
12
nn
n
C
A
kCn
t
For n? 1
4.6 Determination of the reaction
order r = k [A]?[B]?[C]?
Whenever we determine the order of a reaction,we can
write out the rate equation of the reaction and tell the
detail of the kinetic characteristics of the reaction
according to the rate equation.
The rate equation can provide useful information
about the mechanism of the reaction,Therefore,
determination of the order of the reaction is a work of
great importance.
Methods for determination of reaction
order
1) Integration method
2) Differential method
3) Partial order method
4) Isolation method
积分法微分法
4.6.1 Integration methods
The integration methods are to use the
integrated rate equation to determine the
order of the reaction.
Integration methods includes:
1) attempt method
2) graphic method
3) half-life method
1)The attempt method:
the values of k1 can be calculated from
the selected integrated equation from a
knowledge of initial concentration (C0) and
the concentration at various time intervals
(C).
If the reaction is of the selected order of
reaction,the k at different intervals thus
obtained will be the same.
尝试法
A + B? P
C2H5ONa + C2H5(CH3)2SI?
NaI + C2H5O C2H5 + S(CH3)2
r = k[C2H5ONa]?[C2H5(CH3)2SI]?
r = k [A]?[B]?
t/s 102[A]/ mol dm-3 102[B] / mol dm-3
0 9.625 4.920
720 8.578 3.878
1200 8.046 3.342
1800 7.485 2.783
2520 6.985 2.283
3060 6.709 2.005
3780 6.386 1.682
4.704
Table 1,kinetic data for C2H5ONa + C2H5(CH3)2SI at
337.10 K
t?=0?=1?=0?=2?=0?=1
=0?=0?=1?=0?=2?=1
k 105 104 104 103 103 103
0 1.454 1.599 3.313 1.764 7.579 3.642
720 1.108 1.143 3.088 1.604 7.357 3.678
1200 0.935 1.205 3.051 1.550 10.02 3.760
1800 1.042 0.960 2.751 1.333 10.93 3.773
2520 0.511 0.747 2.405 1.093 11.11 3.731
3060 0.449 0.685 2.440 1.042 13.32 3.729
Table 2,k of the reaction of different order
r = k[C2H5ONa][C2H5(CH3)2SI]
Therefore,the rate equation is:
1) The attempt method is a laborious method
2) For reaction without simple order,it is
impossible to ascertain reaction order using
this method.
3) the experimental error may cause confusion
sometimes,Not good yet!
2) The graphic method
the linear relationship of reaction with
different order is different.
order Linear relationship
zeroth C ~ t
first lnC ~ t
second 1/C ~ t
third 1/C2 ~ t
作图法
t / s C / mol dm-3 t / s C / mol dm-3
0 1.000 3000 0.050
500 0.606 3500 0.030
1000 0.368 4000 0.018
1500 0.223 4500 0.011
2000 0.135 5000 0.007
2500 0.082
Table 3,kinetic data for A? P.
The rate equation of A? P can be expressed as
r = k[A]?
0 1000 2000 3000 4000 5000
0,0
0,2
0,4
0,6
0,8
1,0
C
/ m
ol d
m
-3
t / s
0 1000 2000 3000 4000 5000
-5
-4
-3
-2
-1
0
ln (C
/
mol
dm
-3
)
t / s
一级反应
0 1000 2000 3000 4000 5000
0
40
80
120
160
1/
C(/
mo
l dm
-3
)
t / s
0 1000 2000 3000 4000 5000
0
20
40
60
80
100
1 / C
2
t / s
3) half-life method
the half-life of the reaction is proportional
to the initial concentration of the reactant
nkCt 1
02/1
02/1 ln)1(lnln Cnkt
半衰期法斜率
-5 -4 -3 -2 -1 0 1
3
4
5
6
7
8
9
10
ln t
1/2
lnC
0
k = - 1
02/1 ln)1(lnln Cnkt
(1-n) = - 1
n = 2
Therefore,the reaction is of second order.
Graphic method
02/1 ln)1(lnln Cnkt
Calculation
'ln)1(ln'ln 02/1 Cnkt
'
ln
'
ln
1
0
0
2/1
2/1
C
C
t
t
n
C0/mol dm-3 0.05 0.10 0.20
t1/2/h 37.03 19.15 9.45
NH4OCN? CO(NH2)2
'
ln
'
ln
1
0
0
2/1
2/1
C
C
t
t
n
n1 = 2.051,n2 = 2.019
n = 2.035? 2
4.6.2 Differential method
Use the differential form of the rate
equation to determine the order of the
reaction.
nkC
dt
dC
r
Cnkr lnlnln
斜率
Graphic method
Decomposition
percentage
0 5 10 15 20
r / Pa min-1 1137 998.4 898.4 786.5 685.2
Decomposition
percentage
25 30 35 40 45
r / Pa min-1 625.2 574.5 500.0 414.6 356.0
Table 1,Decomposition of CH3CHO?CH4+CO.
3,8 4,0 4,2 4,4 4,6 4,8
5,5
6,0
6,5
7,0
ln
r
/
P
a m
in
-1
ln C / mol dm
-3
ln r = -1.593 + 1.865 ln C
Linear fitting results:
ln r = -1.593 + 1.865 ln C
Linear correlation coefficient,0.998
Therefore,the order of the reaction is 2.
Determination of reaction order through one
experiment.
Reaction
order with
respect to
time,nt
0
0
lnln
ln
Cnk
r t
Determination of reaction order through
several parallel experiments.
Reaction order
with respect to
concentration,
nC
The method of initial rates is applicable
of a wide variety of reactions.
