1. 1 第十二章 化学动力学基础（二） 唯象动力学研究方法，也称经典化学动力学研究方法。 它从化学动力学的原始实验数据 —— 浓度与时间的 关系出发，经过分析获得某些反应动力学参数 —— 反应 速率常数、活化能、指前因子等。 它从化学动力学的原始实验数据 —— 浓度与时间的 关系出发，经过分析获得某些反应动力学参数 —— 反应 速率常数、活化能、指前因子等。

2. 2 分子反应动力学的研究方法：从微观的分子水平来看， 一个化学反应是具有一定量子态的反应物分子间的互相碰撞， 进行原子重排，产生一定量子态的产物分子以至互相分离的 单次反应碰撞行为。 分子反应动力学的研究方法：从微观的分子水平来看， 一个化学反应是具有一定量子态的反应物分子间的互相碰撞， 进行原子重排，产生一定量子态的产物分子以至互相分离的 单次反应碰撞行为。 用过渡态理论解释，它是在反应体系的超势能面上一个 代表体系的质点越过反应势垒的一次行为。 用过渡态理论解释，它是在反应体系的超势能面上一个 代表体系的质点越过反应势垒的一次行为。

3. 3 微观与宏观之间如何建立联系 —— 分子反应动力学的任务 宏观反映动力学基本参数 —— 反应速率常数、活化能 Ea 微观反应动力学基本参数 —— 反应截面、势能面、活化络合物的 热力学函数 热力学函数 反应速率常数 k 活化能 Ea 反应截面势能面活化络合物的热力学函数碰撞理论过渡态理论

4. 4 12.1 Simple Collision theory (SCT) for bimolecular reactions bimolecular reactions 碰撞理论，又称 “ 简单碰撞理论 ” 、 “ 有效碰撞理论 ” 。 假设分子或物种是无结构的硬球，分子要通过碰撞才有可能反应。 假设分子或物种是无结构的硬球，分子要通过碰撞才有可能反应。 并非所有碰撞都有效，多数是弹性碰撞，只有少数碰撞的分子对， 在其中心连线上的相对动能足以克服分子间排斥势能时才能发生反应。 并非所有碰撞都有效，多数是弹性碰撞，只有少数碰撞的分子对， 在其中心连线上的相对动能足以克服分子间排斥势能时才能发生反应。 碰撞理论解释了质量作用定律和阿累尼乌斯公式中指前因子 A 和活 化能 E 的物理意义， 但在定量上与实验值仍有很大偏差。 碰撞理论解释了质量作用定律和阿累尼乌斯公式中指前因子 A 和活 化能 E 的物理意义， 但在定量上与实验值仍有很大偏差。

5. 5 Two important empirical rule: Rate equation (rule of mass action) Rate equation (rule of mass action) Arrhenius equation Arrhenius equation

6. 6 Type of reaction Unimolecular reaction Bimolecular reaction Termolecular reaction A 10 13 s -1 10 11 mol -1 · dm 3 · s -1 10 9 mol -2 · dm 6 · s -1 A seems related to collision frequency. Boltzmann distribution term

7. 7 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. 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. 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. 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.

8. 8 12.1.1 The fundament of SCT For gaseous bimolecular reaction 1) The premise of reaction is the collision between reactants. 1) The premise of reaction is the collision between reactants. The reaction rate of reaction is proportional to the collision frequency Z; The reaction rate of reaction is proportional to the collision frequency Z;

9. 9 2) 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 ( E c ) can lead to reactive collision. Only the molecules posses energy excess to a critical value ( E c ) can lead to reactive collision. The reaction rate should also be in proportion to the fraction of reactive collision (q). The reaction rate should also be in proportion to the fraction of reactive collision (q).

10. 10 According to the collision theory, the rate of the reaction can be expressed by: According to the collision theory, the rate of the reaction can be expressed by: where Z AB is the collision rate of A with B per unit cubic meter per second, q is the portion of effective collision. where Z AB is the collision rate of A with B per unit cubic meter per second, q is the portion of effective collision.

