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

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viii E Laplace transforms 286 F The Gamma function Γ () 288 G Ergebnisse der statistischen Thermodynamik 290 G.1 Boltzmann-Verteilung 291 G.2 Mittelwerte 293 G.3 Anwendung auf ein Zweiniveau-System 295 G.4 Mikrokanonische und makrokanonische Ensembles 298 G.5 Statistische Interpretation der thermodynamischen Zustandsgrößen 300 G.6 Chemisches Gleichgewicht 301 G.7 Zustandssumme für elektronische Zustände 303 G.8 Zustandssumme für die Schwingungsbewegung 304 G.9 Zustandssumme für die Rotationsbewegung 306 G.10 Zustandssumme für die Translationsbewegung 307
ix Preface This scriptum contains lecture notes for the module “Physical Chemistry 3: Chemical Kinetics” (chem0405), the last part of the 3 semester course in Physical Chemistry for B.Sc. students of Chemistry and Business Chemistry at CAU Kiel. It is assumed (but not formally required) that students have previously taken courses on chemical thermodynamics (“Physical Chemistry 1: Chemical Equilibrium” or equivalent) and elementary quantum mechanics (“Physical Chemistry 2: Structure of Matter” or equivalent) as well as “Mathematics for Chemistry” (parts 1 and 2, or equivalent). Module chem0405 includes 3 hours weekly (3 SWS) for lectures and 1 SWS of exercises (56 contact hours combined). Students who started their studies at CAU Kiel should normally be in their 4th semester. The scriptum gives a summary of the material covered in the scheduled lectures to allow students to repeat the material more economically. It covers basic material that all chemistry students should learn irrespective of their possible inclination towards inorganic, organic or physical chemistry, but goes well beyond the standard Physical Chemistry textbooks used in the PC-1 and PC-2 courses. This is done in recognition of the established research focus at the Institute of Physical Chemistry at CAU to enable students to pursue their B.Sc. thesis project in Physical Chemistry. Some more specialized sections have been marked by asterisks and may be omitted on first reading towards the B.Sc. degree. Useful additional reference material is given in the Appendix. A brief lecture scriptum can never replace a textbook. For additional review, students are strongly encouraged (and at places required) to consult the recommended books on Chemical Kinetics beyond the standard Physical Chemistry textbooks. The book by Logan 1 is a comprehensive overview of the field of chemical kinetics and a nice introduction; it also has the advantage that it is written in German. The book by Pilling and Seakins 2 gives a good introduction especially to gas phase kinetics. The book by Houston 3 includes more information on the dynamics of chemical reactions. The book by Barrante 4 is highly recommended for everyone who wants to brush-up some math skills. A highly recommended web site for looking up mathematical definitions and recipies is the MathWorld online encyclopedia (http://mathworld.wolfram.com). The computer has become indispensable in modern research. This applies especially to Chemical Kinetics, where only computers can solve (by numerical integration) the coupled nonlinear partial differential equation systems that describe important complex reaction systems (e.g., related to combustion, the atmosphere or climate change). The integration of differential equations, a major task in chemical kinetics, can be performed using Wolfram Alpha (http://www.wolframalpha.com). More complicated problems can be solved with versatile computer algebra systems, e.g. (in order of increasing power) Derive, 5 MuPad, MathCad, 6 Maple, Mathematica 7 . A graphics program (e.g., Origin, 8 1 S. R. Logan, Grundlagen der Chemischen Kinetik, Wiley-VCH, Weinheim, 1996. 2 M. J. Pilling, P. W. Seakins, Reaction Kinetics, Oxford University Press, Oxford, 1995. 3 P. L. Houston, Chemical Kinetics and Reaction Dynamics, McGraw-Hill, 2001. 4 J. R. Barrante, Applied Mathematics for Physical Chemistry, Prentice Hall, 2003 ($ 47.11). 5 Derive is available as shareware without charge. 6 MathCad is installed in the PC lab. 7 Mathematica has been used by the author for some of the lecture material. 8 Student versions of Origin are available for ≈ 35 − 120 (depending on run time).
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Page 3 and 4: iii 2.7 Temperature dependence of r
Page 5 and 6: v 7.1.2 Formal kinetic model 149 7.
Page 7: vii 12 Photochemical reactions 241
Page 11 and 12: xi Disclaimer Use of this text is e
Page 13 and 14: xiii I Figure 2: Organisational mat
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Page 17 and 18: 1.2 Time scales for chemical reacti
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Page 21 and 22: 1.3 Historical events 6 I Empirical
Page 23 and 24: 1.4 References 8 2. Formal kinetics
Page 25 and 26: 2.1 Definitions and conventions 10
Page 31 and 32: 2.2 Kinetics of irreversible first-
Page 33 and 34: 2.2 Kinetics of irreversible first-
Page 35 and 36: 2.3 Kinetics of reversible first-or
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Page 51 and 52: 2.7 Temperature dependence of rate
Page 57 and 58: 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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8.1 Experimental observations 176 (
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8.2 Lindemann mechanism 178 8.2 Lin
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8.2 Lindemann mechanism 180 I Half-
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8.3 Generalized Lindemann-Hinshelwo
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8.4 The specific unimolecular react
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8.5 Collisional energy transfer* 20
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8.6 Recombination reactions 202 8.7
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9.1 Chain reactions and chain explo
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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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