This method is particularly useful in
reactions that are complicated by
processes involving intermediate or
products.
calculation method
'lnln'ln Cnkr
Cnkr lnlnln
'
ln
'
ln
C
C
r
r
n
t
'
ln
'
ln
0
0
0
0
C
C
r
r
n
C
Decomposition
percentage
0 5 10 15 20
r / Pa min-1 1137 998.4 898.4 786.5 685.2
Decomposition
percentage
25 30 35 40 45
r / Pa min-1 625.2 574.5 500.0 414.6 356.0
nt= 2.534; 1.952; 2.327; 2.274
nt = 2.272? 2
= nt Both intermediate and product do not affect the reaction
nC > nt Intermediate or product catalyze the reaction
< nt Intermediate or product inhibit the reaction
Table 2,Relationship between nC and nt.
r = k[A]?[B]? n =?+?
r = k[A]?[B]?[M]? n =?+?+?
4.6.3 Partial order method
CB
a
A CCkCr?
CCCkr BA lnlnlnlnln
)lnln( l nlnln CBA CCCkr
To plot lnr versus lnCA,if a linear relation
can obtained,? = 0,?=0,
If no linear relation can be observed,
adjust the value of? and? until a line can
be obtained,The slope of this line is?,and
the corresponding value of? and? can be
obtained simultaneously.
4.6.4 The isolation method
CBA CCCkr lnlnlnlnln
CBA CCCkr lnln'lnln'ln
A
A
C
C
r
r
'
ln
'
ln
When CB and CC were controlled
固定浓度法
Three methods,
1) Fixation of concentration method;
2) Excess concentration method;
3) Application of stoichiometric ratio
1) fix the concentration of other reactants
Rate equation of 2NO + 2H2? N2 + 2H2O
is r = k[NO]? [H2]?.
No,Initial pressure / Pa Initial rate
NO H2
1 50662.5 20265 486.36
2 50662.5 10132.5 243.18
3 25331.25 20265 121.59
2) Excess concentration
C12H22O11 + H2O?
C6H12O6 + C6H12O6
]][[ 2112212 OHOHCkr?
][' 112212 OHCkr?
过量浓度法
make the concentration of B and C very
much larger than that of A。
This technique is particularly useful in
determining rate constants for reactions
involving water in aqueous solution,
Pseudo order reaction.
准一级反应
3) Using stoichiometric ratio
aA + bB? P
Initial concentration 1 b/a
Conversion concentration x bx/a
Residual concentration 1-x (b/a)(1-x)
r = k[A]? [B]? = k (b/a)?(1-x)?+?
=k (b/a)?(1-x) n
Temperature-dependence of rate
-- Arrhenius equation
From the middle of 19 century,people
began to study the effect of temperature
on the reaction rate,Many empirical
relations have been founded.
温度依赖关系
Types of rate-temperature curves
Type I:
k increase
exponentially with
T,this kind of
curve can be
observed in most
of the reactions,
指数上升
Type II
This kind of k~T
relation was
observed in
thermal explosions,
At ignition
temperature,the
rate constant
makes a sharp
increase,
热爆炸
Type III
Type III is
usually
encountered in
the catalytic
reaction that
has an optimum
temperature,
催化过程
Type IV:
can be
observed in the
oxidation of
carbon and
gaseous
oxidation of
hydrocarbons,
复杂变化
Type V,
Many radical-
radical reactions
such as CH3+CH3,
O+CH3,etc.
负温度效应
Arrhenius equation
It was found that for homogeneous
reaction,an important generalization is
that reaction rate double or treble for
every 10 degree increase in temperature.
异相反应,温度每升高 10 K,
反应速率增加 2-3倍
Vant’ Hoff Law
3~210
T
T
k
k
B
T
A
dT
kd
2
ln
in which A and B are experimental / empirical
constants,
In 1889,Arrhenius made detailed
theoretical consideration on the hydrolysis
of sucrose.
C12H22O11 + H2O?
C6H12O6 + C6H12O6
Sucrose molecules were surrounded by water,
if all sucrose molecules could react directly with
water,the reaction should completed instantly.
Arrhenius concluded that only a small
part of sucrose molecules with higher
energy (activated molecules) can react
with water and,therefore,the reaction
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,活化能活化分子
2
ln
RT
E
dT
kd a
Arrhenius extended the ideas of Vant’
Hoff and suggested a similar empirical
equation.
Defined the activation energy (Ea)
dT
kd
RTE a
ln2
The first definition of activation energy,
experimental activation energy
活化能
If Ea is independent on temperature,
integration of the equation
2
ln
RT
E
dT
kd a
yields
A
RT
E
k a lnln
RT
E
Ak ae x p
A is the pre-exponential factor which
has the same unit as the rate constant.
指前因子
Arrhenius equation
2
ln
RT
E
dT
kd a
A
RT
E
k a lnln
RT
E
Ak ae x p
In these five r ~ T relation type,only
the type I obey the Arrhenius
equation,Type I is usually named as
Arrhenius type.
