对化学反应的几个解释,
碰撞理论 SCT
过渡态理论 TST
对反应模型的处理,
复杂反应过程,平行,串级,连续,…
稳态近似
In this class,
The last class,
Theories of elementary reaction
Simple Collision theory (SCT)
for bimolecular reactions
Transition state theory (TST)
for bimolecular reactions
Two important empirical rule,
Rate equation (rule of mass action)
Arrhenius equation
RT
E
Ak ae x p
Type of
reaction
Unimolecular
reaction
Bimolecular
reaction
Termolecular
reaction
A 1013
s
1011
mol-1 dm3 s-1
109
mol-2 dm6 s-1
A seems related to collision frequency.
RT
E a
e x p
Boltzmann distribution term
It is obvious that a molecule of A cannot react
with a molecule of B unless the two reactant
molecules can somehow interact,
This interaction can only take place if they
come within a certain distance of each other,i.e.,
collides with each other.
Basic Idea:
相互作用 碰撞 (不一定接触 )
During 1920s,M,Trautz,W,Lewis,C,Hinshelwood
et al,finally established a theory based on the collision,
which is called the simple collision theory,
A reaction can take place only if the molecules of the
reactants collide,Therefore,the rate constant of the
reaction may be predicted by calculation of the
collision frequency of the reactants.
The fundament of SCT
The premise of reaction is the collision between
reactants,
The reaction rate of reaction is proportional to the
collision frequency (Z);
Not all the collision is effective,The collision can
be either non-reactive (elastic) collision or reactive
collision,
Only the molecules posses energy excess to a
critical value (Ec) can lead to reactive collision,
The reaction rate of reaction is proportional to the
collision frequency (Z);
qZr AB?
kinetic theory of gases
SCT assumes that the molecules can be taken as
rigid ball without inner structure,
dA dB
dA and dB are the diameter of A and B molecule,
respectively,
B不动
AB
BA ddd
2
Definition,
mean collision diameter,dAB
Definition,
collision cross-section 2ABdS
2
ABAB dZ V
N B
A?
A?
V
NBmotionless
When the concentration of A is NA/V (molec,M-3):
2
ABAB dZ V
N
V
N BA
A?
“碰撞数”,碰撞频率,
B不动
When both A and B moves,the
relative velocity VAB should be used.
22 BAAB
i
i
M
RT
8
“最可几速率,
RT
AB
8
BA
BA
MM
MM
BA
BA
BA
AB MM
MMRT
M
RT
M
RT?
888
(reduced mass)
]][[
8
8
8
22
2
2
BA
RT
dL
V
Ln
V
LnRT
d
V
N
V
NRT
dZ
AB
BA
AB
BA
ABAB
Decomposition of HI:
2 HI = H2 + I2
222 ][8
2
2
A
M
RT
dLZ
A
AAAA
]][[
822
BA
RT
dLZ ABAB
At 1.01325? 105 Pa and 700 K,d = 3.50
10-10 m,Z HI-HI =?
Example:
3
11
5
41.17
700314.8
1001325.1
][
m o lm
Km o lJK
Pa
RT
P
HI
1334
2
3
210223
222
10017.1
)41.17(
101281 4 1 6.3
700314.88
)1050.3()1002.6(1 4 1 6.3
2
2
][
8
2
2
sm
A
M
RT
LZ
A
AAAA
Generally,ZAB of gaseous
reactions at ambient temperature
and pressure is of the magnitude
of 1035 m-3 s-1.
每秒碰撞大约 1011次
If reaction takes place whenever the
molecules collides:
]][[822 BARTdLZ ABAB
AB
A
ZL
dt
Ad
dt
V
Nd
r
][ ]][[
][ BAk
dt
Ad
RT
Ldk AB
82
k = 7.88?104 mol-1 dm3 s-1
When C0 = 1.00 mol dm-3,the half-life of HI is 1.27?
10-5 s,this result differs great from the experimental
fact.
In 1909,Max Trantz introduced fraction of reactive
collision (q) to explain the great discrepancy,
Only the molecules posses energy excess to a
critical value (Ec) can lead to reactive collision.
Translational energy of motion,is related to the relative
motion of two molecules,And Ec is thus the minimum
translational energy of motion along the connect line between
the mass-point of the two molecules which are to collide,
If the energy exchange between colliding
molecules is much rapid than reaction,the
energy distribution of molecules may still
obey the Maxwell-Boltzmann distribution
equation.
