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

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2.6 Kinetics of simple composite reactions 29 2.6 Kinetics of simple composite reactions 2.6.1 Consecutive first-order reactions A −→ 1 B (2.102) B −→ 2 C (2.103) I Coupled differential equations: [A] = − 1 [A] (2.104) [B] =+ 1 [A] − 2 [B] (2.105) [C] =+ 2 [B] (2.106) In this case, since the DE’s are linear, there is an exact solution which we will examine first. We will also look at an approximate solution which can be obtained with the quasi steady-state approximation and at methods to obtain numerical solutions, which we have to use for complex non-linear inhomogeneous DE systems. I Mass balance: [A] + [B] + [C] = [A] 0 (2.107) I Initial conditions: [A ( =0)] = [A] 0 (2.108) [B ( =0)] = 0 (2.109) [C ( =0)] = 0 (2.110) I Exact solution: • First-order decay of [A]: y [A] = − 1 [A] (2.111) [A] = [A] 0 − 1 (2.112) • Inhomogeneous DE for [B]: [B] =+ 1 [A] − 2 [B] (2.113)
2.6 Kinetics of simple composite reactions 30 • Solution for [B ()] 18 : ⎧ 1 [A] ⎪⎨ 0 ¡ − 1 − ¢ − 2 if 1 6= 2 [B ()] = 2 − 1 (2.114) ⎪⎩ 1 [A] 0 − 1 if 1 = 2 • Reaction products by mass balance: [C ()] = [A] 0 − [A ()] − [B ()] = (2.115) I Figure 2.12: Kinetics of consecutive first-order reactions (case I). 18 ThesolutionisdetailedinAppendixC.
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Page 7 and 8: vii 12 Photochemical reactions 241
Page 9 and 10: ix Preface This scriptum contains l
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4.3 The discharge flow (DF) techniq
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4.4 Flash photolysis (FP) 82 4.4 Fl
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4.4 Flash photolysis (FP) 84 I Figu
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4.6 Stopped flow studies 86 4.6 Sto
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4.8 Relaxation methods 88 4.8 Relax
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4.9 Femtosecond spectroscopy 90 I F
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4.9 Femtosecond spectroscopy 92 I F
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4.10 References 94 5. Collision the
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5.1 Hardspherecollisiontheory 96
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5.1 Hardspherecollisiontheory 98 I
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5.1 Hard sphere collision theory 10
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5.2 Kinetic gas theory 102 I The 1D
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5.2 Kinetic gas theory 104 I Figure
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5.2 Kinetic gas theory 106 5.2.2 Th
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5.2 Kinetic gas theory 108 • Resu
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5.3 Transport processes in gases 11
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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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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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8.4 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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