Experimental measurement
activation energy
Important kinetic parameters:
rate constant,reaction order
activation energy,pre-exponential factor
速率常数,反应级数,
活化能,指前因子
1) experimental measurement:
A
RT
E
k a lnln
(1) graphic method
(2) calculation method
graphic method:
to plot lnk against 1/T,for the reaction
of Arrhenius type,a straight line may be
obtained,the slope of which equaling to
–Ea/R
ClCOOCH3 + H2O? CO2 + CH3OH + H+ + Cl-
T / K 273.72 278.1
8
283.18 288.14
104 k / s-1 0.4209 0.701
6
1.229 2.087
T / K 198.18 308.1
6
318.29
104 k / s-1 5.642 14.05 32.65
3,0x 10
-3
3,2x 10
-3
3,4x 10
-3
3,6x 10
-3
3,8x 10
-3
-11
-10
-9
-8
-7
-6
-5
ln k
(/s
-1
)
1 / T (/K )
06.21
1
9.8515ln
T
k
A
RT
E
k a lnln
R = 0.99992
Ea = 70.80 kJ mol-1,A =1.32? 109
(2) calculation method,
A
RT
E
k a lnln
1
1
A
RT
E
k a lnln
2
2
212
1 11ln
TTR
E
k
k a
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
212
1 11ln
TTR
E
k
k a
Before reaction,molecules must be
activated.
Only the collision of activated molecules
can lead to reaction,while the collisions
between molecules that are not activated
will be of no use and thus no reaction will
take place.
Definition of Ea
活化分子反应的分子需要能量
The minimum energy that the molecules
must absorb before the reaction can take
place is known as the activation energy.
EEE a *
活化能
Boltzmann distribution
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:
EEE a *
Ea and energy change of reaction
Raa UUE,
Paa UUE,
reactant,product,
activated state,
reaction path,
反应途径
,,aa EEU
When Ea,->Ea,+,?U < 0,the reaction is a
exothermic one.
UUUEE RPaa,,
the difference in internal energy
,,aa EEU
When Ea,-< Ea,+,?U
> 0,the reaction is
a endothermic one.
For a strong endothermic reaction,its activation
energy for backward reaction is very small.
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 reaction,usually named as
apparent activation,may be meaningless
physically.
According to the principle of micro-reversibility,
the forward reaction and the backward reaction
pass through the same activated state.
Theoretical evaluation:
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
2) combination reaction of radicals
2 CH3·? CH3CH3
Ea = 0
3) Radicals react with molecules,
A + BC? A-B + C
If the reaction is a exothermal one,Ea
5% DB-C;
4) Molecules react with molecules:
AB + CD?AC + BD
If the reaction is exothermal,Ea = 30%
(DAB + DCD)
Table half-life of first-order reaction with
different activation energy
Ea on reaction rate
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
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.
Ea ranges between 40 ~ 400 kJ mol-1.
Reaction with Ea less than 80 kJ mol-1
belongs to fast reactions,To study their
kinetics,special method have to be used.
For reaction with Ea larger than 100 kJ
mol-1,it is too slow to study.
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:
RT
E
ATk cm e x p
RT
E
TmAk c lnlnln
22
ln
RT
Em R T
RT
E
T
m
dT
kd cc?
经验公式没有任何物理意义 !
22
ln
RT
Em R T
RT
E
T
m
dT
kd cc?
dT
kd
RTE a
ln2
ca Em R TE
This equation suggests that,Ea depends
on temperature.
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,and in a
relatively small temperature range,Ea
seems independent on temperature.
To measure activation energy of the
reaction over a large span of temperature
would result in exceptional difficulties.
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.
What’s for the next class?
对化学反应的几个解释,
碰撞理论 SCT
过渡态理论 TST
单分子反应理论 RRKM
对反应模型的处理,
复杂反应过程,平行,串级,连续,…
稳态近似
Phenomenological Chemical Kinetics
(empirical/classical)
1,Reaction Rate & Rate Equation
2,Theoretical Consideration – SCT & TST
3,Microscopic Mechanism
与讲过的热力学大不相同,
热力学 动力学过程的可能性过程的自发性过程的可逆性过程的快慢过程的步骤过程的机制方向和程度 速率概念理解 推导
Three characteristics of a chemical
reaction
1) Stoichiometric characteristics,
balance of the equation
2) Thermodynamic characteristics,
Spontaneity and equilibrium
3) Kinetic characteristics,
Rate and mechanism
开放系统
Food
Air
Heat
Work
Electronic
work
Work
Expansion
Heat
How fast? Why different? Kinetics
The factor concerned by thermodynamics
is the inherent tendency or the possibility
of the reaction but not reality and rate.
C (diamond)? C (graphite)
is spontaneous,but it is so slow that
it is not detectable.
Chemical kinetics:
the area of chemistry that concerns
reaction rate.
Main concerns of chemical kinetics:
1) Reaction rate:
the factors that determines the rate of
reaction and rate law,
2) Reaction mechanism:
the series of steps by which a reaction
takes place.
3) structure-dependence of reactivity.
The correlation between molecular
structure and reaction ability.
the detailed way by which the
reactants are converted into
products,or the series of steps by
which a reaction takes place.
Reaction mechanism and elementary
reaction
Reaction mechanism / reaction pathway
H2 + I2 = 2 HI
Kinetic experiments suggest that this
reaction occurring as follows:
1) I2 = 2I
2) 2I + H2 = 2HI
并不是相当然的,
也不是表面的东西
H2 + Br2 = 2 HBr
1) Br2 = 2 Br
2) Br + H2 = HBr + H
3) H + Br2 = HBr + Br
4) H + HBr = H2 + Br
5) 2 Br = Br2
More complicate!
The species as H and Br,formed in
one step and consumed in a subsequent
step and never seen as a product is
called an intermediate.
The reaction that completes in one act
is called elementary reaction.
基元反应 (步骤 )
中间体
The sum of the elementary reactions
and their series is called the
mechanism of the overall reaction
总包反应反应机理
Classification of reactions
1) elementary reactions
According to the number of molecules
involved in the reaction,elementary
reactions can be divided into three kinds:
unimolecular reaction
bimolecular reaction
termolecular reaction.
