The rate theory of unimolecular
reaction
单分子反应速率理论
Mechanism of Complex Reactions
复杂反应
SCT,TST ----- bimolecular reaction
collide with each other
双分子反应 ----- 碰撞
Unimolecular reaction?
单分子反应,HOW?
At early 19th century,of first-order.
History:
Single molecule at ground state will not undergo
any reaction
how do reactant molecules attain necessary
energy of activation
In 1919,Perrin – radiation activation theory.
problem,radiation from the wall is not
high enough.
of second-order at low pressure,first-
order at high pressure.
have to be
“collision”
1921,Christiansen
In 1922,Lindemann and Christiansen,The activated
molecules react long after the collision,There is a time
lag between activation and reaction.
some of them may lose their energy due to the further
collision (deactivation),Only part of the activated
molecules can form product.
时滞碰撞活化一部分失活 (稳定化 )
一部分反应 (产物 )
A + M A* + Mk1
k-1
P
k2
Lindemann mechanism
][
][ *
2
*
Ak
dt
Ad
r
stationary-state approximation 稳态近似处理短寿命的“中间体”,
浓度不随时间变化
0
][ *
dt
Ad
A + M A* + Mk1
k-1
P
k2
Lindemann mechanism
*
**
1 1 2
[] [ ] [ ] [ ] [ ] [ ] 0dA k A M k A M k A
dt?
21
1*
][
]][[
][
kMk
MAk
A
21
21
][
]][[
kMk
MAkk
r
][
][ *
2
*
Ak
dt
Ad
r
Case I,pressure is low enough,
21 ][ kMk
21
21
][
]][[
kMk
MAkk
r
]][[1 MAkr?
碰撞失活 远小于 反应二级反应
Case II,High pressure
21 ][ kMk
21
21
][
]][[
kMk
MAkk
r
12
1
[ ] [ ]
[]
[]
k k A M
kM
kA
高压,碰撞失活 远大于 反应一级反应高压限速率常数
]][[1 MAkr?
][ Akr
21
21
][
]][[
kMk
MAkkr
1956 Noble Prize
Mechanisms of chemical
reactions
Sir Cyril N,Hinshelwood Rudolph A,Marcus
1992 Noble Prize
Theories of electron
transfer
RRKM theory,1930 ~ 1950
Rice-Ramsperger-Kassel-Marcus
A + M A* + Mk1
k-1
A* A? Pk2 k?
E*
RRKM
Model complex reactions
reaction contains more than one
elementary reactions
1) Opposing Reaction
2) Parallel Reaction
3) Consecutive Reaction
对峙反应平行反应连续反应
aA + bB gG + hH
k+
k-
ba BAkr ][][
hg HGkr ][][
Opposing Reaction
reversible reactionmajority of the reactions are reversible,i.e.,the forward
and the backward / reverse reaction take place
simultaneously.
hgba HGkBAk ][][][][
ba
hg
BA
HG
k
k
][][
][][?
cK?
k
k
K
c
kinetic equilibrium constant
平衡常数 速率常数
For first-first order opposing reaction,
示例,
A Bk+k-
t = 0 a 0
t = t a-x x
t = te a-xe xe
xkxak
dt
dx
)(
ee xkxak )(
e
e
x
xak
k
)(?
x
x
xa
kxak
dt
dx
e
e )()(
e
e
x
xx
ak
dt
dx )(?
)(
ln
xx
x
at
x
k
e
ee
)(
ln
xx
x
at
xa
k
e
ee
)(
ln
1
xx
x
t
kk
e
e
kttkk
xx
x
e
e
)(
)(
ln
Similar to the rate equation of first-
order reaction
Parallel reaction
Competing reaction
C2H5OH
C2H4 + H2O
C2H5OC2H5 + H2O
(CH3)2CO
HCHO + CH4
C2H4 + CO
竞争反应
A
B
C
k1
k2
][][ 1 Ak
dt
Bd? ][][
2 Akdt
Cd?
1 2 1 2
() ( ) ( ) ( ) ( )d a x k k a x k a x k a x
dt
))(( 21 xakk
dt
dx
21 kk
When
)(1 xak
dt
dx
When
21 kk )(
2 xakdt
dx
The rate of parallel reaction is
determined by the faster one.
