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

More documents

Recommendations

Info

Appendix D 273 Appendix D: Matrix methods This appendix has been taken from the “Introduction to Molecular Spectroscopy” script, not all subsections apply to chemical kinetics. D.1 Definition I Matrices: A matrix is a rectangular, × dimensional array of numbers : A = ⎛ ⎜ ⎝ ⎞ 11 12 13 1 21 22 23 2 ⎟ . . . . ⎠ 1 2 3 (D.1) The are called the matrix elements. We will need to consider only × dimensional square matrices, which we can think of as a collection of column vectors a : ⎛ ⎞ 11 12 1 A = ⎜ 21 22 2 ⎟ ⎝ . . . ⎠ (D.2) 1 2 I Notation: Matrices will be denoted by bold symbols: A (D.3) I Matrix manipulation by computer programs: Matrix manipulations are carried out efficiently using computer programs (see, e.g., Press1992) or with symbolic algebra programs. 56 56 The most commmon symbolic math programs are MathCad, MuPad, Maple, andMathematica. MathCad and Mathematica are available in the PC lab.
Appendix D 274 D.2 Special matrices and matrix operations I Identity matrix: I = 1 I = 1 = ⎛ ⎜ ⎝ 10 0 01 0 . . . 00 1 ⎞ ⎟ ⎠ (D.4) We frequently use the Kronecker : = (D.5) where ½ 1 for = = 0 for 6= (D.6) I Diagonal matrices: ⎛ ⎜ ⎝ ⎞ 11 0 0 22 0 ⎟ . . . . ⎠ 0 0 (D.7) I Block diagonal matrices: ⎛ ⎞ 11 12 0 ⎜ 21 22 0 ⎟ ⎝ . . . . ⎠ 0 0 (D.8) I Complex conjugate (c.c.) of a matrix: A ∗ To obtain the complex conjugate A ∗ of the matrix A, change to −: ( ∗ ) =( ) ∗ (D.9) I Transpose of a matrix: To obtain the transpose A of the matrix A, interchange rows and colums: ¡ ¢ =( ) (D.10)
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:
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 165 and 166:
Page 167 and 168:
Page 169 and 170:
7.2 Applications of transition stat
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
7.3 Thermodynamic interpretation of
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
7.4 Transition state spectroscopy 1
Page 187 and 188:
Page 189 and 190:
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 and 200:
Page 201 and 202:
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
8.4 The specific unimolecular react
Page 209 and 210:
Page 211 and 212:
Page 213 and 214:
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 235 and 236:
10.2 Kinetics of heterogeneous reac
Page 237 and 238: 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 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: Appendix D 272 Final solutions for
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 ...

Create successful ePaper yourself

Delete template?

Save as template?