Xiamen University
Relaxation time
上述结果说明， 上述结果说明，对峙趋向平衡 的过程为一级反应过程， 的过程为一级反应过程，其速率常 数为 k1 + k-1。
在平衡态产生一个微扰使反应偏 离平衡， 离平衡，从微扰态趋向平衡态的过程 称为弛豫过程， 称为弛豫过程，该过程的平均寿命 (xe﹣x=xe/e)，即弛豫时间 ， τ = 1/(k1 + k-1) 通常运用实验技术测量弛豫时 间的方法求k 间的方法求 1 + k-1，再通过平衡关 系把k 的值计算出来。 系把 1和k-1的值计算出来。
II. Kinetics of typical complex reactions III. Steady-State Approximation IV. Pre-equilibria
2011-10-14
2011
Physical Chemistry
Xiamen University
I. Elementary Reactions & Overall Reactions
2011-10-14
2011
Physical Chemistry
Xiamen University
8.7 Elementary & Complex Reactions
Focuses
I. Concepts
Elementary reactions 基元反应 Molecularity 分子数 Overall reactions 总包反应 Reaction order 反应级数 Reaction mechanism 反应机理
Physical Chemistry Xiamen University
A P → A+B P →
2A + B P →
2011-10-14
2011
Law of Mass Action
For an elementary reaction, the rate is proportional to the concentration of of the reactant molecules that meet together.
∆ = ∆0exp { [− kf ([Α]e + [Β]e) + kr([C]e + [D]e)] t} − [ [ ] ] ∆ = ∆0exp (−t/τR) −
Assume微扰 ∆0= [Α]e − [Α]0，∆ = [Α]e −[Α] 微扰 [Α] [Α]
∆ = ∆0exp{−(kf + kr) t} = ∆0exp (−t/τR) − −
τR = 1/(kf + kr)
再结合平衡常数分别求k 以实验方法监测∆～t，求出τR，再结合平衡常数分别求 f 及 kr ，
∫
[A] [A]0
d[A] [A]﹣[A]e
=－
0
∫
t
(k1+k-1)dt
[A]0−[A]e ln = (k1 + k-1) t [A]−[A]e
该式与一级反应表达式极为类似，只不过将 [A]0→[A]0−[A]e, [A] →[A]−[A]e, k →k1 + k-1
2011-10-14
2011
Physical Chemistry
k1 k-1
B
[B]0 [B]0 + x [B]0 + xe
[A]0 [A]0 – x [A]0 – xe
d[A ] − = k 1[ A ] − k - 1[B] dt
[A]0+[B]0=[A]+[B]=[A]e+[B]e k1/k -1 =[B]e/[A]e [B] = [A]e+ [A]ek1/k -1－[A]
An elementary reaction refers to a single-step reaction involving a small number of molecules or ions.
For examples： Cl 2 + M = 2Cl + M
Cl + H 2 = HCl + H H + Cl 2 = HCl + Cl 2Cl + M = Cl 2 + M
More common situation is that the forward and the back reactions may not be elementary reactions, and may be first-, second- or third-order reactions For examples
Elementary reaction
rate law
(1) Cl 2 + M = 2Cl + M (2) Cl + H 2 = HCl + H (3) H + Cl 2 = HCl + Cl (4) 2Cl + M = Cl 2 + M
2011-10-14
k1[Cl 2 ][M] k 2 [Cl][H 2 ] k3 [H][Cl2 ] k 4 [Cl]2 [M ]
Differential equation
d[A ] − = (k 1 + k - 1)([A] − [A ]e) dt
2011-10-14
2011
Physical Chemistry
Xiamen University
Reversible First-Order Reactions: Integrated equation
B C D
连续反应
Ation
k2 A k1 B → C →
2011-10-14
2011
Physical Chemistry
Xiamen University
II. Kinetics of typical complex reactions
Reversible (Opposing) reactions 对峙反应
2011-10-14
2011
Physical Chemistry
Xiamen University
Typical Combinations of Elementary Reactions
Reversible (Opposing) reactions 对峙反应
A
k1
B
平行反应
k1
k-1
Parallel reactions
2011 Physical Chemistry Xiamen University
对于很小的扰动值, 对于很小的扰动值 ∆2≈0
2011-10-14
Relaxation Time for 2nd-order Reversible Reactions
d∆ − = {k f ([A]e + [B]e ) + kr ([C]e + [D]e )}∆ dt 可见， 可见，∆向平衡的趋近可近似为一级 1 弛豫时间 τ R = k f ([A]e + [B]e ) + kr ([C]e + [D]e )
2011-10-14
2011
Physical Chemistry
Xiamen University
Relaxation Time for 1st-order Reversible Reactions
1-1级对峙反应 级对峙反应
A
kf kr
B
Integrated rate equation:
[A]0 − [A]e ln = (kf + kr )t [A] − [A]e [A]−[A]e = ([A]0−[A]e) exp[−(kf + kr) t] − −
A A+B A
kf kb kf kb kf kb
B C B+C
Xiamen University
2011-10-14
2011
Physical Chemistry
Reversible First-Order Reactions: Differential equation
A
t =0 t =t t =te
Xiamen University
2011
Physical Chemistry
Reaction Mechanism
For an overall reaction, the combination of a series of elementary-reaction steps is the reaction mechanism. 同一反应在不同的条件下，可有不同的反应机理。 同一反应在不同的条件下，可有不同的反应机理。 了解反应机理可以掌握反应的内在规律，从而更好的 了解反应机理可以掌握反应的内在规律， 掌握反应的内在规律 驾驭反应。 驾驭反应。一个反应机理需要经得起实验和理论的考 验，有时需要作长期的大量的动力学研究。 有时需要作长期的大量的动力学研究。
2011-10-14
2011
Physical Chemistry
Xiamen University
Relaxation Time for 2nd-order Reversible Reactions
2-2级对峙反应 级对峙反应
A+B
kf kr
C+D
Assume: [Α] = [Α]e − ∆; [Β] = [Β]e − ∆; [C] = [C]e + ∆; [D] = [D]e + ∆;
2011-10-14
2011
Physical Chemistry