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

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iv 4.7 NMR spectroscopy 87 4.8 Relaxation methods 88 4.9 Femtosecond spectroscopy 89 4.10 References 93 5 Collision theory 94 5.1 Hard sphere collision theory 95 5.1.1 The gas kinetic collision frequency 95 5.1.2 Allowance for a threshold energy for reaction 99 5.1.3 Allowance for steric hindrance 100 5.2 Kinetic gas theory 101 5.2.1 The Maxwell-Boltzmann speed distributions of gas molecules in 1D and 3D 101 5.2.2 The rate of wall collisions in 3D 106 5.3 Transport processes in gases 110 5.3.1 The general transport equation 110 5.3.2 Diffusion 112 5.3.3 Heat conduction 113 5.3.4 Viscosity 114 5.4 Advanced collision theory 115 5.4.1 Fundamental equation for reactive scattering in crossed molecular beams 116 5.4.2 Crossed molecular beam experiments 117 5.4.3 From differential cross sections () to reaction rate constants ( ) 120 5.4.4 Laplace transforms in chemistry 121 5.4.5 Bimolecular rate constants from collision theory 123 5.4.6 Long-range intermolecular interactions 132 6 Potential energy surfaces for chemical reactions 138 6.1 Diatomic molecules 138 6.2 Polyatomic molecules 139 6.3 Trajectory Calculations 143 7 Transition state theory 146 7.1 Foundations of transition state theory 146 7.1.1 Basic assumptions of TST 147
v 7.1.2 Formal kinetic model 149 7.1.3 The fundamental equation for ( ) 149 7.1.4 Tolman’s interpretation of the Arrhenius activation energy 153 7.2 Applications of transition state theory 154 7.2.1 The molecular partition functions 154 7.2.2 Example 1: Reactions of two atoms A + B → A···B ‡ → AB 156 7.2.3 Example 2: The reaction F + H 2 → F···H···H ‡ → FH + H 157 7.2.4 Example 3: Deviations from Arrhenius behavior (T dependence of ( ))* 159 7.3 Thermodynamic interpretation of transition state theory 160 7.3.1 Fundamental equation of thermodynamic transition state theory 160 7.3.2 Applications of thermodynamic transition state theory 164 7.3.3 Kinetic isotope effects 166 7.3.4 Gibbs free enthalpy correlations 168 7.3.5 Pressure dependence of 168 7.4 Transition state spectroscopy 170 7.5 References 174 8 Unimolecular reactions 175 8.1 Experimental observations 175 8.2 Lindemann mechanism 178 8.3 Generalized Lindemann-Hinshelwood mechanism 182 8.3.1 Master equation 182 8.3.2 Equilibrium state populations 184 8.3.3 The density of vibrational states () 185 8.3.4 Unimolecular reaction rate constant in the low pressure regime 188 8.3.5 Unimolecular reaction rate constant in the high pressure regime 190 8.4 The specific unimolecular reaction rate constants () 191 8.4.1 Rice-Ramsperger-Kassel (RRK) theory 191 8.4.2 Rice-Ramsperger-Kassel-Marcus (RRKM) theory 193 8.4.3 The SACM and VRRKM model 198 8.4.4 Experimental results 199 8.5 Collisional energy transfer* 200 8.6 Recombination reactions 201
Page 1 and 2: Physical Chemistry 3: — Chemical
Page 3: iii 2.7 Temperature dependence of r
Page 7 and 8: vii 12 Photochemical reactions 241
Page 9 and 10: ix Preface This scriptum contains l
Page 11 and 12: xi Disclaimer Use of this text is e
Page 13 and 14: xiii I Figure 2: Organisational mat
Page 15 and 16: xv I Figure 6: Recommended textbook
Page 17 and 18: 1.2 Time scales for chemical reacti
Page 19 and 20: 1.2 Time scales for chemical reacti
Page 21 and 22: 1.3 Historical events 6 I Empirical
Page 23 and 24: 1.4 References 8 2. Formal kinetics
Page 25 and 26: 2.1 Definitions and conventions 10
Page 31 and 32: 2.2 Kinetics of irreversible first-
Page 33 and 34: 2.2 Kinetics of irreversible first-
Page 35 and 36: 2.3 Kinetics of reversible first-or
Page 37 and 38: 2.3 Kinetics of reversible first-or
Page 39 and 40: 2.4 Kinetics of second-order reacti
Page 41 and 42: 2.4 Kinetics of second-order reacti
Page 43 and 44: 2.5 Kinetics of third-order reactio
Page 45 and 46: 2.6 Kinetics of simple composite re
Page 51 and 52: 2.7 Temperature dependence of rate
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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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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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