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

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7.2 Applications of transition state theory 157 7.2.3 Example 2: The reaction F + H 2 → F···H···H ‡ → FH + H I Exercise 7.1: Evaluatetherateconstantforthereaction F+H 2 → F ···H ···H ‡ → FH + H (7.47) using the data in Table 7.2 at =200, 300, 500, 1000 and 2000 K, determinethe Arrhenius parameters, and compare the results with the experimental value of =2× 10 14 exp (−800 )cm 3 mol s (7.48) ¤ I Table 7.2: Properties of the reactants and transition state of the reaction F + H 2 . parameter F ···H ···H ‡ a F H 2 2 (F ···H) ( Å) 1602 1 (H ···H) ( Å) 0756 07417 b 1 (cm −1 ) 40076 43952 2 (cm −1 ) 3979 3 (cm −1 ) 3979 4 (cm −1 ) 3108 c ³ (u) 21014 189984 2016 u Å 7433 0277 1 2 d 4 4 1 0 ¡ kJ mol −1¢ 657 000 a The transition state FHH ‡ is assumed to be linear. b = (H-H). c One imaginary frequency describes the TS along the RC. d The electronic ground state of F is 2 32 . We neglect the 2 12 spin-orbit component at ( 2 12 )= 404 cm −1 because it does not correlate with the products H + HF. The electronic state of linear FHH ‡ is 2 Π. The ground state of H 2 is 2 Σ + . I Solution 7.1: ( )= ‡ µ exp − ∆ 0 2 Ã ! = ‡ ( )( 2 ) µ × exp − ∆ 0 Ã ! ‡ 2 Ã ! ‡ 2 (7.49) Ã ! ‡ 2 (7.50)
7.2 Applications of transition state theory 158 The different factors can be evaluated separately: Ã ! ‡ µ 32 µ + 2 2 32 = (7.51) ( )( 2 ) 2 2 Ã ! ‡ µ 8 2 ‡ 2 ‡ = = 2 8 2 2 2 2 2 (7.52) 2 Ã ! ‡ 1 − exp (− 2 ) = (7.53) 2 3Y ´i Ã ! ‡ 2 =1 = 4 4 × 1 h 1 − exp ³ − ‡ (7.54) Note: The difference between the TST result and experiment can be ascribed (a) to tunneling and (b) deficiencies of the ab initio PES. Indeed, according to newer ab initio calculations, the TS is actually slightly bent and the TS parameters differ slightly, yielding better agreement with experiment. ¥
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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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Page 131 and 132: 5.4 Advanced collision theory 116 W
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Page 141 and 142: 5.4 Advanced collision theory 126 a
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Page 155 and 156: 6.2 Polyatomic molecules 140 I Figu
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Page 163 and 164: 7.1 Foundations of transition state
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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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