Chapter 4 Study & Description of Organic Reaction Mechanism

1. Chapter 4 Study & Description of Organic Reaction Mechanism Advanced Organic Chemistry (Chapter 4) Sh.Javanshir

2. Tools for Study • To determine a reaction’s mechanism, look at: • Equilibrium constant • Free energy change • Enthalpy • Entropy • Bond dissociation energy • Kinetics • Activation energy

3. 4.1 Thermodynamic Data DG = DH - T DS DG = -RT ln K

5. Standard Condition: p = 1 atm, t = 25 °C

6. MO Calculation Isodesmic Reactions (واکنش های همسان نیرو): A process in which the number of formal bonds of each type is kept constant. (the number and type of bonds in the reactants and in the products is the same.) .

7. After accounting for all different bond types involved in this reaction equation, it is clear that this reaction does classify as an isodesmic reaction. The (standard state) heats of formation for three of the four species are known to good accuracy and are given below the equation. The heat of formation of the fourth species (ethanol) can be estimated now by simply calculating the reaction energy ERXN (or better: the reaction enthalpy HRXN), with quantum mechanical methods and by using the computed reaction energy together with the known heats of formation to estimate that of ethanol:Using cheaply calculated HF/STO-3G energies for all four species, a reaction energy of +10.9 kJ/mol is predicted. Together with the know heats of formation, a value of -220 kJ/mol is predicted for ethanol. This has to be compared to the experimental value of -235.3 kJ/mol.

8. Isodesmic reactionscan also be used to quantify the stability of reactive intermediates in a thermochemical sense. If, for example, we want to quantify the stability of the methanol-1-yl radical, we could simply use the bond dissociation energy of the methanol C-H bonds. This is synonymous to calculating the reaction energy for the following reaction: • Using an appropriate isodesmic reaction such as • This hydrogen transfer reaction between methanol and methyl radical can be constructed as the difference between the C-H bond dissociation reactions in methane and in methanol. The reaction energy of this isodesmic reaction therefore reflects the difference in C-H bond dissociation energies in methane and methanol and thus the differential stability of the methyl and the methanol radical. • Using experimentally determined heats of formation at 298.15K of -17.8 kJ/mol (methanol radical), -74.87 kJ/mol (methane), -201.1 kJ/mol (methanol), and +145.69 kJ/mol (methyl radical) one arrives at an isodesmic heat of reaction of -37.3 kJ/mol. This implies that the methanol radical is substantially more stable than the methyl radical. Similar considerations lead to a gain in radical stability of -17.8 kJ/mol on going from the methyl to the ethyl radical.

9. Cyclopropane Hf(298)= 53.3±0.6 What’s the strain energy of cyclopropane? + CH3CH3  CH3CH2CH2CH2CH3 -83.7±0.4 -146.9±0.9 Hr(298)= (-146.9±0.9) - (-83.7±0.4) -(53.3±0.6) Hr(298)= -116.5±1.2 Hs(298)= 116.5 kJ mol-1

10. cyclopropane Hs(298)= 116.5 ±1.2 What’s the strain energy of spiropentane? Hf(298)= 185.2±0.8 CH3 + 4CH3CH3 2 CH3CH2CH2CH3 +CH3CCH3 CH3 -83.7±0.4 -125.5±0.7-168.1±0.8 Hr(298)= (-168.1±0.8) + 2(-125.5±0.7) - 4(-83.7±0.4) -(185.2±0.8) Hr(298)= (-269.5±2.4) kJ mol-1 Hs(298)= 269.5 - 2(116.5) = 36.5 kJ mol-1

11. Thermodynamic provide no information about energy requirements of pathway and the rate of the reactions.

12. 4.2 Kinetic Data Reaction Rate: 1) Disappearance of the reactants 2) Appearance of the products Methods: 1) Spectroscopy 2) Conductometry (ionic species) 3) Polarimetry (chiral species) Reaction Order: In rate law, each concentration has an exponent that is the ORDER of the reaction with respect to that component.

