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

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3.2 Application of the steady-state assumption 43 3.2 Application of the steady-state assumption The steady state assumption allows us to reduce a large reaction mechanism to a smaller one by eliminating the respective intermediate species. 3.2.1 The reaction H 2 + Br 2 → 2 HBr The reaction between H 2 and Br 2 (Bodenstein et al.; <strong>Christian</strong>sen, Polanyi & Herzfeld) runs as a thermal reaction or as a photochemically induced reaction (initiated by light). In the latter case, it is a chain reaction with a quantum yield of Φ ≈ 10 6 (3.13) I Definition 3.1: Quantum yield Φ: Φ = number of product molecules number of absorbed photons (3.14) I Reaction mechanism (elementary reactions) describing the H 2 -Br 2 system: Br 2 → Br + Br chain initiation by thermal dissociation (1) Br 2 + → Br + Br chain initiation by photolysis () (1 0 ) Br + H 2 → HBr + H chain propagation (2) H+Br 2 → HBr + Br chain propagation (3) H+HBr → H 2 +Br inhibition (4) Br + HBr 6→ Br 2 +H endothermic (∆ ª =+170kJ mol) (6) y reaction (6) can be neglected Br + Br +M → Br 2 chain termination (5) (3.15)
3.2 Application of the steady-state assumption 44 I Rates equations: With the steady state approximations (i.e., [X] ≈ 0) for[Br] and [H], weobtain 23 [H] [Br] [HBr] = + 2 [Br] [H 2 ] − 3 [H] [Br 2 ] − 4 [H] [HBr] ≈ 0 (3.16) y 2 [Br] [H 2 ] − 4 [H] [HBr] = + 3 [H] [Br 2 ] (3.17) 2 [Br] [H 2 ] y [H] = 3 [Br 2 ]+ 4 [HBr] (3.18) (3.19) = +2 1 [Br 2 ] − 2 [Br] [H 2 ]+ 3 [H] [Br 2 ]+ 4 [H] [HBr] | {z } =− [H] ≈0 −2 5 [Br] 2 (3.20) = +2 1 [Br 2 ] − 2 5 [Br] 2 ≈ 0 (3.21) µ 12 1 y [Br] = [Br 2 ] (3.22) 5 µ 12 1 2 [H 2 ] y [H] = [Br 2 ] × (3.23) 5 3 [Br 2 ]+ 4 [HBr] = 2 [Br] [H 2 ]+ 3 [H] [Br 2 ] − 4 [H] [HBr] (3.24) Using 2 [Br] [H 2 ] − 4 [H] [HBr] = + 3 [H] [Br 2 ] (Eq. 3.17) and substituting [H] (Eq. 3.18), the last line simplifies to [HBr] =2 3 [H] [Br 2 ] (3.25) µ 12 1 2 [H 2 ] =2 3 [Br 2 ] × [Br 2 ] × 5 3 [Br 2 ]+ 4 [HBr] (3.26) = 2 2 ( 1 5 ) 12 [H 2 ][Br 2 ] 12 1+( 4 3 )[HBr] [Br 2 ] (3.27) = 0 [H 2 ][Br 2 ] 12 1+ 00 [HBr] [Br 2 ] (3.28) I Result: with [HBr] = 0 [H 2 ][Br 2 ] 12 1+ 00 [HBr] [Br 2 ] (3.29) 0 =2 2 ( 1 5 ) 12 and 00 = 4 3 (3.30) I Conclusion: We see that HBr acts as an inhibitor of the total reaction. 23 For the photolysis induced reaction, 1 has to be replaced by 0 1 ,where is the light intensity and 0 1 the corresponding photolysis rate constants (related to the absorption coefficient).
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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.
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
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Page 39 and 40: 2.4 Kinetics of second-order reacti
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Page 45 and 46: 2.6 Kinetics of simple composite re
Page 51 and 52: 2.7 Temperature dependence of rate
Page 57: 3.1 Determination of the order of a
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Page 63 and 64: 3.4 Generalized first-order kinetic
Page 73 and 74: 3.5 Numerical integration 58 I Surv
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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
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Page 91 and 92: 3.7 References 76 4. Experimental m
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Page 99 and 100: 4.4 Flash photolysis (FP) 84 I Figu
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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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