单分子反应双分子反应三分子反应
unimolecular reaction:
I2 = 2I
bimolecular reaction:
Br + H2 = HBr + H
termolecular reaction:
2I + H2 = 2HI
Because the probability of three
molecules colliding simultaneously is
very small,termolecular reaction are
quite rare.
三体碰撞的几率很小
According to the number of
elementary reactions involved,the
overall reaction can be classified into:
simple reaction
complex reaction
2) overall reactions
简单反应复杂反应
Reaction rates and rate equation
1,Expression of reaction rate
The reaction rate (r) of a chemical
reaction is defined as the change in
concentration of a reactant or product
per unit time.
There are two kinds of reaction rates,
one is the average rate
t
A
r
][
平均速率
The other is the instantaneous rate
defined as:
dt
Ad
r
][
反应速率
N2 + 3H2? 2NH3
dt
dC
r
H
H
2
2
dt
dC
r
N
N
2
2
dt
dC
r
NH
NH
3
3
322 2
1
3
1
NHHN rrr
It is apparent that
When expressed using different species,the
rate of the reaction may attain different
values,which is not convenient and
sometimes may even cause some confusion.
Definition,extent of reaction or the
advancement (?)
i
ii nn
0,?
where?i is the stoichiometric coefficient
of the reaction,
Definition,
The true rate of the reaction (J):
dt
d
J
For general reaction:
aA + bB? gG + hH
When the extent of reaction is d?
h
dn
g
dn
b
dn
a
dn
d HGBA
dt
dn
hdt
dn
gdt
dn
bdt
dn
adt
d
J HGBA
1111
When the reaction takes place in a
container with constant volume
Definition,
V
J
r?
dt
dn
hdt
dn
gdt
dn
bdt
dn
adt
d
J HGBA
1111
dt
Hd
hdt
Gd
gdt
Bd
bdt
Ad
a
r
][1][1][1][1
dt
Cd
r i
i
][1
Unit,mol m-3 s-1
molecule cm-3 s-1
mol L-1 S-1
2,Measurement of reaction rate
i
r
1
Physical meaning:
slope of the C ~ t curve
dt
Cd i ][
C ~ t curve is
usually called
kinetic curve
The rate at a particular time can be obtained by
computing the slope of a line tangent to the curve at
that time point.
动力学曲线
0?
tdt
dC
r
ttdt
dC
r
Initial rate
The key subject of kinetic study is to
measure the concentration of any species
after arbitrary time intervals.
The concentration of the species can be
measured using either chemical methods
or physical ones,
CH3COOC2H5 + NaOH?
CH3COONa + C2H5OH
The reaction can be stopped by removing of
CH3COOC2H5,and the consumption of
NaOH can be determined by chemical
titration.
For example
CH3COOC2H5 + NaOH?
CH3COONa + C2H5OH
the rate of which can be monitored
using pH meter or conductometer.
t = 0 t = t1 t = t
2
The change in physical properties
usually chosen as indicator of progress
of the reaction.
比方说,颜色变化
N2O4? 2NO2
红棕色无色与压缩的速度有关系吗?
The first successful example for measuring
concentration of reactant physically was
made by Wilhelmy in 1850,He determined
the residual concentration of sucrose by
measuring the change of the rotation angle
of a beam of plane-polarized light passing
through the hydrolysis solution.
偏振光方法蔗糖的水解
Polarimeter,旋光光度计
C12H22O11 + H2O?
C6H12O6 (R) + C6H12O6 (L)sucrose
glucose fructose
Substance sucrose glucose fructose
[?]D25 +66.5 o +52 o - 92 o
The rotation angle of the 1:1 mixture of
glucose and fructose is –20 o
N2O5 = N2O4 + 0.5 O2
When this reaction takes place in a
container with constant volume,the rate of
the reaction can be monitored by measuring
the pressure change,And when this reaction
takes place under constant pressure,the
advance of the reaction can be monitored by
measuring the volume increase.
Stretch of
epoxy group
FTIR spectroscopy.
Analyzing methods:
1) Real time analysis
2) Quenching
3) Flow method
The physical parameters usually
used for monitoring reaction process
includes volume,pressure,electric
conductance,pH,refractive index,
thermal conductivity,polarimetry,
spectrometry,chromatography,etc.
Flow method
t = L / V
3,The law of mass action and rate
equation
The concentration-dependence of rate:
r = r(Ci) = r(CA,CB,CC… )
where Ci represents concentration of
individual specie present in rate equation,
质量作用定律
In many instances,the rate of a reaction is
proportional to the concentrations of the
reactants raised to some power.
CBAA CCkC
dt
dC
For example,H2 + I2 = 2 HI
1
2
1
2 ][][ IHkr?
H2 + Cl2 = 2 HCl
5.0
2
1
2 ][][ ClHkr?
where rate coefficient/constant (k) is a
proportional constant independent of
concentration,
The exponent shows the effect of
concentration on the reaction rate,in 1895,
Noyes defined them as partial order of the
reactant.
CBAA CCkC
dt
dC
r
速率常数
,? is the partial order of the
reaction with respect to A or B,
respectively.
5.0
2
1
2 ][][ ClHkr?
This implies that the reaction obeying rate
law is first-order in H2 and 0.5-order in Cl2.
the sum of the partial order n =? +?
+? +… is the overall order of the
reaction,or more simply,the reaction
order.
5.0
2
1
2 ][][ ClHkr?
The overall order is 1.5.