11. 11 12.1.2 Calculation of Z AB 碰撞频率：一般指单位时间单位体积中相同或不同类型分 子间的碰撞数 Z AB Z AB 与那些因素有关？ 分子直径、单位体积中的分子数、分子间平均相对速度。 分子直径、单位体积中的分子数、分子间平均相对速度。

12. 12 SCT assumes that the molecules can be taken as rigid ball without inner structure. SCT assumes that the molecules can be taken as rigid ball without inner structure. d A and d B are the diameter of A and B molecule, respectively. d A and d B are the diameter of A and B molecule, respectively. dAdAdAdA dBdBdBdB

13. 13

14. 14 Definition: mean collision diameter: d AB

15. 15 Definition: collision cross-section collision cross-section

16. 16 motionless

17. 17 When the concentration of A is N A /V (mole. m -3 ):

18. 18

19. 19 When both A and B moves, the relative velocity v AB should be used.

20. 20 according to the kinetic theory of gases

21. 21 (reduced mass)

22. 22

23. 23 Decomposition of HI: 2 HI = H 2 + I 2 ?

24. 24 At 1.01325  10 5 Pa and 700 K, d = 3.50  10 -10 m, Z HI-HI = ? Example:

25. 25

26. 26 Generally, Z AB of gaseous reactions at ambient temperature and pressure is of the magnitude of 10 35 m -3 · s -1.

27. 27 If reaction takes place whenever the molecules collides: If reaction takes place whenever the molecules collides:

28. 28 because

29. 29 k = 7.88  10 4 mol -1 · dm 3 · s -1 When c 0 = 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.

30. 30 12.1.3 calculation of q Only the molecules posses energy excess to a critical value (E c ) can lead to reactive collision. Only the molecules posses energy excess to a critical value (E c ) can lead to reactive collision.

31. 31 It is apparent that E, of translational energy of motion, is related to the relative motion of two molecules. And E c is thus the minimum translational energy of motion along the connect line between the mass-point of the two molecules which are to collide. It is apparent that E, of translational energy of motion, is related to the relative motion of two molecules. And E c is thus the minimum translational energy of motion along the connect line between the mass-point of the two molecules which are to collide.

32. 32 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.

33. 33 The fraction of the collision with the energy equal to or greater than E c is: Boltzmann factor

34. 34 If E c = 120 kJ mol -1, T = 300 K, then q = 1.27  10 -21 This suggest than among 7.8  10 20 collision only one collision is effective.

35. 35 12.1.4 calculation of k

36. 36

37. 37 B is a constant independent of T. Arrhenius equation critical energy Arrhenius activation energy

38. 38 suggests that the experimental activation energy (E a ) depends on temperature. Using E a for substitution of E c,

39. 39 Can be rewritten as: Therefore

40. 40 The pre-exponential factor corresponds to the collision frequency. This is the reason why A is also named as frequency factor.

41. 41 12.1.5 comment on SCT 1) The expression for the rate coefficient given by SCT conforms qualitatively to the Arrhenius equation observed experimentally. This suggests that SCT reveal the principal features of the reaction, i.e., in order to react, molecules have to collide (the pre- exponential term) and the collision should be sufficiently energetic (the exponential term) （ 1 ） advantages

42. 42 SCT gives a vivid physical image of the reaction process:

43. 43 2) As pointed out by SCT, the pre-exponential factor dependent only on the masses of the species involved in the collision, can be calculated easily. SCT reveals the physical meaning of the pre- exponential factor, i.e., the collision frequency. SCT reveals the physical meaning of the pre- exponential factor, i.e., the collision frequency.

44. 44 3) SCT demonstrated theoretically that experimental activation energy depends on temperature.

45. 45 （ 2 ） Shortcomings 1) For calculating k, E c is needed. However, SCT can not give E c. Calculation of k depends on the experimental determination of E a. Therefore, SCT can not predict the kinetic features of the reaction theoretically.

