Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

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5.4 Advanced collision theory 121 I 5 → 6:Thermal averaging over all ² : ( )= X × ( ) = X − × ( ) Z − = × ( ) I 3 → 5 and 4 → 6:Laplace Transformation: Z ∞ ( ) ∝ × ( ) × − (5.152) 0 This expression follows from the fundamental equation (Eq. 5.140) by substituting for . The exact transformation (giving the correct factors before the integral) will be carried out below (see Eq. 5.162). 5.4.4 Laplace transforms in chemistry Formally, the transformation (Eq. 5.152) is a Laplace transformation (see Appendix E). A Laplace transform generally described the transformation from a microscopic (“microcanonical”) quantity such as ( ) to a macroscopic (“macrocanonical”, i.e., dependent) quantity such as ( ). I Definition of the Laplace Transformation: The Laplace transform L [ ()] of a function () is defined as the integral () =L [ ()] = Z ∞ 0 () − (5.153) I Inverse Laplace Transformation: with an arbitrary real number . () =L −1 [ ()] = 1 2 Z +∞ −∞ () (5.154)
5.4 Advanced collision theory 122 I Notes: (1) The so far best known Laplace transform to us is the partition function ( )= X − = Z ∞ 0 () − (5.155) (2) While the pathway from ( ) to ( ) by forward Laplace transformation is straightforward, it is not generally straightforward to derive ( ) by inverse Laplace transformation from ( ), because ( ) would be needed from =0 to = ∞.
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Physical Chemistry 3: — Chemical
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iii 2.7 Temperature dependence of r
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v 7.1.2 Formal kinetic model 149 7.
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vii 12 Photochemical reactions 241
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ix Preface This scriptum contains l
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xi Disclaimer Use of this text is e
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xiii I Figure 2: Organisational mat
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xv I Figure 6: Recommended textbook
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1.2 Time scales for chemical reacti
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1.2 Time scales for chemical reacti
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1.3 Historical events 6 I Empirical
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1.4 References 8 2. Formal kinetics
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2.1 Definitions and conventions 10
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2.2 Kinetics of irreversible first-
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2.2 Kinetics of irreversible first-
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2.3 Kinetics of reversible first-or
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2.3 Kinetics of reversible first-or
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2.4 Kinetics of second-order reacti
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2.4 Kinetics of second-order reacti
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2.5 Kinetics of third-order reactio
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2.6 Kinetics of simple composite re
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2.7 Temperature dependence of rate
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3.1 Determination of the order of a
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3.2 Application of the steady-state
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3.2 Application of the steady-state
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3.4 Generalized first-order kinetic
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3.5 Numerical integration 58 I Surv
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3.5 Numerical integration 60 2 ord
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3.5 Numerical integration 62 3.5.5
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3.5 Numerical integration 64 , Func
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3.6 Oscillating reactions* 66 3.6 O
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3.6 Oscillating reactions* 68 • B
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Page 87 and 88: 3.6 Oscillating reactions* 72 I Fig
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Page 91 and 92: 3.7 References 76 4. Experimental m
Page 93 and 94: 4.3 The discharge flow (DF) techniq
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Page 97 and 98: 4.4 Flash photolysis (FP) 82 4.4 Fl
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Page 103 and 104: 4.8 Relaxation methods 88 4.8 Relax
Page 105 and 106: 4.9 Femtosecond spectroscopy 90 I F
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Page 109 and 110: 4.10 References 94 5. Collision the
Page 111 and 112: 5.1 Hardspherecollisiontheory 96
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Page 115 and 116: 5.1 Hard sphere collision theory 10
Page 117 and 118: 5.2 Kinetic gas theory 102 I The 1D
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Page 123 and 124: 5.2 Kinetic gas theory 108 • Resu
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Page 131 and 132: 5.4 Advanced collision theory 116 W
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Page 155 and 156: 6.2 Polyatomic molecules 140 I Figu
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Page 159 and 160: 6.3 Trajectory Calculations 144 •
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Page 163 and 164: 7.1 Foundations of transition state
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7.4 Transition state spectroscopy 1
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7.4 Transition state spectroscopy 1
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8.1 Experimental observations 176 (
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8.2 Lindemann mechanism 178 8.2 Lin
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8.2 Lindemann mechanism 180 I Half-
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8.3 Generalized Lindemann-Hinshelwo
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8.4 The specific unimolecular react
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8.5 Collisional energy transfer* 20
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8.6 Recombination reactions 202 8.7
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9.1 Chain reactions and chain explo
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9.1 Chain reactions and chain explo
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9.2 Heat explosions 208 • positiv
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9.2 Heat explosions 210 (3) We can
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9.2 Heat explosions 212 9.2.3 Explo
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9.2 Heat explosions 214 10. Catalys
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10.1 Kinetics of enzyme catalyzed r
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10.2 Kinetics of heterogeneous reac
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11.1 Qualitative model of liquid ph
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11.2 Diffusion-controlled reactions
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11.2 Diffusion-controlled reactions
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11.3 Activation controlled reaction
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11.4 Electron transfer reactions (M
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11.5 Reactions of ions in solutions
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11.5 Reactions of ions in solutions
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12.2 Fluorescence quenching (Stern-
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12.4 Radiationless processes in pho
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14 Combustion chemistry* 258 15. As
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16 Energy transfer processes* 260 1
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Appendix B 262 Appendix A: Useful p
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Appendix B 264 The Marquardt-Levenb
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Appendix C 266 • Convolution of t
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Appendix C 268 C.2 Application to t
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Appendix C 270 C.3 Application to p
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Appendix D 272 Final solutions for
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Appendix D 274 D.2 Special matrices
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Appendix D 276 I Multiplication by
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Appendix D 278 D.4 Coordinate trans
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Appendix D 280 D.5 Systems of linea
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Appendix D 282 D.6 Eigenvalue equat
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Appendix E 284 Secular equation: de
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Appendix E 286 Appendix E: Laplace
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Appendix F 288 Appendix F: The Gamm
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Appendix G 290 Appendix G: Ergebnis
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Appendix G 292 I Anschauliche Bedeu
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Appendix G 294 Ergebnis: = 1 X
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Appendix G 296 (2) Grenzfall für
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Appendix G 298 G.4 Mikrokanonische
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Appendix G 300 G.5 Statistische Int
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Appendix G 302 y = (G.7
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Appendix G 304 G.8 Zustandssumme f
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Appendix G 306 G.9 Zustandssumme f
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Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

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