14. The expression for the rate of any single step in a reaction mechanism will contain a term for the concentration of each reacting species. Rate Determining Step: The overall rate will depend on the rate of the slowest step (bottle neck= گلوگاه فرایند).

15. If we specify that the first step is a very rapid but unfavorable equilibrium, and that k2 << k3, then the second step is rate determining. Under these circumstances, the overall rate of the reaction will depend on the rate of the second step. In the reaction under consideration, the final step follows the rate-determining step and does not affect the rate of the overall reaction; k3 does not appear in the overall rate expression. The rate of the reaction is governed by the second step, which is the bottleneck in the process.

16. Steady State Approximation تقریب حالت پایا • When a reaction mechanism has several steps of comparable rates, the rate-determining step is often not obvious. However, there is an intermediate in some of the steps. • Thesteady-state approximationis a method used to derive a rate law. • The steady-state approximation implies that you select an intermediate in the reaction mechanism, and calculate its concentration by assuming that it is consumed as quickly as it is generated. Its concentration remains the same in a duration of the reaction

17. Steady State Approximation تقریب حالت پایا If C is a active, unstable species, its concentration will never be very large. It must then be consumed at a rate that closely approximates that the rate at which it is formed. Under these conditions, it is valid approximation to set the rate of formation of C equal to its rate of destruction.

18. Slide 10

19. Second step is rate determining Two possibilities: Back

20. A0 A0 [C] [A·B] [C] [A·B] xe t n = k2[A·B] = Two possibilities: - rapid breakdown of A·B, k2>>k-1, so n = k1[A][B] t - slow breakdown of the complex: k2<<k1,k-1, so: n = k2[A·B] = = k2K[A][B]

21. Kinetic Investigation • 1) Postulation of likely mechanisms • 2) Comparison of observed rate law • 3)Those mechanisms that are incompatible with the observed kinetics can be eliminated as possibilities.

22. Nitration of Benzene Slide13

23. can not be directly measured. Back

24. Nitration of Benzene

25. can not be directly measured.

26. Nitration of Benzene Slide17

27. can not be directly measured. Back

28. Mechanism B is zero order in the reactant benzene. It has been established for nitration of benzene in several organic solvents. Mechanism A and C are differing only in the inclusion of water concentration. In high water concentration, these mechanisms can not be distinguished from each other.

29. ماهیت ثابت های سرعت بر حسب نظریه حالت گذار

30. Transition State Theory A reaction is assumed to involve the attainment of an activated complex that goes on to product at an extremely rapid rate. نظریه حالت گذار : Rate = k‡[TS] Statistical mechanics gives us the following relation: DG‡ = free energy of activation  : Transmission coefficient (ضریب انتشار)(usually taken to be 1) : which accounts for the possibility that some reactive events will abort and reform the reactants. kB = Boltzmann's constant [1.381·10-23 J · K-1] T = absolute temperature in degrees Kelvin (K) h = Plank constant [6.626·10-34 J · s] DG React Prod

31. If the activated complex is considered to be in equilibrium with its component: Free energy of activation:

32. Comparison with the form of the expression for the rate of any single reaction step: Eyring equation: The magnitude of DG will be the factor that determine the magnitude of kr at any given temperature.

33. Reaction coordinate for single step and two-step reactions Potentiel energy diagrams for singel-step and two-step reactions

34. Evaluation of Enthalpy and Entropy Component of free Energy of Activation: Enthalpy ontribution Entropy contribution Eyring equation: با توجه به وابستگی سرعت واکنش به دما، می توان مؤلفه های آنتالپی وآنتروپی را در انرژی آزاد فعالسازی تعیین کرد. A plot of ln (kr/T) vs. (1/T) is then straight line, and its slope is (-DH /R).

