Reaction-Kinetics Theories of Reaction Rates 简单碰撞理论的基本假设
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1/ 2
e Ethr / RT
for B C for B = C
(23.3) (23.4)
e Ethr / RT
Ethr 1 ln k const ln T 2 RT
E 1 Ea RT 2 T thr RT 2 2
Ea Ethr 1 RT 2 Ea RT 2 d ln k dT
1.24×10 -5 7.3
1.7×10- 6
8
Physical Chemistry
Potential-Energy Surfaces
Reaction Kinetics
The hard-sphere collision theory does not give accurate rate constants.
1/ 2
e Ethr / RT
for B C
(23.3)
(23.5)
1/2RT is small
1 Ea RT 2
Ea Ethr
Ea A ke RT
1 RT 2
Ea Ethr
(17.69)
1/ 2
8RT 1 1 A N A (rB rC ) 2 M B MC
7
Physical Chemistry Reaction Kinetics A comparison of theoretic calculation and experimental measurement
Reaction T K E kJ·mol-1
k0 1011dm3 ·mol-1 ·s-1 measured cal. k0 (theo) k0 (cal)
3
Physical Chemistry
Reaction Kinetics
Hard-Sphere Collision Theory of Gas-Phase Reactions
The number of B reacting in a bimolecular reaction B + C Products Ethr NA thr Z BCe Ethr / RT
supermolecule
Only exists during collision
9
Physical Chemistry
Reaction Kinetics
Morse potential Energy
Potential-Energy Surfaces
Ep (r) De [exp{2a(r r0 )} 2exp{a(r r0 )}]
A---B-------C
12
Physical Chemistry
Reaction Kinetics
Transition-State Theory
Transition-State Theory (TST) Activation-Complex Theory (ACT)
The potential-energy surface for a reaction has a reaction region and a product region that are separated by a barrier. TST chooses a boundary surface located between the reactant and product regions and assumes that all supermolecules that cross this boundary surface (critical dividing surface) become products. The critical dividing surface (Fig. 23.7) is taken to pass through the saddle point of the potential-energy surface.
e 1 / 2
for B C
(23.6)
The hard-sphere threshold energy is nearly the same as the activation energy. The simple collision theory gives only the pre-exponential factor A (but not for the calculation of Ethr)
The use of (15.63) for ZBB
8RT 2 k N Ad B M 21 / 2 B 1
1/ 2
e Ethr / RT
for B = C
(23.4)
5
Physical Chemistry
Theories of Reaction Rates
1/ 2
2
Physical Chemistry
Reaction Kinetics
简单碰撞理论的基本假设
该理论的基本假设(即理论模型）：
(i)反应物分子可看作简单的硬球，无内部结构和相互作用；
(ii)反应分子必须通过碰撞才可能发生反应； (iii)并非所有碰撞都能发生反应，相互碰撞的两个分子— 碰撞 分子对的能量达到或超过某一定值 thr—称为阈能时，反应才能 发生，这样的碰撞叫活化碰撞； (iV)在反应过程中，反应分子的速率分布始终遵守麦克斯韦 — 玻耳兹曼(Maxwell-Boltzmann)分布。
K + Br2 CH3 + CH3
KBr + Br C2H6 CHO
600 300
0 0
10 0.24
2.1 1.1
4.8 0.22
2NOCl
2NO + Cl2 470
CHO 500
102
0.094
0.59
0.16
+ H2 + C2H4
83
1.5×10 -5
3.0
5×10- 6
C2H6 800
180
(17.68) (23.5)
6
Physical Chemistry
Reaction Kinetics
Theories of Reaction Rates
Hard-Sphere Collision Theory of Gas-Phase Reactions
1 1 2 8RT k N A (rB rC ) M M C B
Reaction Kinetics
Potential-Energy Surfaces
A
Rab
B
Rbc C
If < 180o Potential is a function of Rab and Rbc only.
