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

More documents

Recommendations

Info

8.3 Generalized Lindemann-Hinshelwood mechanism 185 8.3.3 The density of vibrational states ρ (E) Thedensityofvibrationalstatesisdefined as () = number of states in energy interval energy interval (8.41) i.e., () = () (8.42) In a polyatomic molecule, as we shall see in the following, () increases with very rapidly owing to the large number of overtone and combination states, and reaches truly astronomical values: a) s =1: () = 1 (8.43) b) s =2: We consider the ways, in which we can distribute two identical energy quanta between the two oscillators: Osc. 1 Osc. 2 Osc. 1 Osc. 2 Osc. 1 Osc. 2 Osc. 1 Osc. 2 0 - - 1 | - - | 2 2 || - | | - || 3 3 ||| - || | | || - ||| 4 4 5 5 6 . . . . (8.44) c) s oscillators: • For simplicity, we consider a molecule with identical harmonic oscillators. • This molecule shall be excited with quanta, eachofsize, i.e., the molecule has the excitation energy = I Question: How can we distribute these quanta over the oscillators?
8.3 Generalized Lindemann-Hinshelwood mechanism 186 I Answer: We are asking for the number of distinguishable possibilities to distribute quanta between oscillators, (). This is identical to the problem of distributing balls between boxes, for example for =11and =8: ••• • • • •• • •• (8.45) That number is identical to the number of distinguishable permutations of balls ( • ) and − 1 walls ( | ), ( + − 1)! () = (8.46) !( − 1)! where ( + − 1)! is the total number of permutations, which is corrected by dividing through !( − 1)! to account for the number of indistinguishable permutations among the balls (!) andwalls(( − 1)!) among each other (which give indistinguishable results). I Answer: We make the following approximation for À : 49 ( + − 1)! !( − 1)! ≈ −1 ( − 1)! (8.49) I Question: How can we compute ()? I Answer: () = () (8.50) (1) We consider the energy interval ∆ = (8.51) at the excitation energy = × (8.52) In this energy interval, we have the number of states ∆() = () (8.53) y () = () ∆ () ≈ ∆ = 1 ( + − 1)! !( − 1)! (8.54) 49 The approximation ( + − 1)! ≈ −1 (8.47) ! can be derived using Stirling’s formula (ln ! = ln − ) and the power series expansion of for || ¿1 (see homework assignment). ln (1 − ) ≈ (8.48)
Page 1 and 2:
Physical Chemistry 3: — Chemical
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 and 8:
vii 12 Photochemical reactions 241
Page 9 and 10:
ix Preface This scriptum contains l
Page 11 and 12:
xi Disclaimer Use of this text is e
Page 13 and 14:
xiii I Figure 2: Organisational mat
Page 15 and 16:
xv I Figure 6: Recommended textbook
Page 17 and 18:
1.2 Time scales for chemical reacti
Page 19 and 20:
1.2 Time scales for chemical reacti
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 27 and 28:
Page 29 and 30:
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
Page 37 and 38:
2.3 Kinetics of reversible first-or
Page 39 and 40:
2.4 Kinetics of second-order reacti
Page 41 and 42:
2.4 Kinetics of second-order reacti
Page 43 and 44:
2.5 Kinetics of third-order reactio
Page 45 and 46:
2.6 Kinetics of simple composite re
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
2.7 Temperature dependence of rate
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
3.1 Determination of the order of a
Page 59 and 60:
3.2 Application of the steady-state
Page 61 and 62:
3.2 Application of the steady-state
Page 63 and 64:
3.4 Generalized first-order kinetic
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
3.5 Numerical integration 58 I Surv
Page 75 and 76:
3.5 Numerical integration 60 2 ord
Page 77 and 78:
3.5 Numerical integration 62 3.5.5
Page 79 and 80:
3.5 Numerical integration 64 , Func
Page 81 and 82:
3.6 Oscillating reactions* 66 3.6 O
Page 83 and 84:
3.6 Oscillating reactions* 68 • B
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
Page 95 and 96:
4.3 The discharge flow (DF) techniq
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
Page 107 and 108:
