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

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7.5 References 175 8. Unimolecular reactions Unimolecular reactions are reactions in which only one species experiences chemical change. I Figure 8.1: Examples of unimolecular reactions. 8.1 Experimental observations (1) There are many reactions governed by a first-order rate law, [A] = − ∞ [A] , (8.1) for example isomerization and dissociation reactions like Cyclopropane → Propene (8.2) -Butene → -Butene (8.3) C 2 H 6 → 2CH 3 (8.4) Cycloheptatriene → Toluene (8.5) (2) In these reactions, no other species than the reactants experience any chemical change. (3) These reactions have the same rates in the gas phase and in solution, gas phase ≈ solution phase , (8.6) i.e., the environment has no effect on the reaction rates!
8.1 Experimental observations 176 (4) There are many similar other reactions, however, for which the rate law is secondorder, i.e., [A] = − 0 [A] [M] (8.7) Examples are Br 2 → Br + Br (8.8) H 2 O 2 → OH + OH (8.9) (5) More detailed measurements show that at a given temperature the order of the reaction may depend on pressure (see Fig. 8.2), for instance for the reaction one has found that CH 3 NC → CH 3 CN (8.10) a) for → 0: [CH 3 NC] = − 0 [CH 3 NC] [M] (8.11) This is called the “low pressure range” for the reaction. b) for →∞: [CH 3 NC] = − ∞ [CH 3 NC] (8.12) This is called the “high pressure range” for the reaction”. (6) The transition from the low to the high pressure range depends a) onthesizeofthemolecule(seeFig.8.3), b) for a given molecule, it depends on temperature. (7) The activation energy in the low pressure regime is much smaller than in the high pressure regime: = 2 ln (8.13) where 0 ∞ (8.14) and ∞ ≈ 0 (8.15) (8) The preexponential factors in the low pressure regime are much higher than the collision frequencies, i.e., 0 (8.16) (9) For all these reactions, the molecules must somehow be “energized”. There are other reactions, in which the molecules are energized chemically (“chemically activated reactions”) or by photons. At the microscopic, i.e., molecular level, these reactions should have related mechanisms.
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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 122 I
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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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