A
B
C
k1
k2
A B C
a 0 0
a-x y z
x = y + z
)(1 xak
dt
dy
])(e x p [)( 21 tkkaxa
])(e x p [ 211 tkkak
dt
dy
]})(e x p [1{ 21
21
1 tkk
kk
ak
y
]})(e x p [1{ 21
21
2 tkk
kk
akz
]})(e x p [1{ 21
21
1 tkk
kk
aky
])(e x p [)( 21 tkkaxa
2
1
k
k
z
y
also indicates the selectivity of the
reaction,
The composition of the
products is fixed.
反应的分支比
A
B
C
k1
k2
Main reaction
k is of much larger value.
Side reaction
主反应副反应
The selectivity of the parallel reaction
can be improved by using catalyst,
FeCl3
Consecutive reaction
Some reactions proceed through the
formation of an intermediate.
CH4 + Cl2 CH3Cl CH2Cl2
CHCl3 CCl4
连续反应
A B Ck1 k2
A B C
t = 0 a 0 0
t = t x y z
a = x + y + z
xk
dt
dx
1? tk
x
a
1ln?
)e x p ( 1 tkax
ykxk
dt
dy
21
yktkak
dt
dy
211 )e x p (
)e x p ()e x p ( 21
12
1 tktk
kk
aky
yk
dt
dz
2?
)e x p ()e x p (1 2
12
1
1
12
2 tk
kk
ktk
kk
kaz
tmax
a
)e x p ()e x p ( 21
12
1 tktk
kk
ak
y
)e x p ()e x p ( 21
12
1 tktk
kk
ak
y
0?
dt
dy
21
21
m a x
)/ln (
kk
kk
t
)e x p ()e x p (1 2
12
1
1
12
2 tk
kk
ktk
kk
kaz
)e x p ()e x p ( 21
12
21 tktk
kk
kak
dt
dC
if k2 >> k1
)e x p ( 11 tkakdtdC
The total rate only determined by k1
)e x p ( 22 tkakdtdC
if k2 << k1
The total rate only determined by k2
The rate of the overall consecutive
reaction is seen to depend only on the
smaller rate coefficient.
速率常数小的反应步骤决定了总反应的快慢 !
The step with the slowest rate is called the
rate-determining step (r,d,s.),速控步
!!It’s a r.d.s
patient !
Establishment of mechanism
collection of information
Setup of possible mechanism
Verification and modification
H C lClH 222
2
1
22 ]][[ ClHkr?
例子,
从何而来?
2
2
2
2
4
3
2
1
2
2
ClCl
ClH C lClH
HH C lHCl
ClCl
k
k
k
k
]][[]][[ 2322 ClHkHClk
dt
d H C l
2 2 3 2
[] [ ] [ ] [ ] [ ] 0dH k Cl H k H Cl
dt
2
1 2 2 2 3 2 4
[] 2 [ ] [ ] [ ] [ ] [ ] 2 [ ]
0
d C l k C l k C l H k H C l k C l
dt
稳态近似
0][2][2 2421 ClkClk
0]][[]][[][ 2322 ClHkHClkdtHd
2
1
2
4
1 ][][ Cl
k
kCl?
]][[2
]][[]][[
22
2322
HClk
ClHkHClk
dt
d H C l
2
1
22
4
1
2 ]][[2
][
ClH
k
k
k
dt
H C ld
2
1
22 ]][[ ClHkr?
is just in the same form of the experimental rate equation
4
1
2 k
k
kk?
The evidence for a mechanism is often indirect,and
there is always the possibility that a different
mechanism is also in accord with all the facts about
the kinetics of the reaction.
Whether or not a proposed mechanism is correct
depends on the certification of experimental results.
猜测反应机理的不确定性
Many efforts have to be made to
construct the mechanism
building,unfortunately,this
build may collapse over night on
any new finding of opposite
experimental fact.
需小心为之 !
需实验检验 !
H2 + Br2 2HBr
Its rate equation is established by M,
Bodenstein and S,C,Lind in 1906,
Exercise:
2
2/1
22
][
1
]][[][
Br
H B r
m
BrHk
dt
H B rd
考试啦！?
