Energy reaction coordinate

Figure 5-9. Free energy reaction coordinate diagram for System 2 of Table 4-3, the formation of a cyclodextrin inclusion complex.

Figure S-10. Hypothetical free energy reaction coordinate diagram for Scheme 11 (TS = transition state).

Strictly speaking, the flow analogy is valid only for consecutive irreversible reactions, and it can be misleading if reverse reactions are significant. Even for irreversible reactions the rds concept has meaning only if one of the reactions is much slower than the others. For reversible reactions the free energy reaction coordinate diagram is a useful aid. In Fig. 5-10, for example, the intermediate 1 is unstable with respect to R and P, and its formation (the kf step) is the rds of the overall reaction. 

When the overall reaction includes more than two elementary steps, the situation may not be easy to analyze. The product of the nth step is the reactant of the (n -I- l)st step, but in order for these two states to be represented by the same free energy they must have the same composition this means that the stoichiometric composition must be constant throughout the entire series of reactions. Suppose that it has been possible to construct the free energy reaction coordinate. Murdoch gives this method for identifying the rds ... 

For the oximation of a ketone (see Fig. 5-12 and aeeompanying text), sketeh the free energy reaction coordinate diagram at pH 7 and pH 2. 

Fig. 5. Potential energy-reaction coordinate diagram for an electron transfer reaction leading to a product adsorbed on the electrode surface.

Fig. 12. Energy-reaction coordinate diagram for electron transfer in solution when there is only weak interaction between the initial and final energy states.

Figure 1. Energy-reaction coordinate diagram for the acid-catalyzed hydration of phenylacetylene. The ordinate is not to scale (20).

Fig. 1 Free energy reaction coordinate profiles for hydration and isomerization of the alkene [2] through the simple tertiary carbocation [1+], The rate constants for partitioning of [1 ] to form [l]-OSolv and [3] are limited by solvent reorganization (ks = kteorg) and proton transfer (kp), respectively. For simplicity, the solvent reorganization step is not shown for the conversion of [1+] to [3], but the barrier for this step is smaller than the chemical barrier to deprotonation of [1 ] (kTtOTg > kp).

Fig. 2 Free energy reaction coordinate profiles for the stepwise acid-catalyzed hydration of an alkene through a carbocation intermediate (Scheme 5). (a) Reaction profile for the case where alkene protonation is rate determining (ks kp). This profile shows a change in rate-determining step as a result of Bronsted catalysis of protonation of the alkene. (b) Reaction profile for the case where addition of solvent to the carbocation is rate determining (ks fcp). This profile shows a change in rate-determining step as a result of trapping of the carbocation by an added nucleophilic reagent.

Fig. 4 Free energy reaction coordinate profiles that illustrate a change in the relative kinetic barriers for partitioning of carbocations between nucleophilic addition of solvent and deprotonation resulting from a change in the curvature of the potential energy surface for the nucleophile addition reaction. This would correspond to an increase in the intrinsic barrier for the thermoneutral carbocation-nucleophile addition reaction.

Fig. 6 Hypothetical free energy reaction coordinate profiles for the interconversion of X-[8]-OH and X-[9] (R = H) and X-[10]-OH and X-[ll] (R = CH3) through the corresponding carbocations. The arrows indicate the proposed eifects of the addition of a pair of ortAo-methyl groups to X-[8]-OH, X-[8+] and X-[9] to give X-[10]-OH, X-[10+] and X-[ll]. A Effect of a pair of or/Ao-methyl groups on the stability of cumyl alcohols. B Effect of a pair of or/Ao-methyl groups on the stability of cumyl carbocations. C Effect of a pair of ortho-methyl groups on the stability of the transition state for nucleophilic addition of water to cumyl carbocations. D Effect of a pair of orf/io-methyl groups on the stability of the transition state for deprotonation of cumyl carbocations.

A FREE-ENERGY REACTION COORDINATE DIAGRAM shows the free energy of the substrate, product, and transition state of a chemical reaction. It tells you how favorable the overall reaction is (AGeq) and how fast (AG1). 

Fig. 2.7 Energy-reaction coordinate diagram for reaction (Z R energy of reactant ...

Draw energy-reaction coordinate diagram and discuss the physical significance of energy of activation. Also differentiate between energy of activation and heat of reaction. 

Fig. 16 Free energy/reaction coordinate diagram for proton transfer from the 4,6-bis(phenylazo)resorcinol monoanion to give the dianion in the presence of 2-methylphenol buffers at a 1 1 buffer ratio and at buffer concentrations of (a) 0.001 and (b) 0.10mol" dm. ...

Fig. 17 Free energy/reaction coordinate diagram for tyrosine activation [see (49)], with wild-type tyrosyl-tRNA synthetase (E) and the Tyr-34 to Phe mutant (E ).

Figure 2.1. One-dimensional (ID) free energy reaction coordinate profiles that show the Dn + An reaction mechanism through a carhocation intermediate and the change to an AnDn reaction in which the intermediate is too unstable to exist in an energy weU for the time of a bond vibration.

According to the potential energy - reaction coordinate graph given above for the reaction, which is wrong ... 

A review of the Journal of Physical Chemistry A, volume 110, issues 6 and 7, reveals that computational chemistry plays a major or supporting role in the majority of papers. Computational tools include use of large Gaussian basis sets and density functional theory, molecular mechanics, and molecular dynamics. There were quantum chemistry studies of complex reaction schemes to create detailed reaction potential energy surfaces/maps, molecular mechanics and molecular dynamics studies of larger chemical systems, and conformational analysis studies. Spectroscopic methods included photoelectron spectroscopy, microwave spectroscopy circular dichroism, IR, UV-vis, EPR, ENDOR, and ENDOR induced EPR. The kinetics papers focused on elucidation of complex mechanisms and potential energy reaction coordinate surfaces. 

Fig. 4.5 Schematic energy - reaction coordinate profiles for symmetrical ET processes having small and large energy splittings at the intersection point.

Fig. 4. Schematic representation of the effect of a change in electrode potential, E, on the free energy—reaction coordinate curves for a heterogeneous single electron transfer step (O + n e - R) at two different electrode potentials (1) E = Ee (solid line) and (2) E

If the free energy—reaction coordinate curves are symmetrical and linear at the cross points A and A of the energy surfaces in Fig. 4, geometrical considerations result in BC = CA [10] and... 

The effect of the chemisorption of electrode reaction intermediates was first considered by Butler for the hydrogen evolution reaction [33]. Considering the adsorption in quasi-equilibrium or the steady-state approach, the effect of adsorption of an intermediate is a vertical shift in the corresponding free energy—reaction coordinate curve as depicted in Fig. 12. 

Marcus attempted to calculate the minimum energy reaction coordinate or reaction trajectory needed for electron transfer to occur. The reaction coordinate includes contributions from all of the trapping vibrations of the system including the solvent and is not simply the normal coordinate illustrated in Figure 1. In general, the reaction coordinate is a complex function of the coordinates of the series of normal modes that are involved in electron trapping. In this approach to the theory of electron transfer the rate constant for outer-sphere electron transfer is given by equation (18). 

Figure 4.4 Energy-reaction coordinate diagram of ground and excited state reactions...

Fig. 9. A tentative potential energy-reaction coordinate diagram (schematic) for the reaction of oxygen atoms with olefins.

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