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

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5.2 Kinetic gas theory 103 I Velocity distribution in 3 dimensions: Since the velocities in direction are independent, the probability that a molecule has a velocity between and + , and + ,and and + is given be the product of ( ) , ( ) , and ( ) : ( ) = ( ) ( ) ( ) µ Ã 32 = × exp − ¡ ¢ ! 2 + 2 + 2 (5.62) 2 2 We are, however, not interested in the distribution of velocities pointing into a specific direction ( ), but in the probability that a molecule has a certain speed || in any direction, i.e., that the velocity vector ends somewhere on a sphere with radius q || = 2 + 2 + 2 (5.63) To obtain this distribution, we must integrate over all polar angles and . This corresponds to replacing the volume element with the volume 4 2 of a spherical shell with radius and thickness y I The 3D Maxwell-Boltzmann speed distribution (Fig. 5.4): () = µ 32 × 4 2 × exp µ− 2 (5.64) 2 2 Note that this distribution is also normalized for Z ∞ () =1 We check this by substituting y Z ∞ 0 r r µ 12 = 2 y = 2 y = 2 (5.65) = 2 2 (5.66) 2 () = µ 32 × 4 2 0 Z ∞ 0 0 µ 2 2 2 −2 12 (5.67) µ 32 Z∞ µ 32 1 1 =4 × 2 −2 =4 × × 1 √ =1 (5.68) 4
5.2 Kinetic gas theory 104 I Figure 5.4: 3D Maxwell-Boltzmann speed distribution. I Notice the differences between the following quantities: • Value at maximum of (): • Mean speed: • Root mean square value: max = = r 2 r 8 ³ 2´12 = r 3 (5.69) (5.70) (5.71) I Table 5.1: Mean molecular speed values for some gases @ =298K gas [m s] H 2511 H 2 1776 He 1255 O 2 444 CO 2 379 Hg 178 238 U 163
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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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3.4 Generalized first-order kinetic
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Page 81 and 82: 3.6 Oscillating reactions* 66 3.6 O
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Page 85 and 86: 3.6 Oscillating reactions* 70 (5) S
Page 87 and 88: 3.6 Oscillating reactions* 72 I Fig
Page 89 and 90: 3.6 Oscillating reactions* 74 [X]
Page 91 and 92: 3.7 References 76 4. Experimental m
Page 93 and 94: 4.3 The discharge flow (DF) techniq
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Page 97 and 98: 4.4 Flash photolysis (FP) 82 4.4 Fl
Page 99 and 100: 4.4 Flash photolysis (FP) 84 I Figu
Page 101 and 102: 4.6 Stopped flow studies 86 4.6 Sto
Page 103 and 104: 4.8 Relaxation methods 88 4.8 Relax
Page 105 and 106: 4.9 Femtosecond spectroscopy 90 I F
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Page 109 and 110: 4.10 References 94 5. Collision the
Page 111 and 112: 5.1 Hardspherecollisiontheory 96
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Page 117: 5.2 Kinetic gas theory 102 I The 1D
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Page 123 and 124: 5.2 Kinetic gas theory 108 • Resu
Page 125 and 126: 5.3 Transport processes in gases 11
Page 131 and 132: 5.4 Advanced collision theory 116 W
Page 133 and 134: 5.4 Advanced collision theory 118 I
Page 135 and 136: 5.4 Advanced collision theory 120 5
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Page 155 and 156: 6.2 Polyatomic molecules 140 I Figu
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Page 159 and 160: 6.3 Trajectory Calculations 144 •
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Page 163 and 164: 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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