课堂表现,10
作业,15
期中,30
期末,45
试卷：
自估得分选做题点名到者,10 分 +
未到者,5分
reaction
单分子反应速率理论
Mechanism of Complex Reactions
复杂反应
SCT,TST ----- bimolecular reaction
collide with each other
双分子反应 ----- 碰撞
Unimolecular reaction?
单分子反应,HOW?
At early 19th century,of first-order.
History:
Single molecule at ground state will not undergo
any reaction
how do reactant molecules attain necessary
energy of activation
In 1919,Perrin – radiation activation theory.
problem,radiation from the wall is not
high enough.
of second-order at low pressure,first-
order at high pressure.
have to be
“collision”
1921,Christiansen
In 1922,Lindemann and Christiansen,The activated
molecules react long after the collision,There is a time
lag between activation and reaction.
some of them may lose their energy due to the further
collision (deactivation),Only part of the activated
molecules can form product.
时滞碰撞活化一部分失活 (稳定化 )
一部分反应 (产物 )
A + M A* + Mk1
k-1
P
k2
Lindemann mechanism
][
][ *
2
*
Ak
dt
Ad
r
stationary-state approximation 稳态近似处理短寿命的“中间体”,
浓度不随时间变化
0
][ *
dt
Ad
A + M A* + Mk1
k-1
P
k2
Lindemann mechanism
*
**
1 1 2
[] [ ] [ ] [ ] [ ] [ ] 0dA k A M k A M k A
dt?
21
1*
][
]][[
][
kMk
MAk
A
21
21
][
]][[
kMk
MAkk
r
][
][ *
2
*
Ak
dt
Ad
r
Case I,pressure is low enough,
21 ][ kMk
21
21
][
]][[
kMk
MAkk
r
]][[1 MAkr?
碰撞失活 远小于 反应二级反应
Case II,High pressure
21 ][ kMk
21
21
][
]][[
kMk
MAkk
r
12
1
[ ] [ ]
[]
[]
k k A M
kM
kA
高压,碰撞失活 远大于 反应一级反应高压限速率常数
]][[1 MAkr?
][ Akr
21
21
][
]][[
kMk
MAkkr
1956 Noble Prize
Mechanisms of chemical
reactions
Sir Cyril N,Hinshelwood Rudolph A,Marcus
1992 Noble Prize
Theories of electron
transfer
RRKM theory,1930 ~ 1950
Rice-Ramsperger-Kassel-Marcus
A + M A* + Mk1
k-1
A* A? Pk2 k?
E*
RRKM
Model complex reactions
reaction contains more than one
elementary reactions
1) Opposing Reaction
2) Parallel Reaction
3) Consecutive Reaction
对峙反应平行反应连续反应
aA + bB gG + hH
k+
k-
ba BAkr ][][
hg HGkr ][][
Opposing Reaction
reversible reactionmajority of the reactions are reversible,i.e.,the forward
and the backward / reverse reaction take place
simultaneously.
hgba HGkBAk ][][][][
ba
hg
BA
HG
k
k
][][
][][?
cK?
k
k
K
c
kinetic equilibrium constant
平衡常数 速率常数
For first-first order opposing reaction,
示例,
A Bk+k-
t = 0 a 0
t = t a-x x
t = te a-xe xe
xkxak
dt
dx
)(
ee xkxak )(
e
e
x
xak
k
)(?
x
x
xa
kxak
dt
dx
e
e )()(
e
e
x
xx
ak
dt
dx )(?
)(
ln
xx
x
at
x
k
e
ee
)(
ln
xx
x
at
xa
k
e
ee
)(
ln
1
xx
x
t
kk
e
e
kttkk
xx
x
e
e
)(
)(
ln
Similar to the rate equation of first-
order reaction
Parallel reaction
Competing reaction
C2H5OH
C2H4 + H2O
C2H5OC2H5 + H2O
(CH3)2CO
HCHO + CH4
C2H4 + CO
竞争反应
A
B
C
k1
k2
][][ 1 Ak
dt
Bd? ][][
2 Akdt
Cd?
1 2 1 2
() ( ) ( ) ( ) ( )d a x k k a x k a x k a x
dt
))(( 21 xakk
dt
dx
21 kk
When
)(1 xak
dt
dx
When
21 kk )(
2 xakdt
dx
The rate of parallel reaction is
determined by the faster one.
