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

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7.3 Thermodynamic interpretation of transition state theory 167 Kinetic isotope effects occur in particular in the case of H/D atom transfer reactions. The reason is that the threshold energy ∆ ‡ 0 depends on the vibrational zero-point energies. We consider the reactions where A+H—R → A—H—R ‡ → products (7.117) A+D—R → A—D—R ‡ → products (7.118) ∆ ‡ 0 (H—R) = ∆ ‡ + ‡ (A—H—R) − (H—R) (7.119) ∆ 0(D—R) ‡ = ∆ ‡ + ‡ (A—D—R) − (D—R) (7.120) with y = 1 2 X (7.121) ∆ ‡ 0(DH) = ∆‡ 0(D—R) − ∆ 0(H—R) ‡ (7.122) =+ ‡ (A—D—R) − ‡ (A—H—R) − ( (D—R) − (H—R)) (7.123) y Ã ! (D—R) (H—R) =exp − ∆‡ 0(D/H) (7.124) I Example 7.2: R-H/R-D substitution. The vibrational frequencies depend on the force constants and reduced masses : = 1 µ 12 (7.125) 2 For H/D substitution: (HR) (DR) ≈ 1 (7.126) 2 y µ 12 (HR) (HR) (DR) = ≈ √ 2 (7.127) (DR) With (HR) = 3000 cm −1 and (DR) = 2100 cm −1 , we find ∆ = 1 2 (3000 − 2100) cm−1 =450cm −1 , by which the DR reactant is stabilized compared to the HR reactant. For =300K: µ (DR) (HR) =exp − 450 ≈ −225 ≈ 01 (7.128) 200 For more realistic estimates, one has to take into account the change of all vibrational frequencies in the reacting molecules and the TS. ¤
7.3 Thermodynamic interpretation of transition state theory 168 7.3.4 Gibbs free enthalpy correlations I Figure 7.6: Linear free enthalpy correlations. Application of the TST expression = µ exp − ∆‡ (7.129) to a series of related reactions (1) and (2) often gives a relation of the type 48 ∆ ‡ 1 − ∆ ‡ 2 = ¡ ¢ ∆ ª 1 − ∆ ª 2 (7.130) y ln 1 = ln 1 (7.131) 2 2 7.3.5 Pressure dependence of k Liquid phase reactions often show a pressure dependence of the rate constant. Using the relation µ = (7.132) we can predict this pressure dependence. Starting with = µ exp − ∆‡ (7.133) we find µ ln = − ∆ ‡ (7.134) 48 A well-known example is the Hammett correlation in organic chemistry.
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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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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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