11
Physical Chemistry
Reaction Kinetics
Potential-Energy Surfaces
Physical Chemistry
Reaction Kinetics (6)
Xuan Cheng Xiamen University
1
Physical Chemistry
Theories of Reaction Rates
Reaction Kinetics
Hard-Sphere Collision Theory of Gas-Phase Reactions
The predict rate constant
r k[ B][C ]
(23.2)
The use of (15.62) for ZBC
8RT 1 1 k N A (rB rC ) 2 M M C B
e Ethr / RT
J 1 1 dnA r V V a dt
Theories of Reaction Rates
(17.3)
Z BCe Ethr / RT k N A[ B][C ] Z BCe Ethr / RT k N A[ B][C ]
1/ 2
r Z BCe
Ethr / RT NA
当r>r0时,有引力,即化学键力。
当r<r0时，有斥力。
=0时的能级为振动基态能级， E0为零点能。 D0为把基态分子离解为孤立 原子所需的能量，它的值可
从光谱数据得到。
10
Physical Chemistry For a reaction
A BC A B C AB C
for B C
(23.3)
4
Physical Chemistry
Reaction Kinetics
Theories of Reaction Rates
Hard-Sphere Collision Theory of Gas-Phase Reactions
For the bimolecular reaction 2B Products
In chemical reactions, bonds are being formed and broken. Intramolecular forces Forces acting on atoms in the molecules
Intermolecular forces
Consiwenku.baidu.comer two molecules to form a single quantum-mechanical entity
(1) all supermolecules that cross the critical dividing surface from the reactant side become products. Once a supermolecule crosses the critical surface it is a downhill journey to products. (2) during the reaction the Boltzmann distribution of energy is maintained for the reactant molecules. (3) the supermolecules crossing the critical surface from the reactant side have a Boltzmann distribution of energy corresponding to the temperature of the reacting system.
图中R点是反应物BC分子的基态,随着A原子的靠近,势能 沿着RT线升高，到达T点形成活化络合物。
随着C原子的离去，势能沿 着TP线下降，到P点是生成 物AB分子的稳态。
A-----B-----C
D点是完全离解为A,B,C原子 时的势能；OEP一侧,是原子 间的相斥能,也很高。
A-------B---C
Reaction Kinetics
Hard-Sphere Collision Theory of Gas-Phase Reactions
8RT 1 1 k N A (rB rC ) 2 M M C B
8RT 2 k N Ad B M 1/ 2 2 B 1
saddle point The maximum point on the
minimum-energy path
13
Physical Chemistry
Reaction Kinetics
Transition-State Theory
Transition-State Theory (TST)
Assumptions
r 1 d [ B] k[ B]2 2 dt
Ethr / RT NA
The rate of disappearance of B
1 d [ B] / dt Z BBe Ethr / RT k 2 [ B]2 N A[ B]2
d [ B] 2Z BCe dt
r k[ B]2
Assumptions
(1) The molecules are hard spheres (2) For a reaction to occur between B and C, the two molecules must collide (3) Not all collisions produce reaction. Reaction occurs if and only if the reactive translational kinetic energy along the line of centers of the colliding molecules exceeds a threshold energy thr (4) The Maxwell-Boltzmann equilibrium distribution of molecular velocities is maintained during the reaction
e Ethr / RT
for B C for B = C
(23.3) (23.4)
e Ethr / RT
Ethr 1 ln k const ln T 2 RT
E 1 Ea RT 2 T thr RT 2 2
Ea Ethr 1 RT 2 Ea RT 2 d ln k dT
1.24×10 -5 7.3
1.7×10- 6
8
Physical Chemistry
Potential-Energy Surfaces
Reaction Kinetics
The hard-sphere collision theory does not give accurate rate constants.
1/ 2
e Ethr / RT
for B C
(23.3)
(23.5)
1/2RT is small
1 Ea RT 2
Ea Ethr
Ea A ke RT
1 RT 2
Ea Ethr
(17.69)
1/ 2
8RT 1 1 A N A (rB rC ) 2 M B MC
7
Physical Chemistry Reaction Kinetics A comparison of theoretic calculation and experimental measurement
Reaction T K E kJ·mol-1
k0 1011dm3 ·mol-1 ·s-1 measured cal. k0 (theo) k0 (cal)
3
Physical Chemistry
Reaction Kinetics
Hard-Sphere Collision Theory of Gas-Phase Reactions
The number of B reacting in a bimolecular reaction B + C Products Ethr NA thr Z BCe Ethr / RT
supermolecule
Only exists during collision
9
Physical Chemistry
Reaction Kinetics
Morse potential Energy
Potential-Energy Surfaces
Ep (r) De [exp{2a(r r0 )} 2exp{a(r r0 )}]
A---B-------C
12
Physical Chemistry
Reaction Kinetics
Transition-State Theory
Transition-State Theory (TST) Activation-Complex Theory (ACT)
The potential-energy surface for a reaction has a reaction region and a product region that are separated by a barrier. TST chooses a boundary surface located between the reactant and product regions and assumes that all supermolecules that cross this boundary surface (critical dividing surface) become products. The critical dividing surface (Fig. 23.7) is taken to pass through the saddle point of the potential-energy surface.