46. 46 2) The quantitative agreement between SCT and experiments is poor. Reaction Reaction EaEaEaEa A cal A exp A cal. /A exp. 2NOCl  2NO+Cl 2 2NOCl  2NO+Cl 2107.82.95e93.23e90.91 C 2 H 5 Br+OH -  C 2 H 5 OH+Br - C 2 H 5 Br+OH -  C 2 H 5 OH+Br -89.5--1.10 C 6 H 5 CH 2 Na+C 3 H 7 I  C 6 H 5 CH 2 C 3 H 7 +NaI C 6 H 5 CH 2 Na+C 3 H 7 I  C 6 H 5 CH 2 C 3 H 7 +NaI89.3--1.05 H+Br 2  HBr+Br H+Br 2  HBr+Br3.764.6e106.76e96.76 NO+O 3  NO 2 +O 2 NO+O 3  NO 2 +O 29.617.94e96.31e71.25e2 CH 3 +CHCl 3  CH 4 +CCl 3 CH 3 +CHCl 3  CH 4 +CCl 324.21.5e101.26e61.19e4 2-cyclopentadiene  dimer 2-cyclopentadiene  dimer60.68.13e92.45e33.32e6

47. 47 The more complex of the reactant molecules, the greater the discrepancy between A cal and A exp. The more complex of the reactant molecules, the greater the discrepancy between A cal and A exp. In some cases, the agreement between experimental and calculated A values ban be quite good. However, in many cases, the observed rate is definitely too small. In some cases, the agreement between experimental and calculated A values ban be quite good. However, in many cases, the observed rate is definitely too small.

48. 48 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. ONBr molecule

49. 49 Reactive collision Non-reactive collision

50. 50 The colliding molecules might not be suitably oriented for reaction. CH 3 + CHCl 3  CH 4 + CCl 3

51. 51 This great discrepancies between experimental and calculated A were recognized by around 1925. The equation This great discrepancies between experimental and calculated A were recognized by around 1925. The equation was then modified by introduction of an empirical factor P called the steric factor / probability factor ( 概率因子 ). was then modified by introduction of an empirical factor P called the steric factor / probability factor ( 概率因子 ).

52. 52 Steric factor (P), ranging between 1~10 -9, represents the fraction of energetically suitable collisions for which the orientation is also favorable.

53. 53

54. 54 can be only determine experimentally, SCT can not give any clue to calculate P. Steric factor P > 0 ?

55. 55 Exercise: 1, 2, 4

56. 56 The fundament of SCT For gaseous bimolecular reaction 1) The premise of reaction is the collision between reactants. 1) The premise of reaction is the collision between reactants. The reaction rate of reaction is proportional to the collision frequency Z; The reaction rate of reaction is proportional to the collision frequency Z; 本节总结

57. 57 2) Not all the collision is effective. [The collision can be either non-reactive (elastic) collision or reactive collision. ] 2) 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 ( E c ) can lead to reactive collision. Only the molecules posses energy excess to a critical value ( E c ) can lead to reactive collision. The reaction rate should also be in proportion to the fraction of reactive collision (q). The reaction rate should also be in proportion to the fraction of reactive collision (q).

58. 58 Arrhenius equation critical energy Arrhenius activation energy

59. 59 The pre-exponential factor corresponds to the collision frequency. -------- frequency factor. The pre-exponential factor corresponds to the collision frequency. -------- frequency factor. Steric factor----- probability factor 概率因子

60. 60

61. 61 12.2 Transition state theory (TST) for bimolecular reactions 过渡态理论

62. 62 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.

63. 63 This process can be generalized as: A + B-C  [A­B­C]   A-B + C A + B-C  [A­B­C]   A-B + C Activated complex Transition state

64. 64 Whether or not the energy change of the reaction can be used to explain the reaction on the basis of thermodynamics? Whether or not the energy change of the reaction can be used to explain the reaction on the basis of thermodynamics? 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. 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.

65. 65 TST treated the reaction rate from a quantum mechanical viewpoint involves the consideration of intramolecular forces at the same time. TST treated the reaction rate from a quantum mechanical viewpoint involves the consideration of intramolecular forces at the same time.

66. 66 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. 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.

67. 67 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. 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.

