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

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3.5 Numerical integration 65 1 c 0.75 0.5 0.25 0 0 1.25 2.5 3.75 5 t (6) The rest is just some fixing up: We combine the two plots, with an increased number of points plotted, add axis labels and colors: 1 c(t) 0.75 0.5 0.25 0 0 1.25 Numerical solution of the DE system defined by Eq. 3.163. Full lines: numeric solutions. Dotted lines: exact solutions. 2.5 t 3.75 5 The exact and the numerical solutions are identical within numeric precision.
3.6 Oscillating reactions* 66 3.6 Oscillating reactions* The reactant and product concentrations normally approach equilibrium in a smooth (often exponenential) fashion. Under special circumstances, however, the concentrations may also show oscillations and/or bistability as they approach equilibrium. Such behavior can occur only if there is a chemical feedback by autocatalysis. 3.6.1 Autocatalysis Example for autocatalysis: A+B → B+B (3.167) Rate law: − [A] = [A] [B] (3.168) To solve this DE, we substitute for [B ()] using the mass balance relation [A] 0 −[A ()] = [B ()] − [B] 0 and introduce =[A()] as reaction progress variable: [B ()] = [A] 0 +[B] 0 − [A ()] (3.169) =[A] 0 +[B] 0 − (3.170) This gives the DE y Z − = ([A] 0 +[B] 0 − ) (3.171) Z ([A] 0 +[B] 0 ) − = − (3.172) 2 Solution: or [B ()] = µ 1 [A]0 [B ()] ln = − (3.173) [A] 0 +[B] 0 [B] 0 [A ()] [A] 0 +[B] 0 1+([A] 0 [B] 0 )exp[− ([A] 0 +[B] 0 ) ] (3.174)
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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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2.1 Definitions and conventions 12
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Page 57 and 58: 3.1 Determination of the order of a
Page 59 and 60: 3.2 Application of the steady-state
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Page 63 and 64: 3.4 Generalized first-order kinetic
Page 73 and 74: 3.5 Numerical integration 58 I Surv
Page 75 and 76: 3.5 Numerical integration 60 2 ord
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Page 83 and 84: 3.6 Oscillating reactions* 68 • B
Page 85 and 86: 3.6 Oscillating reactions* 70 (5) S
Page 87 and 88: 3.6 Oscillating reactions* 72 I Fig
Page 89 and 90: 3.6 Oscillating reactions* 74 [X]
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
Page 99 and 100: 4.4 Flash photolysis (FP) 84 I Figu
Page 101 and 102: 4.6 Stopped flow studies 86 4.6 Sto
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
Page 113 and 114: 5.1 Hardspherecollisiontheory 98 I
Page 115 and 116: 5.1 Hard sphere collision theory 10
Page 117 and 118: 5.2 Kinetic gas theory 102 I The 1D
Page 119 and 120: 5.2 Kinetic gas theory 104 I Figure
Page 121 and 122: 5.2 Kinetic gas theory 106 5.2.2 Th
Page 123 and 124: 5.2 Kinetic gas theory 108 • Resu
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5.4 Advanced collision theory 116 W
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5.4 Advanced collision theory 118 I
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5.4 Advanced collision theory 120 5
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5.4 Advanced collision theory 126 a
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5.4 Advanced collision theory 130 (
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5.4 Advanced collision theory 136
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5.4 Advanced collision theory 138 6
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6.2 Polyatomic molecules 140 I Figu
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6.2 Polyatomic molecules 142 I Mode
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6.3 Trajectory Calculations 144 •
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6.3 Trajectory Calculations 146 7.
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7.1 Foundations of transition state
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7.2 Applications of transition stat
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7.3 Thermodynamic interpretation of
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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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