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

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10.2 <strong>Kinetics</strong> of heterogeneous reactions (surface reactions) 227 11. Reactions in solution “Everyone has problems - chemists have solutions.” I Comparison of gas and liquid phase reactions (@ T = 298 K and p =1bar): • Molecules in the gas phase occupy ≈ 02 % of the total volume, while molecules in the liquid phase occupy ≈ 50 % of the total volume. • Molecules in liquid are in permanent contact with each other, and undergo permanent collisions with each other. • The crossing of a potential barrier in a reaction is not continuous as in gas phase but affected by multiple collisions during the crossing. • As a result of the permanent collisions, we can expect the reactant molecules to be in thermodynamic equilibrium even above 0 . Thus TST should be applicable. • However, it is very difficult to evaluate the partition functions in liquids. Hence, one usually employs the thermodynamic version TST. • Solvent molecules act as an efficient heat bath. I Observations on liquid phase reactions: Experience has shown that reactions in liquids have similar rates as in the gas phase, except if • the reaction occurs with the solvent, • there are strong interactions of the reactant molecules with the solvent (e.g., ionic reactions; ⇒ solvent shells), • the reactions are diffusion controlled. 11.1 Qualitative model of liquid phase reactions In contrast to gas phase reactions for which we have advanced theories (⇒ transition state theory, unimolecular rate theory), the theory for liquid phase reactions is much less well developed. However, we can understand the required basic reaction steps as sketched in Fig. 11.1 and a number of limiting cases resulting from these steps.
11.1 Qualitative model of liquid phase reactions 228 I Figure 11.1: Structure and dynamics of solutions. I Formal kinetics: We distinguish between the formation of the encounter complex in the solvent cage (by diffusion) and the actual reaction: + À − {} → (11.1) y y with [{}] [ ] = [][] − − [{}] − [{}] ≈ 0 (11.2) [{}] = − + [][] (11.3) = [{}] = − + [][] = [][] (11.4) = − + (11.5) I Rate constant for liquid phase reactions: = − + (11.6)
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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 126 a
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5.4 Advanced collision theory 130 (
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5.4 Advanced collision theory 136
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5.4 Advanced collision theory 138 6
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6.2 Polyatomic molecules 140 I Figu
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6.2 Polyatomic molecules 142 I Mode
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6.3 Trajectory Calculations 144 •
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6.3 Trajectory Calculations 146 7.
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7.1 Foundations of transition state
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7.2 Applications of transition stat
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7.3 Thermodynamic interpretation of
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7.4 Transition state spectroscopy 1
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Page 229 and 230: 9.2 Heat explosions 214 10. Catalys
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Page 277 and 278: Appendix B 262 Appendix A: Useful p
Page 279 and 280: Appendix B 264 The Marquardt-Levenb
Page 281 and 282: Appendix C 266 • Convolution of t
Page 283 and 284: Appendix C 268 C.2 Application to t
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Page 289 and 290: Appendix D 274 D.2 Special matrices
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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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