反应级数
2SO2 + O2? 2SO2
2
1
32
3 ]][[2][
SOSOk
dt
SOd
r
is first-order in SO2,-0.5-order in SO3
and 0.5 order overall,
n,?,?,?,etc.,different from the
stoichiometric coefficient,may be
integers,decimals,of plus or
minus values.
For elementary reaction,?=a,?=b,etc.
CBAA CCkC
dt
dC
r
cCbBaAA CCkC
dt
dC
r
Partial order = stoichiometric coefficient
reaction order = number of molecules
involved in the reaction
For example:
2I + H2 = 2HI
][][
][
2
1
2
2 HIk
dt
Id
r
Law of mass action valid only for
elementary reaction
质量作用定律
The overall reaction:
the first-order reaction
the second-order reaction
It was found that reactions with same
reaction order are usually of same
kinetic characteristics,therefore,
reactions are usually classified on the
basis of reaction order.
一级反应二级反应
1
2
1
2 ][][ IHkr?
H2 + I2 = 2 HI
H2 + Cl2 = 2 HCl
5.0
2
1
2 ][][ ClHkr?
H2 + Br2 = 2 HBr
][
][
'1
]][[
2
5.0
22
Br
H B r
k
BrH
kr
Overall
reactions
Reaction with
definite order
Reaction without
definite order
Reaction with
simple order
The purposes of the rate law:
1) Given the composition of the reaction
mixture,the rate law can predict the
reaction rate.
2) Gives clues to the mechanism and testify
the proposed mechanism.
3) To classify reactions on the reaction order.
4,The rate equation of reaction
with simple order
The reaction whose rate only
depends on the concentration of
reactants,and both the partial order
and the reaction order is zero or plus
integer is called reaction with simple
order.
Kinds of reaction with simple order
r = k Cn
n kinds
0 zeroth-order reaction
1 first-order reaction
2 second-order reaction
3 third-order reaction
4.1 the first-order reaction:
Reaction,A? P
C0
C
Differential rate
equation:
Ck
dt
dC
1
can be rearranged into:
Ck
dt
dC
1
dtk
C
dC
1
Which can be integrated directly.
tk
C
C
1
0ln?
The integration rate equation
)ex p ( 10 tkCC
0 1000 2000 3000 4000 5000
0.0
0.2
0.4
0.6
0.8
1.0
C
/
mol
dm
-3
t / s
C~t curve of first-order reaction
)ex p ( 10 tkCC
tkCC 10lnln
The slope of the lnC ~ t curve is
the k1
tk
C
C
1
0ln?
0 1000 2000 3000 4000 5000
-5
-4
-3
-2
-1
0
ln(
C
/m
ol
dm
-3
)
t / s
lnC ~ t curve of the first-order reaction
tkCC 10lnln
tk
C
C
1
0ln?
112
1
6 9 3 2.02ln
kk
t
Half-life
2
0CC?
半衰期
Characteristics of the first-order
reaction
1) Unit of k is s-1
2) lnC is in linear proportion to t
3) Half-life does not depend on C0
Example:
1)Decay of isotopes
2) Decomposition
HeRnRa 422268622688
24252 2
1 OONON
3) Isomerization
1960 Noble Prize
USA
1908/12/17 ~
1980/09/08
Application of 14C for
age determinations
(radiocarbon dating)
Willard F,Libby
4.2 Second-order reaction
2A P
pure second-order reaction
A + B P
mixed second-order reaction
A + B P
a b
CA= a-x CB =b-x
BA
A CCk
dt
dC
2
Differential rate equation:
(a? b)
))((2 xbxak
dt
dx
dtk
xbxa
dx
2))((
tx
dtk
xbxa
dx
0 20 ))((
tx
dtk
xbxa
dx
0 20 ))((
txx
dtk
xaba
dx
xbba
dx
0 200 ))(())((
tk
ba
a
ba
xa
ba
b
ba
xb
2)(
ln
)(
)ln (
)(
ln
)(
)ln (
tk
xba
xab
ba 2)(
)(
ln
)(
1
2
2 Ckdt
dC
When a = b
dtk
C
dCC
C 220
tk
CC
2
0
11
0
20 1
C
C
k C t
2
0
11
kt
CC
0 1000 2000 3000 4000 5000
0.0
0.2
0.4
0.6
0.8
1.0
C / mo
l
dm
-3
t / s
C~t curve of second-order reaction
0
20 1
C
C
k C t
0 1000 2000 3000 4000 5000
0
10
20
30
40
50
1/
C
/ mol dm
-3
t / s
1/C ~ t curve of second-order reaction
2
0
11
kt
CC
tk
CC
2
0
11
02
2/1
1
Ck
t?
Half-life 半衰期
Characteristics of second-order reaction
1) Unit of k is mol-1 m3 s-1
2) 1/C is in linear proportion to t
3) Half-life
02
1
1
C
t?
Increasing the initial concentration of
the reactant will shorten the reaction
time.
For pure second-order reaction
2
22
1
Ck
dt
dC
tk
CC 20
2
11
02
2/1
2
1
Ck
t?
2A P
Example:
1) Dimerization
2) Decomposition
222 IHHI
3) Recombination
6232 HCCH
4) Esterification
OHHC O O CCH
OHHCC O O HCH
2523
523
5) Hydrolysis
C12H22O11 + H2O?
C6H12O6 (R)+ C6H12O6 (L)
In 1850,the experiment done by Wilhelmy
suggested the rate equation of the reaction is:
][ 112212 OHCkr?
]][[ 2112212 OHOHCkr?
C12H22O11 + H2O?
