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

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2.7 Temperature dependence of rate coefficients 37 I I It is important to realize, however, that the value of E is not equal to the true height of the potential energy barrier for the reaction! As said above, is an empirical quantity! Its relation to the true threshold energy 0 , which is the minimum energy above which reaction may occur, will be a main subject in the theory of bimolecular and unimolecular reactions (Sections 5 <strong>—</strong> 8). There is also a statistical interpretation of (see Section 8). Figure 2.15: The reaction HCO → H + CO (G. Friedrichs). 2.7.2 Deviations from Arrhenius behavior In general, is dependent on temperature, i.e., = ( ). For gas phase reactions, for example, there is at least the √ dependence of the hard sphere collision frequency. The -dependence of is often small compared to so that within experimental error the dependence of ( ) is determined by . If the -dependence of is not small compared to ,wewillhavetouseamore general expression for ( ), as explained in the following. I Generalized three-parameter expression for k (T ): To account for deviations from Arrhenius because of ( ), one conveniently employs the three parameter expression ( )= − 0 (2.168) with and 0 now being -independent quantities. Range of values for specific bimolecular reactions (justified by theory; see later): − 15 ≤ ≤ +3 (2.169)
2.7 Temperature dependence of rate coefficients 38 I I Question: What is the relation of Eq. 2.168 with the Arrhenius equation? Answer: We have to evaluate the Arrhenius parameters from Eq. 2.168 according to the definitions of and : (1) : =+ 2 ln (2.170) =+ 2 µ ln + ln − 0 (2.171) y = 0 + (2.172) Onlyinthecasethat ¿ 0 can we neglect the term compared to 0 ! (2) : From the expression for ,wehave y 0 = − (2.173) ( )= −( − ) = − = − (2.174) (2.175) (2.176) Comparing coefficients, we find = (2.177) 2.7.3 Examples for non-Arrhenius behavior Complex forming bimolecular reactions may show extreme non-Arrhenius behavior. An extreme case is the reaction OH + CO → H+CO 2 , which incidentally is the single most important reaction in hydrocarbon combustion next to H+O 2 → OH + O.
Page 1 and 2: Physical Chemistry 3: — Chemical
Page 3 and 4: iii 2.7 Temperature dependence of r
Page 5 and 6: v 7.1.2 Formal kinetic model 149 7.
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: 2.7 Temperature dependence of rate
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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
Page 61 and 62: 3.2 Application of the steady-state
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
Page 77 and 78: 3.5 Numerical integration 62 3.5.5
Page 79 and 80: 3.5 Numerical integration 64 , Func
Page 81 and 82: 3.6 Oscillating reactions* 66 3.6 O
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
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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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