A
B
C
k1
k2
A B C
a 0 0
a-x y z
x = y + z
)(1 xak
dt
dy
])(e x p [)( 21 tkkaxa
])(e x p [ 211 tkkak
dt
dy
]})(e x p [1{ 21
21
1 tkk
kk
ak
y
]})(e x p [1{ 21
21
2 tkk
kk
akz
]})(e x p [1{ 21
21
1 tkk
kk
aky
])(e x p [)( 21 tkkaxa
2
1
k
k
z
y
also indicates the selectivity of the
reaction,
The composition of the
products is fixed.
反应的分支比
A
B
C
k1
k2
Main reaction
k is of much larger value.
Side reaction
主反应副反应
The selectivity of the parallel reaction
can be improved by using catalyst,
FeCl3
Consecutive reaction
Some reactions proceed through the
formation of an intermediate.
CH4 + Cl2 CH3Cl CH2Cl2
CHCl3 CCl4
连续反应
A B Ck1 k2
A B C
t = 0 a 0 0
t = t x y z
a = x + y + z
xk
dt
dx
1? tk
x
a
1ln?
)e x p ( 1 tkax
ykxk
dt
dy
21
yktkak
dt
dy
211 )e x p (
)e x p ()e x p ( 21
12
1 tktk
kk
aky
yk
dt
dz
2?
)e x p ()e x p (1 2
12
1
1
12
2 tk
kk
ktk
kk
kaz
tmax
a
)e x p ()e x p ( 21
12
1 tktk
kk
ak
y
)e x p ()e x p ( 21
12
1 tktk
kk
ak
y
0?
dt
dy
21
21
m a x
)/ln (
kk
kk
t
)e x p ()e x p (1 2
12
1
1
12
2 tk
kk
ktk
kk
kaz
)e x p ()e x p ( 21
12
21 tktk
kk
kak
dt
dC
if k2 >> k1
)e x p ( 11 tkakdtdC
The total rate only determined by k1
)e x p ( 22 tkakdtdC
if k2 << k1
The total rate only determined by k2
The rate of the overall consecutive
reaction is seen to depend only on the
smaller rate coefficient.
速率常数小的反应步骤决定了总反应的快慢 !
The step with the slowest rate is called the
rate-determining step (r,d,s.),速控步
!!It’s a r.d.s
patient !
Establishment of mechanism
collection of information
Setup of possible mechanism
Verification and modification
H C lClH 222
2
1
22 ]][[ ClHkr?
例子,
从何而来?
2
2
2
2
4
3
2
1
2
2
ClCl
ClH C lClH
HH C lHCl
ClCl
k
k
k
k
]][[]][[ 2322 ClHkHClk
dt
d H C l
2 2 3 2
[] [ ] [ ] [ ] [ ] 0dH k Cl H k H Cl
dt
2
1 2 2 2 3 2 4
[] 2 [ ] [ ] [ ] [ ] [ ] 2 [ ]
0
d C l k C l k C l H k H C l k C l
dt
稳态近似
0][2][2 2421 ClkClk
0]][[]][[][ 2322 ClHkHClkdtHd
2
1
2
4
1 ][][ Cl
k
kCl?
]][[2
]][[]][[
22
2322
HClk
ClHkHClk
dt
d H C l
2
1
22
4
1
2 ]][[2
][
ClH
k
k
k
dt
H C ld
2
1
22 ]][[ ClHkr?
is just in the same form of the experimental rate equation
4
1
2 k
k
kk?
The evidence for a mechanism is often indirect,and
there is always the possibility that a different
mechanism is also in accord with all the facts about
the kinetics of the reaction.
Whether or not a proposed mechanism is correct
depends on the certification of experimental results.
猜测反应机理的不确定性
Many efforts have to be made to
construct the mechanism
building,unfortunately,this
build may collapse over night on
any new finding of opposite
experimental fact.
需小心为之 !
需实验检验 !
H2 + Br2 2HBr
Its rate equation is established by M,
Bodenstein and S,C,Lind in 1906,
Exercise:
2
2/1
22
][
1
]][[][
Br
H B r
m
BrHk
dt
H B rd
考试啦！?
课堂表现,10
作业,15
期中,30
期末,45
试卷：
自估得分选做题点名到者,10 分 +
未到者,5分
