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

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Appendix E 285 I Final note: In practice, matrix manipulations such as matrix inversion, the evaluation of determinants, the determination of eigenvalues and eigenvectors, etc., arecarriedout numerically by using computers. I References Press 1992 W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran, Cambridge University Press, Cambridge, 1992. Versions are also available for C and Pascal.
Appendix E 286 Appendix E: Laplace transforms The concept of Laplace and inverse Laplace transforms is extremely useful in chemical kinetics for two reasons: (1) They connect microscopic molecular properties and statistically averaged quantities: a) () ↔ ( ): Collision cross section vs. thermal rate constant for bimolecular reactions (section ??), b) () ↔ ( ): Specific rateconstantvs. thermal rate constant for unimolecular reactions (section 8), c) () ↔ ( ): Density of states vs. partition function in statistical rate theories 8). (2) They provide a convenient method for solving of differential equations (section 3.4.2). I Definition E.1: The Laplace transform L [ ()] of a function () is defined as the integral Z ∞ () =L [ ()] = () − (E.1) where 0 • is a real variable, • () is a real function of the variable with the property () =0for 0, • is a complex variable, • () =L [ ()] is a function of the variable . I Definition E.2: The inverse Laplace transform L −1 [ ()] of the function () is defined as the integral () =L −1 [ ()] = 1 Z 2 +∞ −∞ () (E.2) where • is an arbitrary real constant.
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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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Page 273 and 274: 14 Combustion chemistry* 258 15. As
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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: Appendix E 284 Secular equation: de
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 and 310: Appendix G 294 Ergebnis: = 1 X
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Page 313 and 314: Appendix G 298 G.4 Mikrokanonische
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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