C6H12O6 (R)+ C6H12O6 (L)
Because the amount of water keeps nearly
unchanged during the reaction,[H2O] keeps
nearly constant,and the rate equation
]][[ 2112212 OHOHCkr?
can be then simplified as
][ 112212 OHCkr?
Pesudo first-order reaction 准一级反应
4.3 Third-order reaction
Three kinds of third-order reaction
3A P
A + B + C P
2A + B P
For 3A P
3
33
1
Ck
dt
dC
Differential rate equation
tk
CC
32
0
2
3
11
2
1
Integrated rate equation
tk
CC
32
0
2
6
11
2
032
1
2
1
Ck
t?
For A + B + C P with same initial
concentration
3
3 Ckdt
dC
Differential rate equation
tk
CC
32
0
2
11
2
1
Integrated rate equation
tk
CC
32
0
2
2
11
2
032
1
2
3
Ck
t?
Examples:
2NO + X2? N2O + X2O; X = H,D
2NO + O2? 2NO2;
2NO + X2? 2NOX; X = Br,Cl
r = k [C6H5CHO]2[CN-]
r = k [C2H4O][H+][Br-]
Hydrolysis of sucrose
]][][[ 2112212 HOHOHCkr
During reaction,both [H2O] and [H+]
keep nearly constant and the reaction
behaves as a first-order reaction.
4.4 Zeroth-order reaction
A P
Differential rate equation:
0k
dt
dC
tC
C
dtkdC
0 00
tkCC 00
0
0
2/1
2 k
C
t?
00C k t C
When C = 0,the reaction completes,
the time need is:
0
0
k
C
t?
The zero-order reaction is the only
reaction that can complete.
0 1000 2000 3000 4000 5000
0,0
0,2
0,4
0,6
0,8
1,0
C
/ m
ol d
m
-3
t / s
C ~ t curve for zero-order reaction
00C k t C
Characteristics of zeroth-order reaction
1) Unit of k is mol dm-3 s-1
2) C is in linear proportion to t
3) When C increases,reaction time
will be prolonged.
Examples:
Decomposition over catalysts:
1) 2N2O? 2N2 + O2 over Pt wire
2) 2NH3? N2 + 3H2 over W wire
Photochemical reaction:
r = k I
I,intensity of radiation
4.5 Nth-order reaction
nkCr?
tk
axan nnn
}
1
)(
1
{
1
1
11
1
0
1
0
1
2/1
)1(
12
nn
n
C
A
kCn
t
For n? 1
4.6 Determination of the reaction
order r = k [A]?[B]?[C]?
Whenever we determine the order of a reaction,we can
write out the rate equation of the reaction and tell the
detail of the kinetic characteristics of the reaction
according to the rate equation.
The rate equation can provide useful information
about the mechanism of the reaction,Therefore,
determination of the order of the reaction is a work of
great importance.
Methods for determination of reaction
order
1) Integration method
2) Differential method
3) Partial order method
4) Isolation method
积分法微分法
4.6.1 Integration methods
The integration methods are to use the
integrated rate equation to determine the
order of the reaction.
Integration methods includes:
1) attempt method
2) graphic method
3) half-life method
1)The attempt method:
the values of k1 can be calculated from
the selected integrated equation from a
knowledge of initial concentration (C0) and
the concentration at various time intervals
(C).
If the reaction is of the selected order of
reaction,the k at different intervals thus
obtained will be the same.
尝试法
A + B? P
C2H5ONa + C2H5(CH3)2SI?
NaI + C2H5O C2H5 + S(CH3)2
r = k[C2H5ONa]?[C2H5(CH3)2SI]?
r = k [A]?[B]?
t/s 102[A]/ mol dm-3 102[B] / mol dm-3
0 9.625 4.920
720 8.578 3.878
1200 8.046 3.342
1800 7.485 2.783
2520 6.985 2.283
3060 6.709 2.005
3780 6.386 1.682
4.704
Table 1,kinetic data for C2H5ONa + C2H5(CH3)2SI at
337.10 K
t?=0?=1?=0?=2?=0?=1
=0?=0?=1?=0?=2?=1
k 105 104 104 103 103 103
0 1.454 1.599 3.313 1.764 7.579 3.642
720 1.108 1.143 3.088 1.604 7.357 3.678
1200 0.935 1.205 3.051 1.550 10.02 3.760
1800 1.042 0.960 2.751 1.333 10.93 3.773
2520 0.511 0.747 2.405 1.093 11.11 3.731
3060 0.449 0.685 2.440 1.042 13.32 3.729
Table 2,k of the reaction of different order
r = k[C2H5ONa][C2H5(CH3)2SI]
Therefore,the rate equation is:
1) The attempt method is a laborious method
2) For reaction without simple order,it is
impossible to ascertain reaction order using
this method.
3) the experimental error may cause confusion
sometimes,Not good yet!
2) The graphic method
the linear relationship of reaction with
different order is different.
order Linear relationship
zeroth C ~ t
first lnC ~ t
second 1/C ~ t
third 1/C2 ~ t
作图法
t / s C / mol dm-3 t / s C / mol dm-3
0 1.000 3000 0.050
500 0.606 3500 0.030
1000 0.368 4000 0.018
1500 0.223 4500 0.011
2000 0.135 5000 0.007
2500 0.082
Table 3,kinetic data for A? P.
The rate equation of A? P can be expressed as
r = k[A]?