68. 68 12.2.1 Potential energy surfaces According to the quantum mechanics, the nature of the chemical interaction (chemical bond) is a potential energy which is the function of interatomic distance: According to the quantum mechanics, the nature of the chemical interaction (chemical bond) is a potential energy which is the function of interatomic distance:

69. 69 The function can be obtained by solving Schrödinger equation for a fixed nuclear configuration, i.e., Born-Oppenheimer approximation. The other way is to use empirical equation. The empirical equation usually used for system of two atoms is the Morse equation: 奥本海默 1904-1967, 美国原子物理学家, 原子弹计划主持人

70. 70 where D e is the depth of the wall of potential, or the dissociation energy of the bond. r 0 is the equilibrium interatomic distance, a is a parameter with the unit of cm -1 which can be determined from spectroscopy. where D e is the depth of the wall of potential, or the dissociation energy of the bond. r 0 is the equilibrium interatomic distance, a is a parameter with the unit of cm -1 which can be determined from spectroscopy.

71. 71 When r = r 0, V r (r = r 0 ) = -D e r , V r (r  ) = 0 r , V r (r  ) = 0

72. 72 When r > r 0, interatomic attraction exists, r < r 0, interatomic repulsion appears. The equilibrium distance r 0 is the bond length.

73. 73 The curve obtained by plotting V(r) against r is called Morse curve. Zero point energy E 0 = D e - D 0 decomposition asymptote line

74. 74 For triatomic system ： A + B-C  A-B + C V = V ( r AB, r BC, r AC ) = V ( r AB, r BC,  ) A B C r AB r BC r AC 

75. 75 In 1930, Eyring and Polanyi make  = 180 o, i.e., collinear collision and the potential energy surface can be plotted in a three dimensions / coordination system. In 1930, Eyring and Polanyi make  = 180 o, i.e., collinear collision and the potential energy surface can be plotted in a three dimensions / coordination system. V = V ( r AB, r BC )

76. 76 Eyring et al. calculated the energy of the triatomic system: H A + H B H C  H A H B + H C H A + H B H C  H A H B + H C using the method proposed by London. using the method proposed by London.

77. 77 LEP Potential energy surface

78. 78 LEP Potential energy surface?

79. 79 Contour diagram of the potential energy surface

80. 80

81. 81 LEP Potential energy surface

82. 82 C A B valley Saddle point

83. 83 A+B-CA-B+C ABC Reaction takes place along route C, route C is the reaction path or reaction coordination.

84. 84

85. 85 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

86. 86 12.2.2 Kinetic treatment of the rate constant of TST For reaction: A + B  AB   P The rate of the reaction depends on two factors: 1) the concentration of the activated complex (c  ) 2) the rate at which the activated complex dissociates into products (  )

87. 87 According to equilibrium assumption A + B  AB 

88. 88 According to statistical thermodynamics, K  can be expressed using the molecular partition function. E 0 is the difference between the zero point energy of activated complex and reactants. q is the partition function, f  is the partition function without E 0 item and volume item.

89. 89 For activated complex with three atoms, f  can be written as a product of partition function for three translational, three rotational, and five vibrational degrees of freedom. For activated complex with three atoms, f  can be written as a product of partition function for three translational, three rotational, and five vibrational degrees of freedom.

90. 90 Symmetric stretching asymmetric stretching In-plane bending out-plane bending

91. 91 Only the asymmetric stretching can lead into decomposition of the activated complex and the formation of product. For one-dimension vibrator:

92. 92 For asymmetric stretching – decomposition vibration

93. 93 The statistical expression for the rate constant of TST

94. 94 is a general constant with unit of s -1 of the magnitude of 10 13. For general elementary reaction

95. 95 In which f  ’ can be obtained for partition equation, and E 0 can be obtained from potential surface. k of TST can be theoretically calculated. Absolute rate theory

96. 96 For example: For elementary equation: H 2 + F  H  H  F  H + HF Theoretical: k = 1.17  10 11 exp (-790 / T) Experimental: k = 2  10 11 exp (-800 / T)

97. 97 12.2.3 Thermodynamic treatment of the rate constant of TST For nonideal systems, the intermolecular interaction makes the partition function complex. For these cases, the kinetic treatment becomes impossible. In 1933, Lamer tried to treat TST with thermodynamic method.

