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

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10.1 <strong>Kinetics</strong> of enzyme catalyzed reactions (homogeneous catalysis) 215 10.1.1 The Michaelis-Menten mechanism Basic reaction scheme: E+S 1 À ES (10.2) −1 ES 2 → E+P (10.3) Typical values of 2 : 2 ≈ 10 2 10 3 s −1 (in some cases up to 10 6 s −1 ) (10.4) Reaction rate: [P] = − [S] = 2 [ES] (10.5) [ES] = 1 [E] [S] − −1 [ES] − 2 [ES] (10.6) ≈ 0 (10.7) Mass balance: Steady state ES concentration: [E] 0 = [E]+[ES] (10.8) y [E] = [E] 0 − [ES] (10.9) [S] 0 = [S]+[ES]+[P] (10.10) y [S] = [S] 0 − [ES] − [P] (10.11) [ES] = 1 ([E] 0 − [ES]) ([S] 0 − [ES] − [P]) − ( −1 + 2 )[ES] (10.12) ≈ 0 (10.13) Approximations: y [ES] [E] 0 ¿ [S] 0 (10.14) [ES] ¿ [S] 0 (10.15) [P] ≈ 0 for early times (10.16) = 1 [E] 0 [S] 0 − 1 [S] 0 [ES] − ( −1 + 2 )[ES] (10.17) ≈ 0 (10.18) Steady state ES concentration: [ES] = 1 [E] 0 [S] 0 1 [S] 0 + −1 + 2 (10.19)
10.1 <strong>Kinetics</strong> of enzyme catalyzed reactions (homogeneous catalysis) 216 Resulting rate expression: y = [P] = 2 [ES] (10.20) 1 2 [E] = 0 [S] 0 (10.21) 1 [S] 0 + −1 + 2 2 [E] = 0 1+ (10.22) −1 + 2 1 [S] 0 = with the Michaelis-Menten constant 2 [E] 0 1+ [S] 0 (10.23) = −1 + 2 1 (10.24) Limiting cases: (1) [S] 0 →∞y [S] 0 ¿ 1: y = [P] = 2 [E] 0 (10.25) (2) [S] 0 → 0 y [S] 0 À 1: y = [P] = 2 [E] 0 [S] 0 (10.26) Determination of 2 and from a Lineweaver-Burk plot (Fig. 10.2): 1 = 1 + 1 (10.27) 2 [E] 0 2 [E] 0 [S] 0 ⇒ Aplotof −1 vs. [S] −1 0 should give a straight line with intercept ( 2 [E] 0 ) −1 and slope 2 [E] 0 . y slope intercept = = −1 + 2 (10.28) 1
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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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7.3 Thermodynamic interpretation of
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7.3 Thermodynamic interpretation of
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Page 277 and 278: Appendix B 262 Appendix A: Useful p
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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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