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

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Appendix G 295 G.3 Anwendung auf ein Zweiniveau-System I Chemisch relevante Beispiele für Zweiniveau-Systeme: • Paramagnetische Atome u. Moleküle • NMR-Spektroskopie: Atomkerne mit Kernspin. Typischer Frequenzbereich: 100 MHz. • Molekül mit cis-trans-Isomeren oder 2 Konformeren I Figure G.1: Zwei-Niveau-System: Energiezustände The Two Level System: Energy Levels g g Zustandssumme: Q i 0 / kT 1 / kT 1e 1e 1e i / kT i g e 1 / kT Besetzungsverhältnis: 0/ kT 0 g0e N N N N Q 1 / kT 1 g1e N N Q 1 / kT 1 g1e 0 / kT 0 ge 0 e 1 / kT Physical Chemistry III: Chemical Kinetics • © F. Temps, IPC Kiel 173 I Besetzungsverhältnis: mit 1 = 1 − 1 (G.33) = 0 − 0 + 1 − 1 =1+ − 1 (G.34) (G.35) (1) Grenzfall für → 0: 1 →∞y − 1 → −∞ =0 y Bei → 0 ist nur der tiefste Energiezustand besetzt. (G.36)
Appendix G 296 (2) Grenzfall für →∞: 1 → 0 y − 1 → −0 =1 (G.37) y Bei →∞ergibt sich eine Gleichbesetzung der Energiezustände. Dies ist die maximale Besetzung im oberen Zustand! • Eine Besetzungsinversion ( 1 0 ) würde formal eine negative Temperatur erfordern (→ Laser). I Figure G.2: Zwei-Niveau-System: Boltzmann-Besetzung der Zustände (rot: unterer Zustand, blau: oberer Zustand). The Two Level System: Boltzmann Distribution N i N 1 = 1000 J/mol 0.75 0.5 0.25 0 0 250 500 750 1000 T /(K) Physical Chemistry III: Chemical Kinetics • © F. Temps, IPC Kiel 174 I Mittlere thermische Energie: (1) 1 =125kJ mol (entsprechend =1000cm −1 ; z.B. C-C-Schwingung im IR oder Energieabstand zwischen cis-trans-Isomeren): ½ 1 = − 1 8 × 10 = −3 @ = 300K (G.38) 0 023 @ =1000K (2) 1 =004 kJ mol (entsprechend Energieabstand zwischen Kernspinzuständen bei 100 MHz NMR): 1 0 = − 1 =0999984 @ =300K (G.39) Reihenentwicklung: −1 =1− 1 + ≈ 1 − 1 (G.40) y sehr kleiner Besetzungsunterschied y Wunsch der NMR-Spektroskopiker zu immer größeren Frequenzen (Rekord heute 950 MHz).
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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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3.6 Oscillating reactions* 70 (5) S
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3.6 Oscillating reactions* 72 I Fig
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3.6 Oscillating reactions* 74 [X]
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3.7 References 76 4. Experimental m
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4.3 The discharge flow (DF) techniq
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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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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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Page 277 and 278: Appendix B 262 Appendix A: Useful p
Page 279 and 280: Appendix B 264 The Marquardt-Levenb
Page 281 and 282: Appendix C 266 • Convolution of t
Page 283 and 284: Appendix C 268 C.2 Application to t
Page 285 and 286: Appendix C 270 C.3 Application to p
Page 287 and 288: Appendix D 272 Final solutions for
Page 289 and 290: Appendix D 274 D.2 Special matrices
Page 291 and 292: Appendix D 276 I Multiplication by
Page 293 and 294: Appendix D 278 D.4 Coordinate trans
Page 295 and 296: Appendix D 280 D.5 Systems of linea
Page 297 and 298: Appendix D 282 D.6 Eigenvalue equat
Page 299 and 300: Appendix E 284 Secular equation: de
Page 301 and 302: Appendix E 286 Appendix E: Laplace
Page 303 and 304: Appendix F 288 Appendix F: The Gamm
Page 305 and 306: Appendix G 290 Appendix G: Ergebnis
Page 307 and 308: Appendix G 292 I Anschauliche Bedeu
Page 309: Appendix G 294 Ergebnis: = 1 X
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Page 315 and 316: Appendix G 300 G.5 Statistische Int
Page 317 and 318: Appendix G 302 y = (G.7
Page 319 and 320: Appendix G 304 G.8 Zustandssumme f
Page 321 and 322: Appendix G 306 G.9 Zustandssumme f
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Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

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