The fraction of the collision with the energy
equal to or greater than Ec is:
RT
E
n
nq ce x p* Boltzmann factor
If Ec = 120 kJ mol-1,T = 300,then
q = 1.27? 10-21
This suggest than among 7.8? 1020
collision only one collision is effective.
例,
RT
ERT
Ldk cABS C T e x p
82
RT
EBTk c
S C T e x p
2
1
RT
EAk ae x p
ca ERTE 2
1
RT
ER T e
Ldk aABS C T e x p
82
R T e
LdA AB
82
The pre-exponential factor corresponds to the
collision frequency,This is the reason why A is also
named as frequency factor.
SCT gives a vivid physical image of the
reaction process:
In fact,the reactant molecule is of complex molecular
structure,To take reactant molecules as rigid balls
without inner structure will spontaneously result in
systematic error.
NOBr
Reactive
Non Reactive
The colliding molecules might not be
suitably oriented for reaction.
CH3+CHCl3?CH4+CCl3
取向问题
RT
E
PAk aS C T e x p
Steric factor (P),ranging between 1~10-9,
represents the fraction of energetically
suitable collisions for which the
orientation is also favorable.
Transition state theory (TST) for
bimolecular reactions
A + B-C? A-B + C
During reaction,massive changes of form are
occurring,energies are being redistributed among
bonds,old bonds are being ripped apart and new
bonds formed.
This process can be generalized as:
A + B-C [A B C] A-B + C
Activated complex
Transition state
H+ H–H? H– – –H– –H
H– –H– –H (activated state)
H–H– – –H? H–H + H
Whether or not the energy change of the
reaction can be used to explain the
reaction on the basis of thermodynamics?
热力学?
The transition state theory (TST) of
reaction rates,also known as the Theory
of Absolute reaction Rates or activated
complex theory,attempting to explain
rates on the basis of thermodynamics,was
developed by H,Eyring and M,Polanyi
during 1930-1935.
过渡态理论
TST treated the reaction rate from a
quantum mechanical viewpoint involves
the consideration of intramolecular
forces and intermolecular forces at the
same time.
According to the TST,before undergoing
reaction,molecules of the reactants must
form an activated complex which is in
thermodynamic equilibrium with the
molecules of the reactants.
The activated complexes,the energy of
which is higher than both reactants and
products,is treated as an ordinary
molecule except that it has transient
existence and decomposes at a definite
rate to form the product.
Potential energy surfaces
a potential energy which is the function
of interatomic distance,
The function can be obtained by solving
Schr?dinger equation for a fixed nuclear
configuration,i.e.,Born-Oppenheimer
approximation.
势能面
Contour diagram
of the potential
energy surface
反应途径
Saddle,鞍点
C
A
B
valley
valleySaddle point
A+B-C A-B+C
A
B
C
Reaction takes place along route C,route C is the
reaction path or reaction coordination.
Activated complex has no recovery force.
On any special vibration (asymmetric
stretching),it will undergo decomposition.
Whenever the system attain saddle point,
it will convert to product with no return.
Saddle point = point of no return
Kinetic Treatment
For reaction:
A + B AB P
ABCr?
BA
AB
CC
CK?
BA CCKr
Kk?
RT
E
ff
f
qq
q
CC
C
BABABA
AB 0e x pK
统计热力学
RT
E
ff
f
h
Tk
k
BA
B 0e x p'
h
TkB
is a general constant with unit of s-1 of the
magnitude of 1013.
Absolute rate theory ---- TST
k of TST can be theoretically calculated.
For example:
For elementary equation,
H2+F?H? H? F? H+HF
Theoretical,k = 1.17? 1011 exp(-790/T)
Experimental,k = 2? 1011 exp(-800/T)
Thermodynamic Treatment
In 1933,LaMer tried to treat TST with
thermodynamic method.