98. 98

99. 99 Standard molar entropy of activation, standard molar enthalpy of activation K≠K≠

100. 100

101. 101 The thermodynamic expression of the rate of TST The thermodynamic expression is different from Arrhenius equation.

102. 102

103. 103 According to Gibbs-Holmholtz equation

104. 104

105. 105 For liquid reaction: p  V = 0

106. 106 For gaseous reaction: n is the number of reactant molecules Substituting these relation into For gaseous reaction:

107. 107 The thermodynamic expression of the rate of TST. The rate of reaction depends on both activation energy and activation entropy.

108. 108 The pre-exponential factor depends on the standard entropy of activation and related to the structure of activated complex.

109. 109

110. 110 This formula suggests that the steric factor (probability factor) can be estimated from the activation entropy of the activated complex.

111. 111 Example: reactionsP exp(  S/R) (CH 3 ) 2 PhN + CH 3 I 0.5  10 -7 0.9  10 -8 Hydrolysis of ethyl acetate 2.0  10 -5 5.0  10 -4 Decomposition of HI 0.50.15 Decomposition of N 2 O 11

112. 112 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. 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. 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. 本节总结

113. 113 For liquid reaction: p  V = 0 For gaseous reaction:

114. 114 12.3 The rate theory of unimolecular reaction

115. 115 Both the SCT and TST treated bimolecular reaction. For bimolecular reaction, before the reaction can take place, reactants must collide with each other to acquire enough activation energy. This may lead to a conclusion that all gaseous reaction should be second- ordered. Both the SCT and TST treated bimolecular reaction. For bimolecular reaction, before the reaction can take place, reactants must collide with each other to acquire enough activation energy. This may lead to a conclusion that all gaseous reaction should be second- ordered.

116. 116 Unimolecular reaction is elementary reaction with only one reactant molecule. Unimolecular reaction is elementary reaction with only one reactant molecule. At early 19th century, it was found that all unimolecluar reaction, such as gaseous decomposition and isomerization, is of first-order. At early 19th century, it was found that all unimolecluar reaction, such as gaseous decomposition and isomerization, is of first-order.

117. 117 It is obvious that a single molecule at ground state will not undergo any reaction except that it was activated by energy of some types. A  A *  P For unimolecular reaction, the puzzling question is that how do reactant molecules attain necessary energy of activation.

118. 118 In 1919, Perrin proposed that the molecule was activated by absorption of infrared radiation for the container or other molecules – Radiation Activation Theory. Perrin （ 1870-1942, 法国物理学家，曾获 1926 年诺贝尔物理学奖）

119. 119 The result obtained from the radiation activation theory is in good accordance with the early observation of kinetic characteristics of the unimolecular reaction, i.e., unimolecular reaction is of first-order.

120. 120 Problems proposed by Langmuir : 1) the energy of the infrared radiation of the wall of container is very low and is not sufficient for activation. 1) the energy of the infrared radiation of the wall of container is very low and is not sufficient for activation. 2) some reactant molecules do not have an absorption band in the wave-length region for light quanta. 2) some reactant molecules do not have an absorption band in the wave-length region for light quanta.

121. 121 3) Latterly, it was observed that the unimolecular reaction is of second-order at low pressure and first- order at high pressure. 3) Latterly, it was observed that the unimolecular reaction is of second-order at low pressure and first- order at high pressure.

122. 122 In 1921, Christiansen pointed out that the activation of molecules in unimolecular reaction is also through intermolecular collision. This theory explain the second-ordered feature of unimolecular reaction at low pressure but cannot gave any reasonable explanation to its first-ordered feature at high pressure.

123. 123 In 1922 Lindemann and Christiansen postulated that the activated molecules react long after the collision. There is a time lag between activation and reaction. In 1922 Lindemann and Christiansen postulated that the activated molecules react long after the collision. There is a time lag between activation and reaction. During the stay of activated molecules, some of them may lose their energy due to the further collision (deactivation). Only part of the activated molecules can form product. During the stay of activated molecules, some of them may lose their energy due to the further collision (deactivation). Only part of the activated molecules can form product. 时滞

124. 124 12.3.1 Lindemann mechanism 1)Activation through collision: 2) deactivation through collision during time lag 3) decomposition of activated molecule after time lag

125. 125 It is obvious that the activation and the deactivation processes are bimolecular reactions and the decomposition process is a true a unimolecular reaction.