0 1000 2000 3000 4000 5000
0,0
0,2
0,4
0,6
0,8
1,0
C
/ m
ol d
m
-3
t / s
0 1000 2000 3000 4000 5000
-5
-4
-3
-2
-1
0
ln (C
/
mol
dm
-3
)
t / s
一级反应
0 1000 2000 3000 4000 5000
0
40
80
120
160
1/
C(/
mo
l dm
-3
)
t / s
0 1000 2000 3000 4000 5000
0
20
40
60
80
100
1 / C
2
t / s
3) half-life method
the half-life of the reaction is proportional
to the initial concentration of the reactant
nkCt 1
02/1
02/1 ln)1(lnln Cnkt
半衰期法斜率
-5 -4 -3 -2 -1 0 1
3
4
5
6
7
8
9
10
ln t
1/2
lnC
0
k = - 1
02/1 ln)1(lnln Cnkt
(1-n) = - 1
n = 2
Therefore,the reaction is of second order.
Graphic method
02/1 ln)1(lnln Cnkt
Calculation
'ln)1(ln'ln 02/1 Cnkt
'
ln
'
ln
1
0
0
2/1
2/1
C
C
t
t
n
C0/mol dm-3 0.05 0.10 0.20
t1/2/h 37.03 19.15 9.45
NH4OCN? CO(NH2)2
'
ln
'
ln
1
0
0
2/1
2/1
C
C
t
t
n
n1 = 2.051,n2 = 2.019
n = 2.035? 2
4.6.2 Differential method
Use the differential form of the rate
equation to determine the order of the
reaction.
nkC
dt
dC
r
Cnkr lnlnln
斜率
Graphic method
Decomposition
percentage
0 5 10 15 20
r / Pa min-1 1137 998.4 898.4 786.5 685.2
Decomposition
percentage
25 30 35 40 45
r / Pa min-1 625.2 574.5 500.0 414.6 356.0
Table 1,Decomposition of CH3CHO?CH4+CO.
3,8 4,0 4,2 4,4 4,6 4,8
5,5
6,0
6,5
7,0
ln
r
/
P
a m
in
-1
ln C / mol dm
-3
ln r = -1.593 + 1.865 ln C
Linear fitting results:
ln r = -1.593 + 1.865 ln C
Linear correlation coefficient,0.998
Therefore,the order of the reaction is 2.
Determination of reaction order through one
experiment.
Reaction
order with
respect to
time,nt
0
0
lnln
ln
Cnk
r t
Determination of reaction order through
several parallel experiments.
Reaction order
with respect to
concentration,
nC
The method of initial rates is applicable
of a wide variety of reactions.
This method is particularly useful in
reactions that are complicated by
processes involving intermediate or
products.
calculation method
'lnln'ln Cnkr
Cnkr lnlnln
'
ln
'
ln
C
C
r
r
n
t
'
ln
'
ln
0
0
0
0
C
C
r
r
n
C
Decomposition
percentage
0 5 10 15 20
r / Pa min-1 1137 998.4 898.4 786.5 685.2
Decomposition
percentage
25 30 35 40 45
r / Pa min-1 625.2 574.5 500.0 414.6 356.0
nt= 2.534; 1.952; 2.327; 2.274
nt = 2.272? 2
= nt Both intermediate and product do not affect the reaction
nC > nt Intermediate or product catalyze the reaction
< nt Intermediate or product inhibit the reaction
Table 2,Relationship between nC and nt.
r = k[A]?[B]? n =?+?
r = k[A]?[B]?[M]? n =?+?+?
4.6.3 Partial order method
CB
a
A CCkCr?
CCCkr BA lnlnlnlnln
)lnln( l nlnln CBA CCCkr
To plot lnr versus lnCA,if a linear relation
can obtained,? = 0,?=0,
If no linear relation can be observed,
adjust the value of? and? until a line can
be obtained,The slope of this line is?,and
the corresponding value of? and? can be
obtained simultaneously.
4.6.4 The isolation method
CBA CCCkr lnlnlnlnln
CBA CCCkr lnln'lnln'ln
A
A
C
C
r
r
'
ln
'
ln
When CB and CC were controlled
固定浓度法
Three methods,
1) Fixation of concentration method;
2) Excess concentration method;
3) Application of stoichiometric ratio
1) fix the concentration of other reactants
Rate equation of 2NO + 2H2? N2 + 2H2O
is r = k[NO]? [H2]?.
No,Initial pressure / Pa Initial rate
NO H2
1 50662.5 20265 486.36
2 50662.5 10132.5 243.18
3 25331.25 20265 121.59
2) Excess concentration
C12H22O11 + H2O?
C6H12O6 + C6H12O6
]][[ 2112212 OHOHCkr?
][' 112212 OHCkr?
过量浓度法
make the concentration of B and C very
much larger than that of A。
This technique is particularly useful in
determining rate constants for reactions
involving water in aqueous solution,
Pseudo order reaction.
准一级反应
3) Using stoichiometric ratio
aA + bB? P
Initial concentration 1 b/a
Conversion concentration x bx/a
Residual concentration 1-x (b/a)(1-x)
r = k[A]? [B]? = k (b/a)?(1-x)?+?
=k (b/a)?(1-x) n
Temperature-dependence of rate
-- Arrhenius equation
From the middle of 19 century,people
began to study the effect of temperature
on the reaction rate,Many empirical
relations have been founded.
温度依赖关系
Types of rate-temperature curves
Type I:
k increase
exponentially with
T,this kind of
curve can be
observed in most
of the reactions,
指数上升
Type II
This kind of k~T
relation was
observed in
thermal explosions,
At ignition
temperature,the
rate constant
makes a sharp
increase,
热爆炸
Type III
Type III is
usually
encountered in
the catalytic
reaction that
has an optimum
temperature,
催化过程
Type IV:
can be
observed in the
oxidation of
carbon and
gaseous
oxidation of
hydrocarbons,
复杂变化
Type V,
Many radical-
radical reactions
such as CH3+CH3,
O+CH3,etc.