e 1 / 2
for B C
(23.6)
The hard-sphere threshold energy is nearly the same as the activation energy. The simple collision theory gives only the pre-exponential factor A (but not for the calculation of Ethr)
The use of (15.63) for ZBB
8RT 2 k N Ad B M 21 / 2 B 1
1/ 2
e Ethr / RT
for B = C
(23.4)
5
Physical Chemistry
Theories of Reaction Rates
1/ 2
2
Physical Chemistry
Reaction Kinetics
简单碰撞理论的基本假设
该理论的基本假设(即理论模型）：
(i)反应物分子可看作简单的硬球，无内部结构和相互作用；
(ii)反应分子必须通过碰撞才可能发生反应； (iii)并非所有碰撞都能发生反应，相互碰撞的两个分子— 碰撞 分子对的能量达到或超过某一定值 thr—称为阈能时，反应才能 发生，这样的碰撞叫活化碰撞； (iV)在反应过程中，反应分子的速率分布始终遵守麦克斯韦 — 玻耳兹曼(Maxwell-Boltzmann)分布。
K + Br2 CH3 + CH3
KBr + Br C2H6 CHO
600 300
0 0
10 0.24
2.1 1.1
4.8 0.22
2NOCl
2NO + Cl2 470
CHO 500
102
0.094
0.59
0.16
+ H2 + C2H4
83
1.5×10 -5
3.0
5×10- 6
C2H6 800
180
(17.68) (23.5)
6
Physical Chemistry
Reaction Kinetics
Theories of Reaction Rates
Hard-Sphere Collision Theory of Gas-Phase Reactions
1 1 2 8RT k N A (rB rC ) M M C B
Reaction Kinetics
Potential-Energy Surfaces
A
Rab
B
Rbc C
If < 180o Potential is a function of Rab and Rbc only.
11
Physical Chemistry
Reaction Kinetics
Potential-Energy Surfaces
Physical Chemistry
Reaction Kinetics (6)
Xuan Cheng Xiamen University
1
Physical Chemistry
Theories of Reaction Rates
Reaction Kinetics
Hard-Sphere Collision Theory of Gas-Phase Reactions
The predict rate constant
r k[ B][C ]
(23.2)
The use of (15.62) for ZBC
8RT 1 1 k N A (rB rC ) 2 M M C B
e Ethr / RT
J 1 1 dnA r V V a dt
Theories of Reaction Rates
(17.3)
Z BCe Ethr / RT k N A[ B][C ] Z BCe Ethr / RT k N A[ B][C ]
1/ 2
r Z BCe
Ethr / RT NA
当r>r0时,有引力,即化学键力。
当r<r0时，有斥力。
=0时的能级为振动基态能级， E0为零点能。 D0为把基态分子离解为孤立 原子所需的能量，它的值可
从光谱数据得到。
10
Physical Chemistry For a reaction
A BC A B C AB C
for B C
(23.3)
4
Physical Chemistry
Reaction Kinetics
Theories of Reaction Rates
Hard-Sphere Collision Theory of Gas-Phase Reactions
For the bimolecular reaction 2B Products
In chemical reactions, bonds are being formed and broken. Intramolecular forces Forces acting on atoms in the molecules
Intermolecular forces
Consiwenku.baidu.comer two molecules to form a single quantum-mechanical entity
(1) all supermolecules that cross the critical dividing surface from the reactant side become products. Once a supermolecule crosses the critical surface it is a downhill journey to products. (2) during the reaction the Boltzmann distribution of energy is maintained for the reactant molecules. (3) the supermolecules crossing the critical surface from the reactant side have a Boltzmann distribution of energy corresponding to the temperature of the reacting system.
图中R点是反应物BC分子的基态,随着A原子的靠近,势能 沿着RT线升高，到达T点形成活化络合物。
随着C原子的离去，势能沿 着TP线下降，到P点是生成 物AB分子的稳态。
A-----B-----C
D点是完全离解为A,B,C原子 时的势能；OEP一侧,是原子 间的相斥能,也很高。
A-------B---C
Reaction Kinetics
Hard-Sphere Collision Theory of Gas-Phase Reactions
8RT 1 1 k N A (rB rC ) 2 M M C B
8RT 2 k N Ad B M 1/ 2 2 B 1
saddle point The maximum point on the
minimum-energy path
13
Physical Chemistry
Reaction Kinetics
Transition-State Theory
Transition-State Theory (TST)
Assumptions
r 1 d [ B] k[ B]2 2 dt
Ethr / RT NA
The rate of disappearance of B
1 d [ B] / dt Z BBe Ethr / RT k 2 [ B]2 N A[ B]2
d [ B] 2Z BCe dt
r k[ B]2
Assumptions
(1) The molecules are hard spheres (2) For a reaction to occur between B and C, the two molecules must collide (3) Not all collisions produce reaction. Reaction occurs if and only if the reactive translational kinetic energy along the line of centers of the colliding molecules exceeds a threshold energy thr (4) The Maxwell-Boltzmann equilibrium distribution of molecular velocities is maintained during the reaction