126. 126 A + MA * + M k1k1 k -1 P k2k2 Lindemann mechanism

127. 127 The rate of the reaction can be given as: To determine the concentration of activated molecules, the stationary-state approximation should be used. To determine the concentration of activated molecules, the stationary-state approximation should be used. 12.3.2 rate equation of Lindemann mechanism A + MA * + M k1k1 k -1 P k2k2

128. 128 the stationary-state approximation A * is very active, its concentration is very low and after a short time, its concentration does not vary with time, i.e.,

129. 129 A + MA * + M k1k1 k -1 P k2k2 Lindemann mechanism

130. 130

131. 131 This equation suggests that unimolecular reaction have no definite reaction order. But this equation has two limiting forms:

132. 132 Case I: When the pressure of the system is low enough to satisfy:

133. 133 The expression for the second-order reaction corresponds to the low pressure. When the pressure and the concentration of A and M is low, the collision frequency is low and thus the deactivation is rare.

134. 134 Case II: When the rate of deactivation is much higher than the rate of decomposition

135. 135 This is an expression for the pseudo-first-order reaction. This situation corresponds to the high pressure. When the pressure is high, the concentration of A ([A]) is high, the collision frequency is high and thus the deactivation is fast.

136. 136

137. 137 Therefore, the Lindemann mechanism can satisfactorily explain the phenomena of the unimolecular reaction. However, the quantitative calculation of Lindemann mechanism proved to be not good.

138. 138 To modify the Lindemann mechanism, Hinshelwood used theory of energy partition to calculate k 1, but the result is still not satisfactory. Hinshelwood 1897-1967, 英国化学家, 曾获 1956 年诺贝尔化学奖 Lindemann glass 林德曼玻璃 ( 透 X 射线含锂铍硼玻璃 )

139. 139 1956 Noble Prize United Kingdom 1897/06/19 ~ 1967/10/09 Mechanisms of chemical reactions Sir Cyril N. Hinshelwood

140. 140

141. 141 12.3.3 RRKM theory In 1930s, Rice-Ramsperger-Kassel established another mechanism for unimolecular reaction. In 1950, Marcus innovated the mechanism and introduced TST into the treatment of unimolecular reaction.

142. 142 A + MA * + M k1k1 k -1 Lindemann mechanism A*A* AA P k2k2 k  A  is energized molecules E*E* RRKM theory

143. 143 They postulated that, before A * can decomposed to product, the energy they attained must be transferred to the chemical bond and the molecules would attain the transition state with special configuration A , energized molecule. The time needed for configuration transformation corresponds to the time lag proposed by Lindemann.

144. 144 A*A* AA P k2k2 k  E*E* When E * < E b, k 2 = 0; When E * > E b, k 2 = k 2 (E * )

145. 145 Equilibrium approximation

146. 146 RRKM

147. 147 1992 Noble Prize USA 1923 Theories of electron transfer Rudolph A. Marcus

148. 148 Exercises: 5 6 7 8 9 10 11

149. 149 本节总结 The unimolecular reaction is of second-order at low pressure and first-order at high pressure. The unimolecular reaction is of second-order at low pressure and first-order at high pressure. 12.3 The rate theory of unimolecular reaction

150. 150 12.4 Molecular reaction dynamics Microscopic chemical kinetics 从分子水平上研究分子的一次碰撞行为中的变化，研究基 元反应的微观历程。 分子如何碰撞，如何进行能量交换，旧键如何破坏，新键 如何形成的细节，分子碰撞的角度对反应速率的影响，以及分 子反应产物的角度分布等，进而了解化学反应过程中的各种动 态性质。