负温度效应
Arrhenius equation
It was found that for homogeneous
reaction,an important generalization is
that reaction rate double or treble for
every 10 degree increase in temperature.
异相反应,温度每升高 10 K,
反应速率增加 2-3倍
Vant’ Hoff Law
3~210
T
T
k
k
B
T
A
dT
kd
2
ln
in which A and B are experimental / empirical
constants,
In 1889,Arrhenius made detailed
theoretical consideration on the hydrolysis
of sucrose.
C12H22O11 + H2O?
C6H12O6 + C6H12O6
Sucrose molecules were surrounded by water,
if all sucrose molecules could react directly with
water,the reaction should completed instantly.
Arrhenius concluded that only a small
part of sucrose molecules with higher
energy (activated molecules) can react
with water and,therefore,the reaction
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,活化能活化分子
2
ln
RT
E
dT
kd a
Arrhenius extended the ideas of Vant’
Hoff and suggested a similar empirical
equation.
Defined the activation energy (Ea)
dT
kd
RTE a
ln2
The first definition of activation energy,
experimental activation energy
活化能
If Ea is independent on temperature,
integration of the equation
2
ln
RT
E
dT
kd a
yields
A
RT
E
k a lnln
RT
E
Ak ae x p
A is the pre-exponential factor which
has the same unit as the rate constant.
指前因子
Arrhenius equation
2
ln
RT
E
dT
kd a
A
RT
E
k a lnln
RT
E
Ak ae x p
In these five r ~ T relation type,only
the type I obey the Arrhenius
equation,Type I is usually named as
Arrhenius type.
Experimental measurement
activation energy
Important kinetic parameters:
rate constant,reaction order
activation energy,pre-exponential factor
速率常数,反应级数,
活化能,指前因子
1) experimental measurement:
A
RT
E
k a lnln
(1) graphic method
(2) calculation method
graphic method:
to plot lnk against 1/T,for the reaction
of Arrhenius type,a straight line may be
obtained,the slope of which equaling to
–Ea/R
ClCOOCH3 + H2O? CO2 + CH3OH + H+ + Cl-
T / K 273.72 278.1
8
283.18 288.14
104 k / s-1 0.4209 0.701
6
1.229 2.087
T / K 198.18 308.1
6
318.29
104 k / s-1 5.642 14.05 32.65
3,0x 10
-3
3,2x 10
-3
3,4x 10
-3
3,6x 10
-3
3,8x 10
-3
-11
-10
-9
-8
-7
-6
-5
ln k
(/s
-1
)
1 / T (/K )
06.21
1
9.8515ln
T
k
A
RT
E
k a lnln
R = 0.99992
Ea = 70.80 kJ mol-1,A =1.32? 109
(2) calculation method,
A
RT
E
k a lnln
1
1
A
RT
E
k a lnln
2
2
212
1 11ln
TTR
E
k
k a
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
212
1 11ln
TTR
E
k
k a
Before reaction,molecules must be
activated.
Only the collision of activated molecules
can lead to reaction,while the collisions
between molecules that are not activated
will be of no use and thus no reaction will
take place.
Definition of Ea
活化分子反应的分子需要能量
The minimum energy that the molecules
must absorb before the reaction can take
place is known as the activation energy.
EEE a *
活化能
Boltzmann distribution
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:
EEE a *
Ea and energy change of reaction
Raa UUE,
Paa UUE,
reactant,product,
activated state,
reaction path,
反应途径
,,aa EEU
When Ea,->Ea,+,?U < 0,the reaction is a
exothermic one.
UUUEE RPaa,,
the difference in internal energy
,,aa EEU
When Ea,-< Ea,+,?U
> 0,the reaction is
a endothermic one.
For a strong endothermic reaction,its activation
energy for backward reaction is very small.
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 reaction,usually named as
apparent activation,may be meaningless
physically.
According to the principle of micro-reversibility,
the forward reaction and the backward reaction
pass through the same activated state.
Theoretical evaluation:
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
2) combination reaction of radicals
2 CH3·? CH3CH3
Ea = 0
3) Radicals react with molecules,
A + BC? A-B + C
If the reaction is a exothermal one,Ea
5% DB-C;
4) Molecules react with molecules:
AB + CD?AC + BD
If the reaction is exothermal,Ea = 30%
(DAB + DCD)
Table half-life of first-order reaction with
different activation energy
Ea on reaction rate
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
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.
Ea ranges between 40 ~ 400 kJ mol-1.
Reaction with Ea less than 80 kJ mol-1
belongs to fast reactions,To study their
kinetics,special method have to be used.
For reaction with Ea larger than 100 kJ
mol-1,it is too slow to study.
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:
RT
E
ATk cm e x p
RT
E
TmAk c lnlnln
22
ln
RT
Em R T
RT
E
T
m
dT
kd cc?
经验公式没有任何物理意义 !
22
ln
RT
Em R T
RT
E
T
m
dT
kd cc?
dT
kd
RTE a
ln2
ca Em R TE
This equation suggests that,Ea depends
on temperature.
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,and in a
relatively small temperature range,Ea
seems independent on temperature.
To measure activation energy of the
reaction over a large span of temperature
would result in exceptional difficulties.
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.
What’s for the next class?
对化学反应的几个解释,
碰撞理论 SCT
过渡态理论 TST
单分子反应理论 RRKM
对反应模型的处理,
复杂反应过程,平行,串级,连续,…
稳态近似