35. با تعیین ، میتوان را نیز از رابطه زیر به دست آورد. Activation Energy and Arrhenius Equation: Aplot of ln (kr) vs. (1/T) is then straight line, and its slope is (-Ea/R). For reactions in solution at constant pressure, DH≠andEa are related by:

36. So, the procedure to determine activation parameters is: - determine kr at different temperatures - plotting ln(kr /T) against 1/T gives DH‡ - then gives DS‡ and when you have DH‡ and DS‡, you also have DG‡ since DG = DH-TDS

37. دیمری شدن سیکلوپنتادی ان به دلیل از دست رفتن درجات آزادی انتقالی وچرخشی در تشکیل حالت گذار با آنتروپی منفی همراه است. آنتروپی فعال سازی در تجزیه 1، َ1-آزوبوتان به دلیل جدا شدن قطعات مولکول از هم مطلوب تر است.

38. Unimolecular reactions that take place by way of cyclic transition states typically have negative entropy of activation: از دست رفتن درجه آزادی چرخشی Reactions which generate charged species exhibit negative ENTROPIES of activation in solution: Solvolysis of tert-BuCl in 80% EtOH/H2O:DS= -6.6 eu Reason: Because of its polar character, the T.S. requires a greater ordering of solvent molecules than the nonpolar reactant. The enthalpy and entropy of activation reflect the response of the reacting system as a whole to formation of the activated complex.

39. The Hammett Equation Louis P. Hammett (1894-1987)

40. 4.3 Substituents Effects and Linear Free-Energy Relationships • Such relationships were first studied on a thorough basis by Hammett in the1930’s. slope = m ko: rate constant for the hydrolysis of ethyl benzoate. k: rate constant for the hydrolysis of substituted ethyl benzoates. Ko: acid dissociation constant for the benzoic acid. K: acid dissociation constant for the substituted benzoic acids.

41. linear relationship slope = m change in free energy of activation with change in substituents change in free energy of ionization with change in substituents  i.e.,

43. Hammett: (equilibrium data) (kinetic data) s: reflects the interaction of the substituent with the reacting site. i.e., for electron donor groups, s < 0 for electron acceptor groups, s > 0 r: reflects the sensitivity of the particular reaction to substituent effects definition: r = 1 for Strategy: 1. calculate s for various X groups in above reaction 2. use these s values to calculate r values for other reactions r > 0 reaction has anionic intermediate and are favored by electron-withdrawing groups r < 0 reaction has cationic intermediate and are favored by electron-releasing groups

44. Example

45. Hammet sr Relationships r values: information about reaction mechanisms • For the equilibrium: • definition: r = 1 • For other reactions: • 1. for • 2. for • i.e., r > 0 indicates negative charge development in TS • r < 0 indicates positive charge development in TS i.e., for electron donor groups, s < 0 for electron acceptor groups, s > 0 r > 0 for equilibria favored by electron acceptors r < 0 for equilibria favored by electron donors r > 0 for TS favored by electron acceptors r < 0 for TS favored by electron donors

46. r = + 2.38 r = - 5.0 • larger r indicates greater sensitivity to substituents, i.e., a larger buildup or closer proximity of charge in TS r > 0for all reactions that are favored by electron-withdrawing groups & r < 0 for all reactions that are favored by electron-releasing groups

47. Hammet sr Relationships r values Examples: r = 2.26 more sensitive to substituent effects r = 0.56 less sensitive r = -1.31 r = -4.48 partial charge buildup (SN2-like) greater charge buildup (SN1-like)

48. Hammett equation is applied only to metaand parasubstituents (steric effects). Flexibility of aliphatic compounds means that correlation between transition state structure and equilibrium position may not be strong. Ortho- substituted aromatic rings do no fall on the line owing to steric and through- space effects. ie.increased crowding in the tetrahedral intermediate

49. Factors influence the effect of substituents and cause polarization of charge density around the ring.