RT
G
h
Tk
k B e x p
STHG
K
h
Tk
k B
RT
E
ff
f
h
Tk
k
BA
B 0e x p'
RT
E
ff
f
K
BA
0e x p'
速率常数平衡常数
KRTG ln
RT
G
h
Tk
k B e x p
RT
G
K e x p
STHG
RT
G
h
Tk
k B e x p
RT
H
R
S
h
Tk B
e x pe x p
VPHRTE a
RT
E
e
RT
S
h
Tk
k anB e x pe x p
尝试推导,
热力学活化能
Erying Polanyi
H3 PES
Erying,C.E,Sun
碰撞理论 SCT
过渡态理论 TST
对反应模型的处理,
复杂反应过程,平行,串级,连续,…
稳态近似
In this class,
The last class,
Theories of elementary reaction
Simple Collision theory (SCT)
for bimolecular reactions
Transition state theory (TST)
for bimolecular reactions
Two important empirical rule,
Rate equation (rule of mass action)
Arrhenius equation
RT
E
Ak ae x p
Type of
reaction
Unimolecular
reaction
Bimolecular
reaction
Termolecular
reaction
A 1013
s
1011
mol-1 dm3 s-1
109
mol-2 dm6 s-1
A seems related to collision frequency.
RT
E a
e x p
Boltzmann distribution term
It is obvious that a molecule of A cannot react
with a molecule of B unless the two reactant
molecules can somehow interact,
This interaction can only take place if they
come within a certain distance of each other,i.e.,
collides with each other.
Basic Idea:
相互作用 碰撞 (不一定接触 )
During 1920s,M,Trautz,W,Lewis,C,Hinshelwood
et al,finally established a theory based on the collision,
which is called the simple collision theory,
A reaction can take place only if the molecules of the
reactants collide,Therefore,the rate constant of the
reaction may be predicted by calculation of the
collision frequency of the reactants.
The fundament of SCT
The premise of reaction is the collision between
reactants,
The reaction rate of reaction is proportional to the
collision frequency (Z);
Not all the collision is effective,The collision can
be either non-reactive (elastic) collision or reactive
collision,
Only the molecules posses energy excess to a
critical value (Ec) can lead to reactive collision,
The reaction rate of reaction is proportional to the
collision frequency (Z);
qZr AB?
kinetic theory of gases
SCT assumes that the molecules can be taken as
rigid ball without inner structure,
dA dB
dA and dB are the diameter of A and B molecule,
respectively,
B不动
AB
BA ddd
2
Definition,
mean collision diameter,dAB
Definition,
collision cross-section 2ABdS
2
ABAB dZ V
N B
A?
A?
V
NBmotionless
When the concentration of A is NA/V (molec,M-3):
2
ABAB dZ V
N
V
N BA
A?
“碰撞数”,碰撞频率,
B不动
When both A and B moves,the
relative velocity VAB should be used.
22 BAAB
i
i
M
RT
8
“最可几速率,
RT
AB
8
BA
BA
MM
MM
BA
BA
BA
AB MM
MMRT
M
RT
M
RT?
888
(reduced mass)
]][[
8
8
8
22
2
2
BA
RT
dL
V
Ln
V
LnRT
d
V
N
V
NRT
dZ
AB
BA
AB
BA
ABAB
Decomposition of HI:
2 HI = H2 + I2
222 ][8
2
2
A
M
RT
dLZ
A
AAAA
]][[
822
BA
RT
dLZ ABAB
At 1.01325? 105 Pa and 700 K,d = 3.50
10-10 m,Z HI-HI =?
Example:
3
11
5
41.17
700314.8
1001325.1
][
m o lm
Km o lJK
Pa
RT
P
HI
1334
2
3
210223
222
10017.1
)41.17(
101281 4 1 6.3
700314.88
)1050.3()1002.6(1 4 1 6.3
2
2
][
8
2
2
sm
A
M
RT
LZ
A
AAAA
Generally,ZAB of gaseous
reactions at ambient temperature
and pressure is of the magnitude
of 1035 m-3 s-1.
每秒碰撞大约 1011次
If reaction takes place whenever the
molecules collides:
]][[822 BARTdLZ ABAB
AB
A
ZL
dt
Ad
dt
V
Nd
r
][ ]][[
][ BAk
dt
Ad
RT
Ldk AB
82
k = 7.88?104 mol-1 dm3 s-1
When C0 = 1.00 mol dm-3,the half-life of HI is 1.27?
10-5 s,this result differs great from the experimental
fact.
In 1909,Max Trantz introduced fraction of reactive
collision (q) to explain the great discrepancy,
Only the molecules posses energy excess to a
critical value (Ec) can lead to reactive collision.
Translational energy of motion,is related to the relative
motion of two molecules,And Ec is thus the minimum
translational energy of motion along the connect line between
the mass-point of the two molecules which are to collide,
If the energy exchange between colliding
molecules is much rapid than reaction,the
energy distribution of molecules may still
obey the Maxwell-Boltzmann distribution
equation.
