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 )}]

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)
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
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
(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.
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/ 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
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
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)
(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
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
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
In chemical reactions, bonds are being formed and broken. Intramolecular forces Forces acting on atoms in the molecules
Intermolecular forces
Consider two molecules to form a single quantum-mechanical entity
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.
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
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
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
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.
Physical Chemistry
Reaction Kinetics (6)
Xuan Cheng Xiamen University
1
Physical Chemistry
Theories of Reaction Rates
Reaction Kinetics