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

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7.3 Thermodynamic interpretation of transition state theory 163 • Note: and are given above in units of lmol −1 s −1 (we may denote this by writing them as and ), while ∆ ª‡ and ∆ ª‡ used above are referred to the standard state for gases of ª =1bar. <strong>—</strong> For ideal gases, ∆ ‡ and ∆ ‡ are related via ∆ ª‡ = ∆ ª‡ + ∆ ‡ ( )=∆ ª‡ − = ∆ +‡ − (7.87) <strong>—</strong> Likewise, ∆ ª‡ and ∆ +‡ for are related via ∆ +‡ − ∆ ª‡ = y Z + ª Z + = ª = Z + ª = Z + ª ∆ ‡ (7.88) = ∆ ‡ + ln + 0 = + ª ∆‡ ln + 0 = ª ª ∆‡ ln (7.89) + 0 = ∆ ‡ ln + 0 (7.90) ª with ª =1barand + = + + =1moll−1 . ∆ ª‡ = ∆ +‡ − ln + 0 ª (7.91) c) Thermodynamic transition state theory for reactions in the liquid phase For reactions in condensed phases, ∆ ≈ ∆ (7.92) and y £ ABC ‡ ¤ ‡ ( ) = [A] [BC] = ¡ +¢ ∆ ‡ exp ≈ ¡ +¢ ∆ ‡ exp µ− ∆+‡ exp • for unimolecular reactions: ( )= µ exp • for bimolecular reactions: ( )= µ + exp − ∆+‡ µ− ∆+‡ − ∆+‡ µ− ∆+‡ exp exp +‡ ∆ exp µ− µ− ∆+‡ µ− ∆+‡ (7.93) (7.94) (7.95) (7.96) Note: The conversion between values for ∆ +‡ and ∆ ª‡ and, likewise, between values for ∆ +‡ and ∆ ª‡ for a given reaction in the liquid and gas phase requires some caution. 46 46 See,e.g.,D.M.Golden,J.Chem.Ed.48, 235 (1971).
7.3 Thermodynamic interpretation of transition state theory 164 7.3.2 Applications of thermodynamic transition state theory a) Comparison of ∆S ‡ -values for different types of transition states I Bimolecular reactions: A+BC→ ABC ‡ (7.97) y ∆ ‡ 0 (7.98) or even ∆ ‡ ¿ 0 (7.99) Furthermore, for chemically otherwise similar molecules (nonlinear molecule) (linear molecule) À (cyclic molecule) (7.100) Thus, ¯ ¯∆ ‡ (nonlinear molecule)¯¯ ¯¯∆ ‡ (linear molecule)¯¯ ¿ ¯¯∆ ‡ (cyclic molecule)¯¯ (7.101) For example: ⎛ A ··· B ∆ ‡ ⎜ ⎝ ¯ y ... ⎞ ‡ ⎛ ‡ ⎞ ⎛ ⎟ A ··· B ¯ C ⎠¯¯¯¯¯¯¯ ¯∆‡ ⎝ A ··· B ··· C ⎠¯ ⎞ ‡ ¯ ¿ ∆ ‡ ⎜ ⎟ ⎝ . . ¯ C ··· D ⎠¯¯¯¯¯¯¯ (7.102) cyclic ¿ linear nonlinear (7.103) I Unimolecular reactions: ABC → ABC ‡ (7.104) • For isomerization reactions with a tight transition state: ∆ ‡ ⎛ ⎝ • For bond fission reactions with a loose transition state: ‡ B ⎞ Á Â ⎠ . 0 (7.105) A – C ∆ ‡ ¡ AB ···C ‡¢ 0 (7.106) y loose tight (7.107)
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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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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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