4.9 Femtosecond spectroscopy 92 I F
Page 109 and 110:
4.10 References 94 5. Collision the
Page 111 and 112:
5.1 Hardspherecollisiontheory 96
Page 113 and 114:
5.1 Hardspherecollisiontheory 98 I
Page 115 and 116:
5.1 Hard sphere collision theory 10
Page 117 and 118:
5.2 Kinetic gas theory 102 I The 1D
Page 119 and 120:
5.2 Kinetic gas theory 104 I Figure
Page 121 and 122:
5.2 Kinetic gas theory 106 5.2.2 Th
Page 123 and 124:
5.2 Kinetic gas theory 108 • Resu
Page 125 and 126:
5.3 Transport processes in gases 11
Page 127 and 128:
Page 129 and 130:
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
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
5.4 Advanced collision theory 126 a
Page 143 and 144:
Page 145 and 146:
5.4 Advanced collision theory 130 (
Page 147 and 148:
Page 149 and 150: 5.4 Advanced collision theory 134 I
Page 151 and 152: 5.4 Advanced collision theory 136
Page 153 and 154: 5.4 Advanced collision theory 138 6
Page 155 and 156: 6.2 Polyatomic molecules 140 I Figu
Page 157 and 158: 6.2 Polyatomic molecules 142 I Mode
Page 159 and 160: 6.3 Trajectory Calculations 144 •
Page 161 and 162: 6.3 Trajectory Calculations 146 7.
Page 163 and 164: 7.1 Foundations of transition state
Page 169 and 170: 7.2 Applications of transition stat
Page 175 and 176: 7.3 Thermodynamic interpretation of
Page 185 and 186: 7.4 Transition state spectroscopy 1
Page 191 and 192: 8.1 Experimental observations 176 (
Page 193 and 194: 8.2 Lindemann mechanism 178 8.2 Lin
Page 195 and 196: 8.2 Lindemann mechanism 180 I Half-
Page 197 and 198: 8.3 Generalized Lindemann-Hinshelwo
Page 199: 8.3 Generalized Lindemann-Hinshelwo
Page 207 and 208: 8.4 The specific unimolecular react
Page 215 and 216: 8.5 Collisional energy transfer* 20
Page 217 and 218: 8.6 Recombination reactions 202 8.7
Page 219 and 220: 9.1 Chain reactions and chain explo
Page 221 and 222: 9.1 Chain reactions and chain explo
Page 223 and 224: 9.2 Heat explosions 208 • positiv
Page 225 and 226: 9.2 Heat explosions 210 (3) We can
Page 227 and 228: 9.2 Heat explosions 212 9.2.3 Explo
Page 229 and 230: 9.2 Heat explosions 214 10. Catalys
Page 231 and 232: 10.1 Kinetics of enzyme catalyzed r
Page 233 and 234: 10.2 Kinetics of heterogeneous reac
Page 243 and 244: 11.1 Qualitative model of liquid ph
Page 245 and 246: 11.2 Diffusion-controlled reactions
Page 247 and 248: 11.2 Diffusion-controlled reactions
Page 249 and 250: 11.3 Activation controlled reaction
Page 251 and 252:
11.4 Electron transfer reactions (M
Page 253 and 254:
11.5 Reactions of ions in solutions
Page 255 and 256:
11.5 Reactions of ions in solutions
Page 257 and 258:
12.2 Fluorescence quenching (Stern-
Page 259 and 260:
12.4 Radiationless processes in pho
Page 261 and 262:
Page 263 and 264:
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
14 Combustion chemistry* 258 15. As
Page 275 and 276:
16 Energy transfer processes* 260 1
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
Page 285 and 286:
Appendix C 270 C.3 Application to p
Page 287 and 288:
Appendix D 272 Final solutions for
Page 289 and 290:
Appendix D 274 D.2 Special matrices
Page 291 and 292:
Appendix D 276 I Multiplication by
Page 293 and 294:
Appendix D 278 D.4 Coordinate trans
Page 295 and 296:
Appendix D 280 D.5 Systems of linea
Page 297 and 298:
Appendix D 282 D.6 Eigenvalue equat
Page 299 and 300:
Appendix E 284 Secular equation: de
Page 301 and 302:
Appendix E 286 Appendix E: Laplace
Page 303 and 304:
Appendix F 288 Appendix F: The Gamm
Page 305 and 306:
Appendix G 290 Appendix G: Ergebnis
Page 307 and 308:
Appendix G 292 I Anschauliche Bedeu
Page 309 and 310:
Appendix G 294 Ergebnis: = 1 X
Page 311 and 312:
Appendix G 296 (2) Grenzfall für
Page 313 and 314:
Appendix G 298 G.4 Mikrokanonische
Page 315 and 316:
Appendix G 300 G.5 Statistische Int
Page 317 and 318:
Appendix G 302 y = (G.7
Page 319 and 320:
Appendix G 304 G.8 Zustandssumme f
Page 321 and 322:
Appendix G 306 G.9 Zustandssumme f
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?