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

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7.2 Applications of transition state theory 155 I Separation of degrees of freedom: For separable degrees of freedom, we can write the molecular partition function as = × × × (7.41) Nuclear spin ( ) may have to be taken into account in some cases as well. I Table 7.1: Molecular partition functions. type of motion energy partition function magnitude µ translation (1-D) 2 2 12 2 10 8 × 8 2 µ µ 2 translation (3-D) 2 2 32 + 2 + 2 2 10 24 × 8 2 2 2 µ 2 rotation (1-D) a ~ 2 12 2 2 2 10 µ ~ 2 rotation (2-D) b ~ 2 2 ( +1) 10 2 2 ~ 2 µ rotation (3-D) c 12 32 2 or ( ~ 2 ) 12 10 3 10 4 vibration d [1 − exp (− )] −1 1 10 electronic P exp (− ) 1 a Free internal rotor. For a hindered rotor (torsional vibrational mode), the partition function has to be determined by an explicit calculation over the hindered rotor quantum states. b Linear molecule. c Nonlinear molecule. d For each harmonic oscillator degree of freedom measured from zero-point level.
7.2 Applications of transition state theory 156 7.2.2 Example 1: Reactions of two atoms A + B → A···B ‡ → AB This example is somewhat artifical unless there is some mechanism to remove the bond energy (for example, in associative ionization, A + B → A···B ‡ → AB + + − ). ‡ µ exp − ∆ 0 Ã ! Ã ! = ‡ ‡ ( )( ) 1 = µ 2 ( + ) 2 2 2 µ × exp − ∆ 0 = µ 2 + 2 µ × exp − ∆ 0 ( )= µ exp − ∆ 0 2 2 32 µ 8 2 ‡ 2 32 Ã ! 8 2 ( + ) 2 2 + y µ 12 µ 8 ( )= ( + ) 2 exp − ∆ 0 This result is identical to that obtained by the LC model in collision theory! (7.42) (7.43) (7.44) (7.45) (7.46)
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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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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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