The fraction of the collision with the energy
equal to or greater than Ec is:
RT
E
n
nq ce x p* Boltzmann factor
If Ec = 120 kJ mol-1,T = 300,then
q = 1.27? 10-21
This suggest than among 7.8? 1020
collision only one collision is effective.
例,
RT
ERT
Ldk cABS C T e x p
82
RT
EBTk c
S C T e x p
2
1
RT
EAk ae x p
ca ERTE 2
1
RT
ER T e
Ldk aABS C T e x p
82
R T e
LdA AB
82
The pre-exponential factor corresponds to the
collision frequency,This is the reason why A is also
named as frequency factor.
SCT gives a vivid physical image of the
reaction process:
In fact,the reactant molecule is of complex molecular
structure,To take reactant molecules as rigid balls
without inner structure will spontaneously result in
systematic error.
NOBr
Reactive
Non Reactive
The colliding molecules might not be
suitably oriented for reaction.
CH3+CHCl3?CH4+CCl3
取向问题
RT
E
PAk aS C T e x p
Steric factor (P),ranging between 1~10-9,
represents the fraction of energetically
suitable collisions for which the
orientation is also favorable.
Transition state theory (TST) for
bimolecular reactions
A + B-C? A-B + C
During reaction,massive changes of form are
occurring,energies are being redistributed among
bonds,old bonds are being ripped apart and new
bonds formed.
This process can be generalized as:
A + B-C [A B C] A-B + C
Activated complex
Transition state
H+ H–H? H– – –H– –H
H– –H– –H (activated state)
H–H– – –H? H–H + H
Whether or not the energy change of the
reaction can be used to explain the
reaction on the basis of thermodynamics?
热力学?
The transition state theory (TST) of
reaction rates,also known as the Theory
of Absolute reaction Rates or activated
complex theory,attempting to explain
rates on the basis of thermodynamics,was
developed by H,Eyring and M,Polanyi
during 1930-1935.
过渡态理论
TST treated the reaction rate from a
quantum mechanical viewpoint involves
the consideration of intramolecular
forces and intermolecular forces at the
same time.
According to the TST,before undergoing
reaction,molecules of the reactants must
form an activated complex which is in
thermodynamic equilibrium with the
molecules of the reactants.
The activated complexes,the energy of
which is higher than both reactants and
products,is treated as an ordinary
molecule except that it has transient
existence and decomposes at a definite
rate to form the product.
Potential energy surfaces
a potential energy which is the function
of interatomic distance,
The function can be obtained by solving
Schr?dinger equation for a fixed nuclear
configuration,i.e.,Born-Oppenheimer
approximation.
势能面
Contour diagram
of the potential
energy surface
反应途径
Saddle,鞍点
C
A
B
valley
valleySaddle point
A+B-C A-B+C
A
B
C
Reaction takes place along route C,route C is the
reaction path or reaction coordination.
Activated complex has no recovery force.
On any special vibration (asymmetric
stretching),it will undergo decomposition.
Whenever the system attain saddle point,
it will convert to product with no return.
Saddle point = point of no return
Kinetic Treatment
For reaction:
A + B AB P
ABCr?
BA
AB
CC
CK?
BA CCKr
Kk?
RT
E
ff
f
q
CC
C
BABABA
AB 0e x pK
统计热力学
RT
E
ff
f
h
Tk
k
BA
B 0e x p'
h
TkB
is a general constant with unit of s-1 of the
magnitude of 1013.
Absolute rate theory ---- TST
k of TST can be theoretically calculated.
For example:
For elementary equation,
H2+F?H? H? F? H+HF
Theoretical,k = 1.17? 1011 exp(-790/T)
Experimental,k = 2? 1011 exp(-800/T)
Thermodynamic Treatment
In 1933,LaMer tried to treat TST with
thermodynamic method.
RT
G
h
Tk
k B e x p
STHG
K
h
Tk
k B
RT
E
ff
f
h
Tk
k
BA
B 0e x p'
RT
E
ff
f
K
BA
0e x p'
速率常数平衡常数
KRTG ln
RT
G
h
Tk
k B e x p
RT
G
K e x p
STHG
RT
G
h
Tk
k B e x p
RT
H
R
S
h
Tk B
e x pe x p
VPHRTE a
RT
E
e
RT
S
h
Tk
k anB e x pe x p
尝试推导,
热力学活化能
Erying Polanyi
H3 PES
Erying,C.E,Sun
