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

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9.2 Heat explosions 209 I Conclusions: • The quantity that determines whether the system is stable or not is the wall temperature 0 ,because 0 determines the initial point of the heat removal line. • Smaller surface-to-volume ratio is dangerous, because smaller surface at a given volume leads to a smaller slope of the heat removal line y instability! • Security measure: internal cooling system (cold water pipes, heat exchanger). • Emergency measure: when cooling system fails, the reaction mixture should be strongly diluted by addition of solvent immediately! I Quantitative estimation of the stability limits:* At point (4) in Fig. 9.4, we have: = (9.27) y ( − 0 )= ∆ ª 0 − (9.28) = (9.29) y = ∆ ª 0 − 2 (9.30) Eq Eq y 2 =( − 0 ) (9.31) y 2 − + y = 2 ± s µ 2 0 =0 (9.32) 2 − 0 (9.33) Solution is: ⎧ ⎪⎨ = 1 ³ + p ´ ⎫ ( 2 2 − 4 0 ) ⎪⎬ ⎪ ⎩ = 1 ³ − p ´ ( 2 2 − 4 0 ) ⎪⎭ This can be simplified: (9.34) (1) For practically important reactions, we have: À 0 y 0 ¿ (9.35) (2) We also can exclude unreasonably hight temperatures y only the −-sign before ∗ s = µ 2 2 − − 2 0 (9.36) = 2 − r 1 − 4 0 (9.37) 2 √ counts: y = 2 Ã r 1 − ! 1 − 4 0 (9.38)
9.2 Heat explosions 210 (3) We can expand the √ : = 4 0 ; 1; (9.39) y √ 1 − =1− 1 2 − 1 2 · 4 2 − (9.40) y ∗ = µ 1 − 1+ 2 0 + 16 · 2 0 2 2 2 · 4 · ( ) 2 + (9.41) y ∗ = 0 + 2 0 (9.42) y ∗ − 0 = 2 0 (9.43) (4) Insert into in (I) and power expansion: · · (5) Explosion limit: 2 0 2 · exp µ 2 0 ∙ − ¸ = 0 ⎡ = · ∆ ª · 0 · exp ⎣− ´ ⎦ · · (9.44) 0 ³1+ 0 ∙ = · ∆ ª · 0 · · exp − ¸ · 2 · · (9.45) 0 · · · ∆ ª · · · 0 · · = (9.46) ⎤ y ∝ · (9.47) Power expansion of the exponent in step (4): ⎡ ⎤ ∙ exp ⎣− ´ ⎦ =exp − 0 ³1+ 1 ¸ 1 0 1+ ∙ =exp − 1 ≈ exp ∙− 1 (1 − )¸ ∙ =exp 1 − 1 ¸ ∙ = 1 · exp − 1 ¸ ∙ = · exp − ¸ 0 ¡ 1 − + 2 ¢¸ = 0 ¿ 1(9.48) (9.49) (9.50) (9.51) (9.52) (9.53)
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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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7.2 Applications of transition stat
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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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