Chemical kinetics: the rates of reactions

1. Chemical kinetics:the rates of reactions 자연과학대학 화학과 박영동 교수 Atkins, physical chemistry, 5th ed.

2. Table 10.1 Kinetic techniques for fast reactions * EPR is electron paramagnetic resonance (or electron spin resonance); NMR is nuclear magnetic resonance; see Chapter 21.

3. Spectrophotometry and the Beer–Lambert law Sample I0→ → I A = ε[J]L

4. stopped-flow technique The location of the spectrometer corresponds to different times after initiation.

5. The rate of a reaction

6. Reaction order ath-order in A. second-order in NO2 half orderin A, first orderin B, and3/2-th orderoverall. for the gas-phase reaction H2(g) + Br2(g) →2 HBr(g) Enzyme kinetics a rate law is established experimentally, and cannot in general be inferred from the chemical equation for the reaction.

7. Simple reaction order

8. The rates of reaction of 2 I(g) + Ar(g) → I2(g) + Ar(g) (c) (c) (b) (b) slopes are 2 slope is 1 (a) (a) The Ar concentrations are (a) 1.0 × 10−3mol dm−3, (b) 5.0 × 10−3mol dm−3, and (c) 1.0 × 10−2mol dm−3.

9. Integrated rate laws • A → P Figure 10.8  The exponential decay of the reactant in a first-order reaction.

10. First Order Reaction intercept = – 2.3 slope = – 4.04 × 10−4 The variation in the partial pressure pA of azomethane with time was followed at 460 K

11. Second Order Reaction The determination of the rate constant of a second-order reaction.

12. Table 10.3 Kinetic data for second-order reactions The rate constant is for the rate of formation or consumption of the species in bold type. The rate laws for the other species may be obtained from the reaction stoichiometry.

13. First Order vs Second Order

14. half-life t1/2 = ln(2)/k In each successive period of duration t1/2, the concentration of a reactant in a first-order reaction decays to half its value at the start of that period The molar concentration of N2O5 after a succession of half-lives

15. the Arrhenius equation A : the pre-exponential factor, Ea: the activation energy. The general form of an Arrhenius plot of lnkr against 1/T.

16. Reaction rate and Temperature The rate of the second-order decomposition of acetaldehyde (ethanal, CH3CHO) ln(kr) = −2.265 × 104/T+27.7 ln(kr) = −2.265 × 104/T+27.7 The Arrhenius plot for the decomposition of CH3CHO, and the best-fit.

17. Table 10.5 Arrhenius parameters

18. Collision theory In the collision theory of gas-phase chemical reactions, reaction occurs when two molecules collide, but only if the collision is sufficiently vigorous. (a) An insufficiently vigorous collision: the reactant molecules collide but bounce apart unchanged. (b) A sufficiently vigorous collision results in a reaction. A reaction profile.

19. Collision theory The criterion for a successful collision is that the two reactant species should collide with a kinetic energy along their line of approach that exceeds a certain minimum value that is characteristic of the reaction According to the Maxwell distribution of speeds (Section 1.2.6), as the temperature increases, so does the fraction of gas-phase molecules with a speed that exceeds a minimum value smin. Because the kinetic energy is proportional to the square of the speed, it follows that more molecules can collide with a minimum kinetic energy Ea (the activation energy) at higher temperatures.

20. collision frequency Z: the collision frequency ρ:the steric factor

21. Transition-state theory(aka activated complex theory) Energy is not the only criterion of a successful reactive encounter, for relative orientation may also play a role. (a) In this collision, the reactants approach in an inappropriate relative orientation, and no reaction occurs even though their energy is sufficient. (b) In this encounter, both the energy and the orientation are suitable for reaction.

23. source: Dr. UweHöfker ,The Transition State of  Reactions, at www.chemapedia.de

24. Schematics depicting two possible trajectories of protein folding. (a) A single crossing of the transition state as predicted by TST. (b) Multiple crossings of the transition state in the limiting case of high friction due to ruggedness. www.pnas.orgcgidoi10.1073pnas.0509768103

25. Traditional Crossed Molecular Beam Scattering or Imaging Expts are a good way to probe “Direct” Chemical Reactions Eg. D2 + F  D…D…F  D + DF D…D…F D-D  F Angular and Velocity Distribution of DF product shows Backward Scattered DF product source: The Butler Group, uchicago.edu

26. Transition-state theory The factor κ is the transmission coefficient,

27. Transition-state theory enthalpy of activation, Δ‡H entropy of activation, Δ‡S,

28. Transition-state theory Activatedcomplex Transition state Reactants Potential Energy Products Reaction Coordinate

29. Transition-state theory Activatedcomplex Association (of molecules or atoms) more resembles the reactant Association (of molecules or atoms) more resembles the product Potential Energy Reaction Coordinate

30. Transition-state theory • The Eyring Equation: • Reaction between A and B proceeds through the formation of the activated complex (AB)‡ in a rapid pre-equilibrium. K‡ k‡ A + B (AB)‡→ product • Rate, v = k‡[(AB)‡] • Now, rate, v = k2[A][B]

31. Transition-state theory Rate of decay of activated complex • Factors affecting the Activated Complex going through the Transition State: •  – vibration frequency • Centrifugal effect of rotation • It is supposed that k‡ andk‡=  • is the transmission coefficient (the probability that the activated complex will pass through the transition state to form product). • Usually assume,   1

32. Transition-state theory Concentration of activated complex: • If reaction is in gas phase, then:‡ A + B (AB)‡ • Recall the Ideal Gas Law: • Substituting for gas pressure in K‡:

33. Transition-state theory Concentration of activated complex (cont’d): • Recall: rate, v = k‡[(AB)‡] • Therefore: rate, v = k‡ K‡RT[A][B] • For a bimolecular reaction • rate, v = k2[A][B] • Therefore: k2 = k‡ K‡RT Need to determine: k‡ andK‡

34. Transition-state theory • K‡, the equilibrium constant between the reactants and the activated complex can be written in terms of the standard molar partition functions (qө) of the species involved. Φ Φ Φ • Where: • And Eo is the molar energy of the species involved Obtain qө from spectroscopic data for A and B but not for (AB)‡

35. Transition-state theory • Assume that a vibration of the activated complex (AB)‡ tips it through the transition state (TS). (i.e. a vibrational mode converts to translation and TS breaks a bond). The partition function for this vibration is: •  is the same frequency that determines k‡. •  is much less than a normal molecular vibration frequency, since the complex is falling apart (hence much weaker bond) and force constant is very low.

36. Transition-state theory • For small values of , assume: • The partition function reduces to: • We can therefore write: where denotes the partition function for all the other modes (trans, rot …) of the complex.

37. Transition-state theory • K‡ can now be written as: • where is a modified equilibrium constant with one mode of vibration of (AB)‡ removed. The rate constant: Recall that: k2 = k‡ K‡RT where k‡=  Substitution gives:

38. Transition-state theory • In terms of molar concentration (and application of the Ideal Gas Law), it can be shown that: • Substitution gives: Eyring Equation

39. Eyring Equation(Thermodynamic Aspects) • Assume  = 1, and rearranging gives: • recall: • and: •  • Substitution and rearrangement gives: Plot LHS vs 1/T Slope = -H‡ / R Intercept = S‡ / R Another form of Eyring Equation

40. Transition-state theory