151. 151 实验技术 实验技术 计算机技术 计算机技术 反应速率理论 反应速率理论 宏观领域  微观领域   分子与分子间的反应特征指定能态粒子之间反应规律微观化学反应所经历的历程（态－态反应特征） 1. 意义： 1. 对反应理论有重要贡献（赫希巴赫 D. R. Herschbach, 李远哲） 1986 年 2. 对应用研究有一定的意义。

152. 152 2. 实验方法 p 817 Fig.11.13 分子束装置. 交叉分子束技术 （ crossed molecular beam ）  分子反应碰撞研究中最强有力的工具 条件：很低压力  分子间的碰撞可以忽略 在高真空容器中飞行的二束分子  反应器中交叉发生反应散射 （分子束的平动能量可控） （窗口检测：反应产物） 罗渝然，高盘良. 分子反应动态学讲座. 化学通报， 1986 ，（ 8 ）（ 9 ）（ 10 ）

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154. 154 与气相反应有很大的差别。 溶剂  反应物分子的离解，传能作用，离子与离子、离子与 溶剂分子间的相互作用，溶剂的催化作用，溶剂有时参加反应。 11.5 溶液中进行的反应  溶液反应动力学 1. 笼效应（ cage effect ） 溶液中起反应的分子要通过扩散穿过周围的溶剂分子之后， 才能彼此接近而发生接触，反应后生成物分子也要穿过周围的溶 剂分子通过扩散而离去。 溶剂分子就象形成一个笼，反应物处于笼中。

155. 155 笼效应是指反应分子在溶剂分子形成的笼中进行的多次碰撞。 通过笼所需的活化能一般不超过 20 kJ · mol -1 。 化学反应活化能一般为 40 ～ 400 kJ · mol -1 。 A + B [AB] kdkd k -d P k r 遭遇对

156. 156 a. 若活化能很小时， k r >> k -d ， r = k d [A][B] 反应受扩散控制 b. 若活化能很大时， k r << k -d 反应受活化控制 K 为反应物分子形成遭遇对的平衡常数

157. 157 1. 原盐效应（ salt effect ） 电解质溶液的离子强度对反应速率的影响称为原盐效应。

158. 158 速率常数 k 与活度系数 γ 的关系

159. 159 原盐效应 Z A Z B = 0 Z A Z B > 0 Z A Z B < 0 Z A Z B = 0 Z A Z B > 0 Z A Z B < 0

160. 160 半衰期： 10 0 ～ 10 8 s （传统） 10 -13 ～ 10 -15 s （单分子反应） k ： 10 12 ～ 10 14 s -1 11.6 快速反应 驰豫法（ relaxation method ） 测定一个平衡体系受到快速绕动而偏离平衡，在新的条件下 趋向新的平衡态的时间或速度。 一级快速对峙反应： P A k1k1 k -1

161. 161 a 为 A 的原始浓度， x 为 P 的浓度 如果先让此体系在某一温度下达到平衡，然后使温度发生突 变（ T 跳跃），原平衡被破坏，体系向新条件下的平衡转移。若 新的平衡条件下产物的平衡浓度为 Xe k 1 （ a – x e ） = k -1 x e 令 Δx = x – x e 两个平衡浓度之差

162. 162 即与新平衡的偏离值 Δx 随时间的变化率 d(Δx)/dt 与一级反应 中浓度随时间的变化规律相似。 体系向新平衡位 置的转移速率 如果扰动刚停止就开始记时， t = 0, Δx = (Δx) o, 经过 t 时间后 偏离值 Δx 。

163. 163 τ 为当 Δx 达到 ( Δx ) 0 的 36.79 ％ 所需的时间 …… ……… 驰豫时间

164. 164 用实验方法确定驰豫时间 (time of relaxation), 求出 k 1 + k -1. 再结合 K ＝ k 1 / k -1, 分别求出 k 1 和 k -1 。 p 264 Table 12.13 例题 p265 闪光光解 应用强烈闪光脉冲，激发反应物反应，再测定其光解产物. 一般闪光： 20μs 左右， t 1/2 = 10 -6 s. 激光： t 1/2 = 10 -9 ～ 10 -12 s. p306-307 习题 12 、 16

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